(0) Obligation:
Runtime Complexity TRS:
The TRS R consists of the following rules:
active(from(X)) → mark(cons(X, from(s(X))))
active(2ndspos(0, Z)) → mark(rnil)
active(2ndspos(s(N), cons(X, Z))) → mark(2ndspos(s(N), cons2(X, Z)))
active(2ndspos(s(N), cons2(X, cons(Y, Z)))) → mark(rcons(posrecip(Y), 2ndsneg(N, Z)))
active(2ndsneg(0, Z)) → mark(rnil)
active(2ndsneg(s(N), cons(X, Z))) → mark(2ndsneg(s(N), cons2(X, Z)))
active(2ndsneg(s(N), cons2(X, cons(Y, Z)))) → mark(rcons(negrecip(Y), 2ndspos(N, Z)))
active(pi(X)) → mark(2ndspos(X, from(0)))
active(plus(0, Y)) → mark(Y)
active(plus(s(X), Y)) → mark(s(plus(X, Y)))
active(times(0, Y)) → mark(0)
active(times(s(X), Y)) → mark(plus(Y, times(X, Y)))
active(square(X)) → mark(times(X, X))
active(s(X)) → s(active(X))
active(posrecip(X)) → posrecip(active(X))
active(negrecip(X)) → negrecip(active(X))
active(cons(X1, X2)) → cons(active(X1), X2)
active(cons2(X1, X2)) → cons2(X1, active(X2))
active(rcons(X1, X2)) → rcons(active(X1), X2)
active(rcons(X1, X2)) → rcons(X1, active(X2))
active(from(X)) → from(active(X))
active(2ndspos(X1, X2)) → 2ndspos(active(X1), X2)
active(2ndspos(X1, X2)) → 2ndspos(X1, active(X2))
active(2ndsneg(X1, X2)) → 2ndsneg(active(X1), X2)
active(2ndsneg(X1, X2)) → 2ndsneg(X1, active(X2))
active(pi(X)) → pi(active(X))
active(plus(X1, X2)) → plus(active(X1), X2)
active(plus(X1, X2)) → plus(X1, active(X2))
active(times(X1, X2)) → times(active(X1), X2)
active(times(X1, X2)) → times(X1, active(X2))
active(square(X)) → square(active(X))
s(mark(X)) → mark(s(X))
posrecip(mark(X)) → mark(posrecip(X))
negrecip(mark(X)) → mark(negrecip(X))
cons(mark(X1), X2) → mark(cons(X1, X2))
cons2(X1, mark(X2)) → mark(cons2(X1, X2))
rcons(mark(X1), X2) → mark(rcons(X1, X2))
rcons(X1, mark(X2)) → mark(rcons(X1, X2))
from(mark(X)) → mark(from(X))
2ndspos(mark(X1), X2) → mark(2ndspos(X1, X2))
2ndspos(X1, mark(X2)) → mark(2ndspos(X1, X2))
2ndsneg(mark(X1), X2) → mark(2ndsneg(X1, X2))
2ndsneg(X1, mark(X2)) → mark(2ndsneg(X1, X2))
pi(mark(X)) → mark(pi(X))
plus(mark(X1), X2) → mark(plus(X1, X2))
plus(X1, mark(X2)) → mark(plus(X1, X2))
times(mark(X1), X2) → mark(times(X1, X2))
times(X1, mark(X2)) → mark(times(X1, X2))
square(mark(X)) → mark(square(X))
proper(0) → ok(0)
proper(s(X)) → s(proper(X))
proper(posrecip(X)) → posrecip(proper(X))
proper(negrecip(X)) → negrecip(proper(X))
proper(nil) → ok(nil)
proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(cons2(X1, X2)) → cons2(proper(X1), proper(X2))
proper(rnil) → ok(rnil)
proper(rcons(X1, X2)) → rcons(proper(X1), proper(X2))
proper(from(X)) → from(proper(X))
proper(2ndspos(X1, X2)) → 2ndspos(proper(X1), proper(X2))
proper(2ndsneg(X1, X2)) → 2ndsneg(proper(X1), proper(X2))
proper(pi(X)) → pi(proper(X))
proper(plus(X1, X2)) → plus(proper(X1), proper(X2))
proper(times(X1, X2)) → times(proper(X1), proper(X2))
proper(square(X)) → square(proper(X))
s(ok(X)) → ok(s(X))
posrecip(ok(X)) → ok(posrecip(X))
negrecip(ok(X)) → ok(negrecip(X))
cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
cons2(ok(X1), ok(X2)) → ok(cons2(X1, X2))
rcons(ok(X1), ok(X2)) → ok(rcons(X1, X2))
from(ok(X)) → ok(from(X))
2ndspos(ok(X1), ok(X2)) → ok(2ndspos(X1, X2))
2ndsneg(ok(X1), ok(X2)) → ok(2ndsneg(X1, X2))
pi(ok(X)) → ok(pi(X))
plus(ok(X1), ok(X2)) → ok(plus(X1, X2))
times(ok(X1), ok(X2)) → ok(times(X1, X2))
square(ok(X)) → ok(square(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))
Rewrite Strategy: INNERMOST
(1) CpxTrsToCdtProof (BOTH BOUNDS(ID, ID) transformation)
Converted Cpx (relative) TRS to CDT
(2) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(2ndspos(0, z0)) → mark(rnil)
active(2ndspos(s(z0), cons(z1, z2))) → mark(2ndspos(s(z0), cons2(z1, z2)))
active(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(z1, z2))) → mark(2ndsneg(s(z0), cons2(z1, z2)))
active(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
active(pi(z0)) → mark(2ndspos(z0, from(0)))
active(plus(0, z0)) → mark(z0)
active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
active(times(0, z0)) → mark(0)
active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
active(square(z0)) → mark(times(z0, z0))
active(s(z0)) → s(active(z0))
active(posrecip(z0)) → posrecip(active(z0))
active(negrecip(z0)) → negrecip(active(z0))
active(cons(z0, z1)) → cons(active(z0), z1)
active(cons2(z0, z1)) → cons2(z0, active(z1))
active(rcons(z0, z1)) → rcons(active(z0), z1)
active(rcons(z0, z1)) → rcons(z0, active(z1))
active(from(z0)) → from(active(z0))
active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
active(pi(z0)) → pi(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(times(z0, z1)) → times(active(z0), z1)
active(times(z0, z1)) → times(z0, active(z1))
active(square(z0)) → square(active(z0))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
posrecip(mark(z0)) → mark(posrecip(z0))
posrecip(ok(z0)) → ok(posrecip(z0))
negrecip(mark(z0)) → mark(negrecip(z0))
negrecip(ok(z0)) → ok(negrecip(z0))
cons(mark(z0), z1) → mark(cons(z0, z1))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
cons2(z0, mark(z1)) → mark(cons2(z0, z1))
cons2(ok(z0), ok(z1)) → ok(cons2(z0, z1))
rcons(mark(z0), z1) → mark(rcons(z0, z1))
rcons(z0, mark(z1)) → mark(rcons(z0, z1))
rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
from(mark(z0)) → mark(from(z0))
from(ok(z0)) → ok(from(z0))
2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
pi(mark(z0)) → mark(pi(z0))
pi(ok(z0)) → ok(pi(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
times(mark(z0), z1) → mark(times(z0, z1))
times(z0, mark(z1)) → mark(times(z0, z1))
times(ok(z0), ok(z1)) → ok(times(z0, z1))
square(mark(z0)) → mark(square(z0))
square(ok(z0)) → ok(square(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(posrecip(z0)) → posrecip(proper(z0))
proper(negrecip(z0)) → negrecip(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(cons2(z0, z1)) → cons2(proper(z0), proper(z1))
proper(rnil) → ok(rnil)
proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
proper(pi(z0)) → pi(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(times(z0, z1)) → times(proper(z0), proper(z1))
proper(square(z0)) → square(proper(z0))
top(mark(z0)) → top(proper(z0))
top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(from(z0)) → c(CONS(z0, from(s(z0))), FROM(s(z0)), S(z0))
ACTIVE(2ndspos(0, z0)) → c1
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c2(2NDSPOS(s(z0), cons2(z1, z2)), S(z0), CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c3(RCONS(posrecip(z2), 2ndsneg(z0, z3)), POSRECIP(z2), 2NDSNEG(z0, z3))
ACTIVE(2ndsneg(0, z0)) → c4
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c5(2NDSNEG(s(z0), cons2(z1, z2)), S(z0), CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c6(RCONS(negrecip(z2), 2ndspos(z0, z3)), NEGRECIP(z2), 2NDSPOS(z0, z3))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)), FROM(0))
ACTIVE(plus(0, z0)) → c8
ACTIVE(plus(s(z0), z1)) → c9(S(plus(z0, z1)), PLUS(z0, z1))
ACTIVE(times(0, z0)) → c10
ACTIVE(times(s(z0), z1)) → c11(PLUS(z1, times(z0, z1)), TIMES(z0, z1))
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(s(z0)) → c13(S(active(z0)), ACTIVE(z0))
ACTIVE(posrecip(z0)) → c14(POSRECIP(active(z0)), ACTIVE(z0))
ACTIVE(negrecip(z0)) → c15(NEGRECIP(active(z0)), ACTIVE(z0))
ACTIVE(cons(z0, z1)) → c16(CONS(active(z0), z1), ACTIVE(z0))
ACTIVE(cons2(z0, z1)) → c17(CONS2(z0, active(z1)), ACTIVE(z1))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(from(z0)) → c20(FROM(active(z0)), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(pi(z0)) → c25(PI(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
ACTIVE(square(z0)) → c30(SQUARE(active(z0)), ACTIVE(z0))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
PROPER(0) → c62
PROPER(s(z0)) → c63(S(proper(z0)), PROPER(z0))
PROPER(posrecip(z0)) → c64(POSRECIP(proper(z0)), PROPER(z0))
PROPER(negrecip(z0)) → c65(NEGRECIP(proper(z0)), PROPER(z0))
PROPER(nil) → c66
PROPER(cons(z0, z1)) → c67(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(cons2(z0, z1)) → c68(CONS2(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(rnil) → c69
PROPER(rcons(z0, z1)) → c70(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c71(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c72(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c73(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c74(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c75(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c76(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c77(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c78(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c79(TOP(active(z0)), ACTIVE(z0))
S tuples:
ACTIVE(from(z0)) → c(CONS(z0, from(s(z0))), FROM(s(z0)), S(z0))
ACTIVE(2ndspos(0, z0)) → c1
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c2(2NDSPOS(s(z0), cons2(z1, z2)), S(z0), CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c3(RCONS(posrecip(z2), 2ndsneg(z0, z3)), POSRECIP(z2), 2NDSNEG(z0, z3))
ACTIVE(2ndsneg(0, z0)) → c4
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c5(2NDSNEG(s(z0), cons2(z1, z2)), S(z0), CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c6(RCONS(negrecip(z2), 2ndspos(z0, z3)), NEGRECIP(z2), 2NDSPOS(z0, z3))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)), FROM(0))
ACTIVE(plus(0, z0)) → c8
ACTIVE(plus(s(z0), z1)) → c9(S(plus(z0, z1)), PLUS(z0, z1))
ACTIVE(times(0, z0)) → c10
ACTIVE(times(s(z0), z1)) → c11(PLUS(z1, times(z0, z1)), TIMES(z0, z1))
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(s(z0)) → c13(S(active(z0)), ACTIVE(z0))
ACTIVE(posrecip(z0)) → c14(POSRECIP(active(z0)), ACTIVE(z0))
ACTIVE(negrecip(z0)) → c15(NEGRECIP(active(z0)), ACTIVE(z0))
ACTIVE(cons(z0, z1)) → c16(CONS(active(z0), z1), ACTIVE(z0))
ACTIVE(cons2(z0, z1)) → c17(CONS2(z0, active(z1)), ACTIVE(z1))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(from(z0)) → c20(FROM(active(z0)), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(pi(z0)) → c25(PI(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
ACTIVE(square(z0)) → c30(SQUARE(active(z0)), ACTIVE(z0))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
PROPER(0) → c62
PROPER(s(z0)) → c63(S(proper(z0)), PROPER(z0))
PROPER(posrecip(z0)) → c64(POSRECIP(proper(z0)), PROPER(z0))
PROPER(negrecip(z0)) → c65(NEGRECIP(proper(z0)), PROPER(z0))
PROPER(nil) → c66
PROPER(cons(z0, z1)) → c67(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(cons2(z0, z1)) → c68(CONS2(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(rnil) → c69
PROPER(rcons(z0, z1)) → c70(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c71(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c72(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c73(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c74(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c75(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c76(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c77(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c78(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c79(TOP(active(z0)), ACTIVE(z0))
K tuples:none
Defined Rule Symbols:
active, s, posrecip, negrecip, cons, cons2, rcons, from, 2ndspos, 2ndsneg, pi, plus, times, square, proper, top
Defined Pair Symbols:
ACTIVE, S, POSRECIP, NEGRECIP, CONS, CONS2, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP
Compound Symbols:
c, c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c78, c79
(3) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID) transformation)
Removed 7 trailing nodes:
ACTIVE(times(0, z0)) → c10
PROPER(0) → c62
ACTIVE(2ndsneg(0, z0)) → c4
PROPER(nil) → c66
ACTIVE(2ndspos(0, z0)) → c1
ACTIVE(plus(0, z0)) → c8
PROPER(rnil) → c69
(4) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(2ndspos(0, z0)) → mark(rnil)
active(2ndspos(s(z0), cons(z1, z2))) → mark(2ndspos(s(z0), cons2(z1, z2)))
active(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(z1, z2))) → mark(2ndsneg(s(z0), cons2(z1, z2)))
active(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
active(pi(z0)) → mark(2ndspos(z0, from(0)))
active(plus(0, z0)) → mark(z0)
active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
active(times(0, z0)) → mark(0)
active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
active(square(z0)) → mark(times(z0, z0))
active(s(z0)) → s(active(z0))
active(posrecip(z0)) → posrecip(active(z0))
active(negrecip(z0)) → negrecip(active(z0))
active(cons(z0, z1)) → cons(active(z0), z1)
active(cons2(z0, z1)) → cons2(z0, active(z1))
active(rcons(z0, z1)) → rcons(active(z0), z1)
active(rcons(z0, z1)) → rcons(z0, active(z1))
active(from(z0)) → from(active(z0))
active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
active(pi(z0)) → pi(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(times(z0, z1)) → times(active(z0), z1)
active(times(z0, z1)) → times(z0, active(z1))
active(square(z0)) → square(active(z0))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
posrecip(mark(z0)) → mark(posrecip(z0))
posrecip(ok(z0)) → ok(posrecip(z0))
negrecip(mark(z0)) → mark(negrecip(z0))
negrecip(ok(z0)) → ok(negrecip(z0))
cons(mark(z0), z1) → mark(cons(z0, z1))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
cons2(z0, mark(z1)) → mark(cons2(z0, z1))
cons2(ok(z0), ok(z1)) → ok(cons2(z0, z1))
rcons(mark(z0), z1) → mark(rcons(z0, z1))
rcons(z0, mark(z1)) → mark(rcons(z0, z1))
rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
from(mark(z0)) → mark(from(z0))
from(ok(z0)) → ok(from(z0))
2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
pi(mark(z0)) → mark(pi(z0))
pi(ok(z0)) → ok(pi(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
times(mark(z0), z1) → mark(times(z0, z1))
times(z0, mark(z1)) → mark(times(z0, z1))
times(ok(z0), ok(z1)) → ok(times(z0, z1))
square(mark(z0)) → mark(square(z0))
square(ok(z0)) → ok(square(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(posrecip(z0)) → posrecip(proper(z0))
proper(negrecip(z0)) → negrecip(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(cons2(z0, z1)) → cons2(proper(z0), proper(z1))
proper(rnil) → ok(rnil)
proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
proper(pi(z0)) → pi(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(times(z0, z1)) → times(proper(z0), proper(z1))
proper(square(z0)) → square(proper(z0))
top(mark(z0)) → top(proper(z0))
top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(from(z0)) → c(CONS(z0, from(s(z0))), FROM(s(z0)), S(z0))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c2(2NDSPOS(s(z0), cons2(z1, z2)), S(z0), CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c3(RCONS(posrecip(z2), 2ndsneg(z0, z3)), POSRECIP(z2), 2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c5(2NDSNEG(s(z0), cons2(z1, z2)), S(z0), CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c6(RCONS(negrecip(z2), 2ndspos(z0, z3)), NEGRECIP(z2), 2NDSPOS(z0, z3))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)), FROM(0))
ACTIVE(plus(s(z0), z1)) → c9(S(plus(z0, z1)), PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(PLUS(z1, times(z0, z1)), TIMES(z0, z1))
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(s(z0)) → c13(S(active(z0)), ACTIVE(z0))
ACTIVE(posrecip(z0)) → c14(POSRECIP(active(z0)), ACTIVE(z0))
ACTIVE(negrecip(z0)) → c15(NEGRECIP(active(z0)), ACTIVE(z0))
ACTIVE(cons(z0, z1)) → c16(CONS(active(z0), z1), ACTIVE(z0))
ACTIVE(cons2(z0, z1)) → c17(CONS2(z0, active(z1)), ACTIVE(z1))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(from(z0)) → c20(FROM(active(z0)), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(pi(z0)) → c25(PI(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
ACTIVE(square(z0)) → c30(SQUARE(active(z0)), ACTIVE(z0))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
PROPER(s(z0)) → c63(S(proper(z0)), PROPER(z0))
PROPER(posrecip(z0)) → c64(POSRECIP(proper(z0)), PROPER(z0))
PROPER(negrecip(z0)) → c65(NEGRECIP(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c67(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(cons2(z0, z1)) → c68(CONS2(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(rcons(z0, z1)) → c70(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c71(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c72(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c73(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c74(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c75(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c76(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c77(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c78(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c79(TOP(active(z0)), ACTIVE(z0))
S tuples:
ACTIVE(from(z0)) → c(CONS(z0, from(s(z0))), FROM(s(z0)), S(z0))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c2(2NDSPOS(s(z0), cons2(z1, z2)), S(z0), CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c3(RCONS(posrecip(z2), 2ndsneg(z0, z3)), POSRECIP(z2), 2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c5(2NDSNEG(s(z0), cons2(z1, z2)), S(z0), CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c6(RCONS(negrecip(z2), 2ndspos(z0, z3)), NEGRECIP(z2), 2NDSPOS(z0, z3))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)), FROM(0))
ACTIVE(plus(s(z0), z1)) → c9(S(plus(z0, z1)), PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(PLUS(z1, times(z0, z1)), TIMES(z0, z1))
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(s(z0)) → c13(S(active(z0)), ACTIVE(z0))
ACTIVE(posrecip(z0)) → c14(POSRECIP(active(z0)), ACTIVE(z0))
ACTIVE(negrecip(z0)) → c15(NEGRECIP(active(z0)), ACTIVE(z0))
ACTIVE(cons(z0, z1)) → c16(CONS(active(z0), z1), ACTIVE(z0))
ACTIVE(cons2(z0, z1)) → c17(CONS2(z0, active(z1)), ACTIVE(z1))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(from(z0)) → c20(FROM(active(z0)), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(pi(z0)) → c25(PI(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
ACTIVE(square(z0)) → c30(SQUARE(active(z0)), ACTIVE(z0))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
PROPER(s(z0)) → c63(S(proper(z0)), PROPER(z0))
PROPER(posrecip(z0)) → c64(POSRECIP(proper(z0)), PROPER(z0))
PROPER(negrecip(z0)) → c65(NEGRECIP(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c67(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(cons2(z0, z1)) → c68(CONS2(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(rcons(z0, z1)) → c70(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c71(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c72(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c73(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c74(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c75(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c76(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c77(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c78(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c79(TOP(active(z0)), ACTIVE(z0))
K tuples:none
Defined Rule Symbols:
active, s, posrecip, negrecip, cons, cons2, rcons, from, 2ndspos, 2ndsneg, pi, plus, times, square, proper, top
Defined Pair Symbols:
ACTIVE, S, POSRECIP, NEGRECIP, CONS, CONS2, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP
Compound Symbols:
c, c2, c3, c5, c6, c7, c9, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c63, c64, c65, c67, c68, c70, c71, c72, c73, c74, c75, c76, c77, c78, c79
(5) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 5 trailing tuple parts
(6) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(2ndspos(0, z0)) → mark(rnil)
active(2ndspos(s(z0), cons(z1, z2))) → mark(2ndspos(s(z0), cons2(z1, z2)))
active(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(z1, z2))) → mark(2ndsneg(s(z0), cons2(z1, z2)))
active(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
active(pi(z0)) → mark(2ndspos(z0, from(0)))
active(plus(0, z0)) → mark(z0)
active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
active(times(0, z0)) → mark(0)
active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
active(square(z0)) → mark(times(z0, z0))
active(s(z0)) → s(active(z0))
active(posrecip(z0)) → posrecip(active(z0))
active(negrecip(z0)) → negrecip(active(z0))
active(cons(z0, z1)) → cons(active(z0), z1)
active(cons2(z0, z1)) → cons2(z0, active(z1))
active(rcons(z0, z1)) → rcons(active(z0), z1)
active(rcons(z0, z1)) → rcons(z0, active(z1))
active(from(z0)) → from(active(z0))
active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
active(pi(z0)) → pi(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(times(z0, z1)) → times(active(z0), z1)
active(times(z0, z1)) → times(z0, active(z1))
active(square(z0)) → square(active(z0))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
posrecip(mark(z0)) → mark(posrecip(z0))
posrecip(ok(z0)) → ok(posrecip(z0))
negrecip(mark(z0)) → mark(negrecip(z0))
negrecip(ok(z0)) → ok(negrecip(z0))
cons(mark(z0), z1) → mark(cons(z0, z1))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
cons2(z0, mark(z1)) → mark(cons2(z0, z1))
cons2(ok(z0), ok(z1)) → ok(cons2(z0, z1))
rcons(mark(z0), z1) → mark(rcons(z0, z1))
rcons(z0, mark(z1)) → mark(rcons(z0, z1))
rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
from(mark(z0)) → mark(from(z0))
from(ok(z0)) → ok(from(z0))
2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
pi(mark(z0)) → mark(pi(z0))
pi(ok(z0)) → ok(pi(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
times(mark(z0), z1) → mark(times(z0, z1))
times(z0, mark(z1)) → mark(times(z0, z1))
times(ok(z0), ok(z1)) → ok(times(z0, z1))
square(mark(z0)) → mark(square(z0))
square(ok(z0)) → ok(square(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(posrecip(z0)) → posrecip(proper(z0))
proper(negrecip(z0)) → negrecip(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(cons2(z0, z1)) → cons2(proper(z0), proper(z1))
proper(rnil) → ok(rnil)
proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
proper(pi(z0)) → pi(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(times(z0, z1)) → times(proper(z0), proper(z1))
proper(square(z0)) → square(proper(z0))
top(mark(z0)) → top(proper(z0))
top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c2(2NDSPOS(s(z0), cons2(z1, z2)), S(z0), CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c3(RCONS(posrecip(z2), 2ndsneg(z0, z3)), POSRECIP(z2), 2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c5(2NDSNEG(s(z0), cons2(z1, z2)), S(z0), CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c6(RCONS(negrecip(z2), 2ndspos(z0, z3)), NEGRECIP(z2), 2NDSPOS(z0, z3))
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(s(z0)) → c13(S(active(z0)), ACTIVE(z0))
ACTIVE(posrecip(z0)) → c14(POSRECIP(active(z0)), ACTIVE(z0))
ACTIVE(negrecip(z0)) → c15(NEGRECIP(active(z0)), ACTIVE(z0))
ACTIVE(cons(z0, z1)) → c16(CONS(active(z0), z1), ACTIVE(z0))
ACTIVE(cons2(z0, z1)) → c17(CONS2(z0, active(z1)), ACTIVE(z1))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(from(z0)) → c20(FROM(active(z0)), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(pi(z0)) → c25(PI(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
ACTIVE(square(z0)) → c30(SQUARE(active(z0)), ACTIVE(z0))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
PROPER(s(z0)) → c63(S(proper(z0)), PROPER(z0))
PROPER(posrecip(z0)) → c64(POSRECIP(proper(z0)), PROPER(z0))
PROPER(negrecip(z0)) → c65(NEGRECIP(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c67(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(cons2(z0, z1)) → c68(CONS2(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(rcons(z0, z1)) → c70(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c71(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c72(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c73(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c74(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c75(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c76(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c77(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c78(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c79(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c9(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(TIMES(z0, z1))
S tuples:
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c2(2NDSPOS(s(z0), cons2(z1, z2)), S(z0), CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c3(RCONS(posrecip(z2), 2ndsneg(z0, z3)), POSRECIP(z2), 2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c5(2NDSNEG(s(z0), cons2(z1, z2)), S(z0), CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c6(RCONS(negrecip(z2), 2ndspos(z0, z3)), NEGRECIP(z2), 2NDSPOS(z0, z3))
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(s(z0)) → c13(S(active(z0)), ACTIVE(z0))
ACTIVE(posrecip(z0)) → c14(POSRECIP(active(z0)), ACTIVE(z0))
ACTIVE(negrecip(z0)) → c15(NEGRECIP(active(z0)), ACTIVE(z0))
ACTIVE(cons(z0, z1)) → c16(CONS(active(z0), z1), ACTIVE(z0))
ACTIVE(cons2(z0, z1)) → c17(CONS2(z0, active(z1)), ACTIVE(z1))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(from(z0)) → c20(FROM(active(z0)), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(pi(z0)) → c25(PI(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
ACTIVE(square(z0)) → c30(SQUARE(active(z0)), ACTIVE(z0))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
PROPER(s(z0)) → c63(S(proper(z0)), PROPER(z0))
PROPER(posrecip(z0)) → c64(POSRECIP(proper(z0)), PROPER(z0))
PROPER(negrecip(z0)) → c65(NEGRECIP(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c67(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(cons2(z0, z1)) → c68(CONS2(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(rcons(z0, z1)) → c70(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c71(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c72(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c73(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c74(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c75(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c76(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c77(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c78(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c79(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c9(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(TIMES(z0, z1))
K tuples:none
Defined Rule Symbols:
active, s, posrecip, negrecip, cons, cons2, rcons, from, 2ndspos, 2ndsneg, pi, plus, times, square, proper, top
Defined Pair Symbols:
ACTIVE, S, POSRECIP, NEGRECIP, CONS, CONS2, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP
Compound Symbols:
c2, c3, c5, c6, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c63, c64, c65, c67, c68, c70, c71, c72, c73, c74, c75, c76, c77, c78, c79, c, c7, c9, c11
(7) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID) transformation)
Split RHS of tuples not part of any SCC
(8) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(2ndspos(0, z0)) → mark(rnil)
active(2ndspos(s(z0), cons(z1, z2))) → mark(2ndspos(s(z0), cons2(z1, z2)))
active(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(z1, z2))) → mark(2ndsneg(s(z0), cons2(z1, z2)))
active(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
active(pi(z0)) → mark(2ndspos(z0, from(0)))
active(plus(0, z0)) → mark(z0)
active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
active(times(0, z0)) → mark(0)
active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
active(square(z0)) → mark(times(z0, z0))
active(s(z0)) → s(active(z0))
active(posrecip(z0)) → posrecip(active(z0))
active(negrecip(z0)) → negrecip(active(z0))
active(cons(z0, z1)) → cons(active(z0), z1)
active(cons2(z0, z1)) → cons2(z0, active(z1))
active(rcons(z0, z1)) → rcons(active(z0), z1)
active(rcons(z0, z1)) → rcons(z0, active(z1))
active(from(z0)) → from(active(z0))
active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
active(pi(z0)) → pi(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(times(z0, z1)) → times(active(z0), z1)
active(times(z0, z1)) → times(z0, active(z1))
active(square(z0)) → square(active(z0))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
posrecip(mark(z0)) → mark(posrecip(z0))
posrecip(ok(z0)) → ok(posrecip(z0))
negrecip(mark(z0)) → mark(negrecip(z0))
negrecip(ok(z0)) → ok(negrecip(z0))
cons(mark(z0), z1) → mark(cons(z0, z1))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
cons2(z0, mark(z1)) → mark(cons2(z0, z1))
cons2(ok(z0), ok(z1)) → ok(cons2(z0, z1))
rcons(mark(z0), z1) → mark(rcons(z0, z1))
rcons(z0, mark(z1)) → mark(rcons(z0, z1))
rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
from(mark(z0)) → mark(from(z0))
from(ok(z0)) → ok(from(z0))
2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
pi(mark(z0)) → mark(pi(z0))
pi(ok(z0)) → ok(pi(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
times(mark(z0), z1) → mark(times(z0, z1))
times(z0, mark(z1)) → mark(times(z0, z1))
times(ok(z0), ok(z1)) → ok(times(z0, z1))
square(mark(z0)) → mark(square(z0))
square(ok(z0)) → ok(square(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(posrecip(z0)) → posrecip(proper(z0))
proper(negrecip(z0)) → negrecip(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(cons2(z0, z1)) → cons2(proper(z0), proper(z1))
proper(rnil) → ok(rnil)
proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
proper(pi(z0)) → pi(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(times(z0, z1)) → times(proper(z0), proper(z1))
proper(square(z0)) → square(proper(z0))
top(mark(z0)) → top(proper(z0))
top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(s(z0)) → c13(S(active(z0)), ACTIVE(z0))
ACTIVE(posrecip(z0)) → c14(POSRECIP(active(z0)), ACTIVE(z0))
ACTIVE(negrecip(z0)) → c15(NEGRECIP(active(z0)), ACTIVE(z0))
ACTIVE(cons(z0, z1)) → c16(CONS(active(z0), z1), ACTIVE(z0))
ACTIVE(cons2(z0, z1)) → c17(CONS2(z0, active(z1)), ACTIVE(z1))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(from(z0)) → c20(FROM(active(z0)), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(pi(z0)) → c25(PI(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
ACTIVE(square(z0)) → c30(SQUARE(active(z0)), ACTIVE(z0))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
PROPER(s(z0)) → c63(S(proper(z0)), PROPER(z0))
PROPER(posrecip(z0)) → c64(POSRECIP(proper(z0)), PROPER(z0))
PROPER(negrecip(z0)) → c65(NEGRECIP(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c67(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(cons2(z0, z1)) → c68(CONS2(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(rcons(z0, z1)) → c70(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c71(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c72(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c73(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c74(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c75(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c76(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c77(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c78(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c79(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c9(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(2NDSPOS(s(z0), cons2(z1, z2)))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(2NDSNEG(s(z0), cons2(z1, z2)))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
S tuples:
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(s(z0)) → c13(S(active(z0)), ACTIVE(z0))
ACTIVE(posrecip(z0)) → c14(POSRECIP(active(z0)), ACTIVE(z0))
ACTIVE(negrecip(z0)) → c15(NEGRECIP(active(z0)), ACTIVE(z0))
ACTIVE(cons(z0, z1)) → c16(CONS(active(z0), z1), ACTIVE(z0))
ACTIVE(cons2(z0, z1)) → c17(CONS2(z0, active(z1)), ACTIVE(z1))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(from(z0)) → c20(FROM(active(z0)), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(pi(z0)) → c25(PI(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
ACTIVE(square(z0)) → c30(SQUARE(active(z0)), ACTIVE(z0))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
PROPER(s(z0)) → c63(S(proper(z0)), PROPER(z0))
PROPER(posrecip(z0)) → c64(POSRECIP(proper(z0)), PROPER(z0))
PROPER(negrecip(z0)) → c65(NEGRECIP(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c67(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(cons2(z0, z1)) → c68(CONS2(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(rcons(z0, z1)) → c70(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c71(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c72(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c73(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c74(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c75(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c76(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c77(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c78(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c79(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c9(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(2NDSPOS(s(z0), cons2(z1, z2)))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(2NDSNEG(s(z0), cons2(z1, z2)))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
K tuples:none
Defined Rule Symbols:
active, s, posrecip, negrecip, cons, cons2, rcons, from, 2ndspos, 2ndsneg, pi, plus, times, square, proper, top
Defined Pair Symbols:
ACTIVE, S, POSRECIP, NEGRECIP, CONS, CONS2, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP
Compound Symbols:
c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c63, c64, c65, c67, c68, c70, c71, c72, c73, c74, c75, c76, c77, c78, c79, c, c7, c9, c11, c1
(9) CdtUsableRulesProof (EQUIVALENT transformation)
The following rules are not usable and were removed:
top(mark(z0)) → top(proper(z0))
top(ok(z0)) → top(active(z0))
(10) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(2ndspos(0, z0)) → mark(rnil)
active(2ndspos(s(z0), cons(z1, z2))) → mark(2ndspos(s(z0), cons2(z1, z2)))
active(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(z1, z2))) → mark(2ndsneg(s(z0), cons2(z1, z2)))
active(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
active(pi(z0)) → mark(2ndspos(z0, from(0)))
active(plus(0, z0)) → mark(z0)
active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
active(times(0, z0)) → mark(0)
active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
active(square(z0)) → mark(times(z0, z0))
active(s(z0)) → s(active(z0))
active(posrecip(z0)) → posrecip(active(z0))
active(negrecip(z0)) → negrecip(active(z0))
active(cons(z0, z1)) → cons(active(z0), z1)
active(cons2(z0, z1)) → cons2(z0, active(z1))
active(rcons(z0, z1)) → rcons(active(z0), z1)
active(rcons(z0, z1)) → rcons(z0, active(z1))
active(from(z0)) → from(active(z0))
active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
active(pi(z0)) → pi(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(times(z0, z1)) → times(active(z0), z1)
active(times(z0, z1)) → times(z0, active(z1))
active(square(z0)) → square(active(z0))
2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
cons2(z0, mark(z1)) → mark(cons2(z0, z1))
cons2(ok(z0), ok(z1)) → ok(cons2(z0, z1))
rcons(mark(z0), z1) → mark(rcons(z0, z1))
rcons(z0, mark(z1)) → mark(rcons(z0, z1))
rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
posrecip(ok(z0)) → ok(posrecip(z0))
posrecip(mark(z0)) → mark(posrecip(z0))
2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
negrecip(ok(z0)) → ok(negrecip(z0))
negrecip(mark(z0)) → mark(negrecip(z0))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
cons(mark(z0), z1) → mark(cons(z0, z1))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
from(mark(z0)) → mark(from(z0))
from(ok(z0)) → ok(from(z0))
pi(mark(z0)) → mark(pi(z0))
pi(ok(z0)) → ok(pi(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
times(mark(z0), z1) → mark(times(z0, z1))
times(ok(z0), ok(z1)) → ok(times(z0, z1))
times(z0, mark(z1)) → mark(times(z0, z1))
square(mark(z0)) → mark(square(z0))
square(ok(z0)) → ok(square(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(posrecip(z0)) → posrecip(proper(z0))
proper(negrecip(z0)) → negrecip(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(cons2(z0, z1)) → cons2(proper(z0), proper(z1))
proper(rnil) → ok(rnil)
proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
proper(pi(z0)) → pi(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(times(z0, z1)) → times(proper(z0), proper(z1))
proper(square(z0)) → square(proper(z0))
Tuples:
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(s(z0)) → c13(S(active(z0)), ACTIVE(z0))
ACTIVE(posrecip(z0)) → c14(POSRECIP(active(z0)), ACTIVE(z0))
ACTIVE(negrecip(z0)) → c15(NEGRECIP(active(z0)), ACTIVE(z0))
ACTIVE(cons(z0, z1)) → c16(CONS(active(z0), z1), ACTIVE(z0))
ACTIVE(cons2(z0, z1)) → c17(CONS2(z0, active(z1)), ACTIVE(z1))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(from(z0)) → c20(FROM(active(z0)), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(pi(z0)) → c25(PI(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
ACTIVE(square(z0)) → c30(SQUARE(active(z0)), ACTIVE(z0))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
PROPER(s(z0)) → c63(S(proper(z0)), PROPER(z0))
PROPER(posrecip(z0)) → c64(POSRECIP(proper(z0)), PROPER(z0))
PROPER(negrecip(z0)) → c65(NEGRECIP(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c67(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(cons2(z0, z1)) → c68(CONS2(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(rcons(z0, z1)) → c70(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c71(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c72(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c73(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c74(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c75(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c76(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c77(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c78(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c79(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c9(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(2NDSPOS(s(z0), cons2(z1, z2)))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(2NDSNEG(s(z0), cons2(z1, z2)))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
S tuples:
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(s(z0)) → c13(S(active(z0)), ACTIVE(z0))
ACTIVE(posrecip(z0)) → c14(POSRECIP(active(z0)), ACTIVE(z0))
ACTIVE(negrecip(z0)) → c15(NEGRECIP(active(z0)), ACTIVE(z0))
ACTIVE(cons(z0, z1)) → c16(CONS(active(z0), z1), ACTIVE(z0))
ACTIVE(cons2(z0, z1)) → c17(CONS2(z0, active(z1)), ACTIVE(z1))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(from(z0)) → c20(FROM(active(z0)), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(pi(z0)) → c25(PI(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
ACTIVE(square(z0)) → c30(SQUARE(active(z0)), ACTIVE(z0))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
PROPER(s(z0)) → c63(S(proper(z0)), PROPER(z0))
PROPER(posrecip(z0)) → c64(POSRECIP(proper(z0)), PROPER(z0))
PROPER(negrecip(z0)) → c65(NEGRECIP(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c67(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(cons2(z0, z1)) → c68(CONS2(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(rcons(z0, z1)) → c70(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c71(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c72(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c73(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c74(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c75(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c76(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c77(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c78(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c79(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c9(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(2NDSPOS(s(z0), cons2(z1, z2)))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(2NDSNEG(s(z0), cons2(z1, z2)))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
K tuples:none
Defined Rule Symbols:
active, 2ndspos, cons2, rcons, posrecip, 2ndsneg, negrecip, s, cons, from, pi, plus, times, square, proper
Defined Pair Symbols:
ACTIVE, S, POSRECIP, NEGRECIP, CONS, CONS2, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP
Compound Symbols:
c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c63, c64, c65, c67, c68, c70, c71, c72, c73, c74, c75, c76, c77, c78, c79, c, c7, c9, c11, c1
(11) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
ACTIVE(
s(
z0)) →
c13(
S(
active(
z0)),
ACTIVE(
z0)) by
ACTIVE(s(from(z0))) → c13(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, z2)))) → c13(S(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(s(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, z2)))) → c13(S(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(s(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c13(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c13(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c13(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c13(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c13(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c13(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c13(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c13(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(cons2(z0, z1))) → c13(S(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c13(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c13(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c13(S(square(active(z0))), ACTIVE(square(z0)))
(12) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(2ndspos(0, z0)) → mark(rnil)
active(2ndspos(s(z0), cons(z1, z2))) → mark(2ndspos(s(z0), cons2(z1, z2)))
active(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(z1, z2))) → mark(2ndsneg(s(z0), cons2(z1, z2)))
active(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
active(pi(z0)) → mark(2ndspos(z0, from(0)))
active(plus(0, z0)) → mark(z0)
active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
active(times(0, z0)) → mark(0)
active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
active(square(z0)) → mark(times(z0, z0))
active(s(z0)) → s(active(z0))
active(posrecip(z0)) → posrecip(active(z0))
active(negrecip(z0)) → negrecip(active(z0))
active(cons(z0, z1)) → cons(active(z0), z1)
active(cons2(z0, z1)) → cons2(z0, active(z1))
active(rcons(z0, z1)) → rcons(active(z0), z1)
active(rcons(z0, z1)) → rcons(z0, active(z1))
active(from(z0)) → from(active(z0))
active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
active(pi(z0)) → pi(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(times(z0, z1)) → times(active(z0), z1)
active(times(z0, z1)) → times(z0, active(z1))
active(square(z0)) → square(active(z0))
2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
cons2(z0, mark(z1)) → mark(cons2(z0, z1))
cons2(ok(z0), ok(z1)) → ok(cons2(z0, z1))
rcons(mark(z0), z1) → mark(rcons(z0, z1))
rcons(z0, mark(z1)) → mark(rcons(z0, z1))
rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
posrecip(ok(z0)) → ok(posrecip(z0))
posrecip(mark(z0)) → mark(posrecip(z0))
2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
negrecip(ok(z0)) → ok(negrecip(z0))
negrecip(mark(z0)) → mark(negrecip(z0))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
cons(mark(z0), z1) → mark(cons(z0, z1))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
from(mark(z0)) → mark(from(z0))
from(ok(z0)) → ok(from(z0))
pi(mark(z0)) → mark(pi(z0))
pi(ok(z0)) → ok(pi(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
times(mark(z0), z1) → mark(times(z0, z1))
times(ok(z0), ok(z1)) → ok(times(z0, z1))
times(z0, mark(z1)) → mark(times(z0, z1))
square(mark(z0)) → mark(square(z0))
square(ok(z0)) → ok(square(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(posrecip(z0)) → posrecip(proper(z0))
proper(negrecip(z0)) → negrecip(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(cons2(z0, z1)) → cons2(proper(z0), proper(z1))
proper(rnil) → ok(rnil)
proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
proper(pi(z0)) → pi(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(times(z0, z1)) → times(proper(z0), proper(z1))
proper(square(z0)) → square(proper(z0))
Tuples:
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(posrecip(z0)) → c14(POSRECIP(active(z0)), ACTIVE(z0))
ACTIVE(negrecip(z0)) → c15(NEGRECIP(active(z0)), ACTIVE(z0))
ACTIVE(cons(z0, z1)) → c16(CONS(active(z0), z1), ACTIVE(z0))
ACTIVE(cons2(z0, z1)) → c17(CONS2(z0, active(z1)), ACTIVE(z1))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(from(z0)) → c20(FROM(active(z0)), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(pi(z0)) → c25(PI(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
ACTIVE(square(z0)) → c30(SQUARE(active(z0)), ACTIVE(z0))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
PROPER(s(z0)) → c63(S(proper(z0)), PROPER(z0))
PROPER(posrecip(z0)) → c64(POSRECIP(proper(z0)), PROPER(z0))
PROPER(negrecip(z0)) → c65(NEGRECIP(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c67(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(cons2(z0, z1)) → c68(CONS2(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(rcons(z0, z1)) → c70(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c71(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c72(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c73(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c74(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c75(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c76(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c77(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c78(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c79(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c9(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(2NDSPOS(s(z0), cons2(z1, z2)))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(2NDSNEG(s(z0), cons2(z1, z2)))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c13(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, z2)))) → c13(S(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(s(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, z2)))) → c13(S(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(s(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c13(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c13(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c13(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c13(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c13(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c13(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c13(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c13(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(cons2(z0, z1))) → c13(S(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c13(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c13(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c13(S(square(active(z0))), ACTIVE(square(z0)))
S tuples:
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(posrecip(z0)) → c14(POSRECIP(active(z0)), ACTIVE(z0))
ACTIVE(negrecip(z0)) → c15(NEGRECIP(active(z0)), ACTIVE(z0))
ACTIVE(cons(z0, z1)) → c16(CONS(active(z0), z1), ACTIVE(z0))
ACTIVE(cons2(z0, z1)) → c17(CONS2(z0, active(z1)), ACTIVE(z1))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(from(z0)) → c20(FROM(active(z0)), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(pi(z0)) → c25(PI(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
ACTIVE(square(z0)) → c30(SQUARE(active(z0)), ACTIVE(z0))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
PROPER(s(z0)) → c63(S(proper(z0)), PROPER(z0))
PROPER(posrecip(z0)) → c64(POSRECIP(proper(z0)), PROPER(z0))
PROPER(negrecip(z0)) → c65(NEGRECIP(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c67(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(cons2(z0, z1)) → c68(CONS2(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(rcons(z0, z1)) → c70(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c71(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c72(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c73(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c74(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c75(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c76(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c77(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c78(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c79(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c9(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(2NDSPOS(s(z0), cons2(z1, z2)))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(2NDSNEG(s(z0), cons2(z1, z2)))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c13(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, z2)))) → c13(S(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(s(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, z2)))) → c13(S(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(s(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c13(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c13(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c13(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c13(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c13(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c13(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c13(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c13(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(cons2(z0, z1))) → c13(S(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c13(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c13(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c13(S(square(active(z0))), ACTIVE(square(z0)))
K tuples:none
Defined Rule Symbols:
active, 2ndspos, cons2, rcons, posrecip, 2ndsneg, negrecip, s, cons, from, pi, plus, times, square, proper
Defined Pair Symbols:
ACTIVE, S, POSRECIP, NEGRECIP, CONS, CONS2, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP
Compound Symbols:
c12, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c63, c64, c65, c67, c68, c70, c71, c72, c73, c74, c75, c76, c77, c78, c79, c, c7, c9, c11, c1, c13
(13) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
ACTIVE(
posrecip(
z0)) →
c14(
POSRECIP(
active(
z0)),
ACTIVE(
z0)) by
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c14(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c14(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c14(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c14(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c14(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c14(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c14(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c14(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(cons2(z0, z1))) → c14(POSRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
(14) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(2ndspos(0, z0)) → mark(rnil)
active(2ndspos(s(z0), cons(z1, z2))) → mark(2ndspos(s(z0), cons2(z1, z2)))
active(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(z1, z2))) → mark(2ndsneg(s(z0), cons2(z1, z2)))
active(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
active(pi(z0)) → mark(2ndspos(z0, from(0)))
active(plus(0, z0)) → mark(z0)
active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
active(times(0, z0)) → mark(0)
active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
active(square(z0)) → mark(times(z0, z0))
active(s(z0)) → s(active(z0))
active(posrecip(z0)) → posrecip(active(z0))
active(negrecip(z0)) → negrecip(active(z0))
active(cons(z0, z1)) → cons(active(z0), z1)
active(cons2(z0, z1)) → cons2(z0, active(z1))
active(rcons(z0, z1)) → rcons(active(z0), z1)
active(rcons(z0, z1)) → rcons(z0, active(z1))
active(from(z0)) → from(active(z0))
active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
active(pi(z0)) → pi(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(times(z0, z1)) → times(active(z0), z1)
active(times(z0, z1)) → times(z0, active(z1))
active(square(z0)) → square(active(z0))
2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
cons2(z0, mark(z1)) → mark(cons2(z0, z1))
cons2(ok(z0), ok(z1)) → ok(cons2(z0, z1))
rcons(mark(z0), z1) → mark(rcons(z0, z1))
rcons(z0, mark(z1)) → mark(rcons(z0, z1))
rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
posrecip(ok(z0)) → ok(posrecip(z0))
posrecip(mark(z0)) → mark(posrecip(z0))
2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
negrecip(ok(z0)) → ok(negrecip(z0))
negrecip(mark(z0)) → mark(negrecip(z0))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
cons(mark(z0), z1) → mark(cons(z0, z1))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
from(mark(z0)) → mark(from(z0))
from(ok(z0)) → ok(from(z0))
pi(mark(z0)) → mark(pi(z0))
pi(ok(z0)) → ok(pi(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
times(mark(z0), z1) → mark(times(z0, z1))
times(ok(z0), ok(z1)) → ok(times(z0, z1))
times(z0, mark(z1)) → mark(times(z0, z1))
square(mark(z0)) → mark(square(z0))
square(ok(z0)) → ok(square(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(posrecip(z0)) → posrecip(proper(z0))
proper(negrecip(z0)) → negrecip(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(cons2(z0, z1)) → cons2(proper(z0), proper(z1))
proper(rnil) → ok(rnil)
proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
proper(pi(z0)) → pi(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(times(z0, z1)) → times(proper(z0), proper(z1))
proper(square(z0)) → square(proper(z0))
Tuples:
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(negrecip(z0)) → c15(NEGRECIP(active(z0)), ACTIVE(z0))
ACTIVE(cons(z0, z1)) → c16(CONS(active(z0), z1), ACTIVE(z0))
ACTIVE(cons2(z0, z1)) → c17(CONS2(z0, active(z1)), ACTIVE(z1))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(from(z0)) → c20(FROM(active(z0)), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(pi(z0)) → c25(PI(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
ACTIVE(square(z0)) → c30(SQUARE(active(z0)), ACTIVE(z0))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
PROPER(s(z0)) → c63(S(proper(z0)), PROPER(z0))
PROPER(posrecip(z0)) → c64(POSRECIP(proper(z0)), PROPER(z0))
PROPER(negrecip(z0)) → c65(NEGRECIP(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c67(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(cons2(z0, z1)) → c68(CONS2(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(rcons(z0, z1)) → c70(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c71(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c72(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c73(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c74(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c75(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c76(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c77(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c78(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c79(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c9(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(2NDSPOS(s(z0), cons2(z1, z2)))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(2NDSNEG(s(z0), cons2(z1, z2)))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c13(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, z2)))) → c13(S(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(s(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, z2)))) → c13(S(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(s(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c13(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c13(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c13(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c13(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c13(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c13(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c13(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c13(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(cons2(z0, z1))) → c13(S(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c13(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c13(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c13(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c14(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c14(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c14(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c14(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c14(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c14(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c14(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c14(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(cons2(z0, z1))) → c14(POSRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
S tuples:
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(negrecip(z0)) → c15(NEGRECIP(active(z0)), ACTIVE(z0))
ACTIVE(cons(z0, z1)) → c16(CONS(active(z0), z1), ACTIVE(z0))
ACTIVE(cons2(z0, z1)) → c17(CONS2(z0, active(z1)), ACTIVE(z1))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(from(z0)) → c20(FROM(active(z0)), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(pi(z0)) → c25(PI(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
ACTIVE(square(z0)) → c30(SQUARE(active(z0)), ACTIVE(z0))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
PROPER(s(z0)) → c63(S(proper(z0)), PROPER(z0))
PROPER(posrecip(z0)) → c64(POSRECIP(proper(z0)), PROPER(z0))
PROPER(negrecip(z0)) → c65(NEGRECIP(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c67(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(cons2(z0, z1)) → c68(CONS2(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(rcons(z0, z1)) → c70(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c71(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c72(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c73(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c74(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c75(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c76(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c77(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c78(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c79(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c9(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(2NDSPOS(s(z0), cons2(z1, z2)))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(2NDSNEG(s(z0), cons2(z1, z2)))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c13(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, z2)))) → c13(S(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(s(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, z2)))) → c13(S(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(s(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c13(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c13(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c13(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c13(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c13(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c13(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c13(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c13(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(cons2(z0, z1))) → c13(S(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c13(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c13(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c13(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c14(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c14(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c14(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c14(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c14(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c14(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c14(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c14(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(cons2(z0, z1))) → c14(POSRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
K tuples:none
Defined Rule Symbols:
active, 2ndspos, cons2, rcons, posrecip, 2ndsneg, negrecip, s, cons, from, pi, plus, times, square, proper
Defined Pair Symbols:
ACTIVE, S, POSRECIP, NEGRECIP, CONS, CONS2, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP
Compound Symbols:
c12, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c63, c64, c65, c67, c68, c70, c71, c72, c73, c74, c75, c76, c77, c78, c79, c, c7, c9, c11, c1, c13, c14
(15) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
ACTIVE(
negrecip(
z0)) →
c15(
NEGRECIP(
active(
z0)),
ACTIVE(
z0)) by
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c15(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c15(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c15(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c15(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c15(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c15(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c15(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c15(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(cons2(z0, z1))) → c15(NEGRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
(16) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(2ndspos(0, z0)) → mark(rnil)
active(2ndspos(s(z0), cons(z1, z2))) → mark(2ndspos(s(z0), cons2(z1, z2)))
active(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(z1, z2))) → mark(2ndsneg(s(z0), cons2(z1, z2)))
active(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
active(pi(z0)) → mark(2ndspos(z0, from(0)))
active(plus(0, z0)) → mark(z0)
active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
active(times(0, z0)) → mark(0)
active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
active(square(z0)) → mark(times(z0, z0))
active(s(z0)) → s(active(z0))
active(posrecip(z0)) → posrecip(active(z0))
active(negrecip(z0)) → negrecip(active(z0))
active(cons(z0, z1)) → cons(active(z0), z1)
active(cons2(z0, z1)) → cons2(z0, active(z1))
active(rcons(z0, z1)) → rcons(active(z0), z1)
active(rcons(z0, z1)) → rcons(z0, active(z1))
active(from(z0)) → from(active(z0))
active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
active(pi(z0)) → pi(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(times(z0, z1)) → times(active(z0), z1)
active(times(z0, z1)) → times(z0, active(z1))
active(square(z0)) → square(active(z0))
2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
cons2(z0, mark(z1)) → mark(cons2(z0, z1))
cons2(ok(z0), ok(z1)) → ok(cons2(z0, z1))
rcons(mark(z0), z1) → mark(rcons(z0, z1))
rcons(z0, mark(z1)) → mark(rcons(z0, z1))
rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
posrecip(ok(z0)) → ok(posrecip(z0))
posrecip(mark(z0)) → mark(posrecip(z0))
2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
negrecip(ok(z0)) → ok(negrecip(z0))
negrecip(mark(z0)) → mark(negrecip(z0))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
cons(mark(z0), z1) → mark(cons(z0, z1))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
from(mark(z0)) → mark(from(z0))
from(ok(z0)) → ok(from(z0))
pi(mark(z0)) → mark(pi(z0))
pi(ok(z0)) → ok(pi(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
times(mark(z0), z1) → mark(times(z0, z1))
times(ok(z0), ok(z1)) → ok(times(z0, z1))
times(z0, mark(z1)) → mark(times(z0, z1))
square(mark(z0)) → mark(square(z0))
square(ok(z0)) → ok(square(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(posrecip(z0)) → posrecip(proper(z0))
proper(negrecip(z0)) → negrecip(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(cons2(z0, z1)) → cons2(proper(z0), proper(z1))
proper(rnil) → ok(rnil)
proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
proper(pi(z0)) → pi(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(times(z0, z1)) → times(proper(z0), proper(z1))
proper(square(z0)) → square(proper(z0))
Tuples:
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(cons(z0, z1)) → c16(CONS(active(z0), z1), ACTIVE(z0))
ACTIVE(cons2(z0, z1)) → c17(CONS2(z0, active(z1)), ACTIVE(z1))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(from(z0)) → c20(FROM(active(z0)), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(pi(z0)) → c25(PI(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
ACTIVE(square(z0)) → c30(SQUARE(active(z0)), ACTIVE(z0))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
PROPER(s(z0)) → c63(S(proper(z0)), PROPER(z0))
PROPER(posrecip(z0)) → c64(POSRECIP(proper(z0)), PROPER(z0))
PROPER(negrecip(z0)) → c65(NEGRECIP(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c67(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(cons2(z0, z1)) → c68(CONS2(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(rcons(z0, z1)) → c70(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c71(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c72(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c73(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c74(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c75(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c76(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c77(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c78(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c79(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c9(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(2NDSPOS(s(z0), cons2(z1, z2)))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(2NDSNEG(s(z0), cons2(z1, z2)))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c13(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, z2)))) → c13(S(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(s(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, z2)))) → c13(S(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(s(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c13(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c13(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c13(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c13(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c13(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c13(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c13(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c13(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(cons2(z0, z1))) → c13(S(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c13(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c13(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c13(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c14(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c14(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c14(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c14(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c14(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c14(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c14(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c14(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(cons2(z0, z1))) → c14(POSRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c15(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c15(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c15(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c15(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c15(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c15(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c15(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c15(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(cons2(z0, z1))) → c15(NEGRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
S tuples:
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(cons(z0, z1)) → c16(CONS(active(z0), z1), ACTIVE(z0))
ACTIVE(cons2(z0, z1)) → c17(CONS2(z0, active(z1)), ACTIVE(z1))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(from(z0)) → c20(FROM(active(z0)), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(pi(z0)) → c25(PI(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
ACTIVE(square(z0)) → c30(SQUARE(active(z0)), ACTIVE(z0))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
PROPER(s(z0)) → c63(S(proper(z0)), PROPER(z0))
PROPER(posrecip(z0)) → c64(POSRECIP(proper(z0)), PROPER(z0))
PROPER(negrecip(z0)) → c65(NEGRECIP(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c67(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(cons2(z0, z1)) → c68(CONS2(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(rcons(z0, z1)) → c70(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c71(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c72(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c73(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c74(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c75(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c76(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c77(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c78(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c79(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c9(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(2NDSPOS(s(z0), cons2(z1, z2)))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(2NDSNEG(s(z0), cons2(z1, z2)))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c13(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, z2)))) → c13(S(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(s(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, z2)))) → c13(S(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(s(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c13(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c13(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c13(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c13(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c13(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c13(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c13(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c13(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(cons2(z0, z1))) → c13(S(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c13(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c13(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c13(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c14(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c14(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c14(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c14(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c14(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c14(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c14(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c14(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(cons2(z0, z1))) → c14(POSRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c15(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c15(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c15(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c15(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c15(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c15(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c15(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c15(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(cons2(z0, z1))) → c15(NEGRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
K tuples:none
Defined Rule Symbols:
active, 2ndspos, cons2, rcons, posrecip, 2ndsneg, negrecip, s, cons, from, pi, plus, times, square, proper
Defined Pair Symbols:
ACTIVE, S, POSRECIP, NEGRECIP, CONS, CONS2, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP
Compound Symbols:
c12, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c63, c64, c65, c67, c68, c70, c71, c72, c73, c74, c75, c76, c77, c78, c79, c, c7, c9, c11, c1, c13, c14, c15
(17) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
ACTIVE(
cons(
z0,
z1)) →
c16(
CONS(
active(
z0),
z1),
ACTIVE(
z0)) by
ACTIVE(cons(from(z0), x1)) → c16(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndspos(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndspos(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndsneg(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndsneg(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c16(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c16(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c16(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c16(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c16(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c16(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c16(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c16(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(cons2(z0, z1), x1)) → c16(CONS(cons2(z0, active(z1)), x1), ACTIVE(cons2(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
(18) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(2ndspos(0, z0)) → mark(rnil)
active(2ndspos(s(z0), cons(z1, z2))) → mark(2ndspos(s(z0), cons2(z1, z2)))
active(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(z1, z2))) → mark(2ndsneg(s(z0), cons2(z1, z2)))
active(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
active(pi(z0)) → mark(2ndspos(z0, from(0)))
active(plus(0, z0)) → mark(z0)
active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
active(times(0, z0)) → mark(0)
active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
active(square(z0)) → mark(times(z0, z0))
active(s(z0)) → s(active(z0))
active(posrecip(z0)) → posrecip(active(z0))
active(negrecip(z0)) → negrecip(active(z0))
active(cons(z0, z1)) → cons(active(z0), z1)
active(cons2(z0, z1)) → cons2(z0, active(z1))
active(rcons(z0, z1)) → rcons(active(z0), z1)
active(rcons(z0, z1)) → rcons(z0, active(z1))
active(from(z0)) → from(active(z0))
active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
active(pi(z0)) → pi(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(times(z0, z1)) → times(active(z0), z1)
active(times(z0, z1)) → times(z0, active(z1))
active(square(z0)) → square(active(z0))
2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
cons2(z0, mark(z1)) → mark(cons2(z0, z1))
cons2(ok(z0), ok(z1)) → ok(cons2(z0, z1))
rcons(mark(z0), z1) → mark(rcons(z0, z1))
rcons(z0, mark(z1)) → mark(rcons(z0, z1))
rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
posrecip(ok(z0)) → ok(posrecip(z0))
posrecip(mark(z0)) → mark(posrecip(z0))
2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
negrecip(ok(z0)) → ok(negrecip(z0))
negrecip(mark(z0)) → mark(negrecip(z0))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
cons(mark(z0), z1) → mark(cons(z0, z1))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
from(mark(z0)) → mark(from(z0))
from(ok(z0)) → ok(from(z0))
pi(mark(z0)) → mark(pi(z0))
pi(ok(z0)) → ok(pi(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
times(mark(z0), z1) → mark(times(z0, z1))
times(ok(z0), ok(z1)) → ok(times(z0, z1))
times(z0, mark(z1)) → mark(times(z0, z1))
square(mark(z0)) → mark(square(z0))
square(ok(z0)) → ok(square(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(posrecip(z0)) → posrecip(proper(z0))
proper(negrecip(z0)) → negrecip(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(cons2(z0, z1)) → cons2(proper(z0), proper(z1))
proper(rnil) → ok(rnil)
proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
proper(pi(z0)) → pi(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(times(z0, z1)) → times(proper(z0), proper(z1))
proper(square(z0)) → square(proper(z0))
Tuples:
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(cons2(z0, z1)) → c17(CONS2(z0, active(z1)), ACTIVE(z1))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(from(z0)) → c20(FROM(active(z0)), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(pi(z0)) → c25(PI(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
ACTIVE(square(z0)) → c30(SQUARE(active(z0)), ACTIVE(z0))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
PROPER(s(z0)) → c63(S(proper(z0)), PROPER(z0))
PROPER(posrecip(z0)) → c64(POSRECIP(proper(z0)), PROPER(z0))
PROPER(negrecip(z0)) → c65(NEGRECIP(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c67(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(cons2(z0, z1)) → c68(CONS2(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(rcons(z0, z1)) → c70(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c71(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c72(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c73(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c74(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c75(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c76(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c77(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c78(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c79(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c9(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(2NDSPOS(s(z0), cons2(z1, z2)))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(2NDSNEG(s(z0), cons2(z1, z2)))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c13(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, z2)))) → c13(S(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(s(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, z2)))) → c13(S(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(s(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c13(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c13(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c13(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c13(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c13(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c13(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c13(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c13(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(cons2(z0, z1))) → c13(S(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c13(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c13(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c13(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c14(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c14(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c14(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c14(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c14(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c14(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c14(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c14(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(cons2(z0, z1))) → c14(POSRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c15(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c15(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c15(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c15(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c15(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c15(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c15(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c15(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(cons2(z0, z1))) → c15(NEGRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndspos(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndspos(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndsneg(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndsneg(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c16(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c16(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c16(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c16(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c16(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c16(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c16(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c16(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(cons2(z0, z1), x1)) → c16(CONS(cons2(z0, active(z1)), x1), ACTIVE(cons2(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
S tuples:
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(cons2(z0, z1)) → c17(CONS2(z0, active(z1)), ACTIVE(z1))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(from(z0)) → c20(FROM(active(z0)), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(pi(z0)) → c25(PI(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
ACTIVE(square(z0)) → c30(SQUARE(active(z0)), ACTIVE(z0))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
PROPER(s(z0)) → c63(S(proper(z0)), PROPER(z0))
PROPER(posrecip(z0)) → c64(POSRECIP(proper(z0)), PROPER(z0))
PROPER(negrecip(z0)) → c65(NEGRECIP(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c67(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(cons2(z0, z1)) → c68(CONS2(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(rcons(z0, z1)) → c70(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c71(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c72(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c73(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c74(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c75(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c76(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c77(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c78(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c79(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c9(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(2NDSPOS(s(z0), cons2(z1, z2)))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(2NDSNEG(s(z0), cons2(z1, z2)))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c13(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, z2)))) → c13(S(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(s(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, z2)))) → c13(S(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(s(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c13(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c13(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c13(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c13(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c13(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c13(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c13(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c13(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(cons2(z0, z1))) → c13(S(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c13(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c13(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c13(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c14(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c14(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c14(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c14(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c14(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c14(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c14(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c14(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(cons2(z0, z1))) → c14(POSRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c15(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c15(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c15(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c15(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c15(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c15(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c15(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c15(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(cons2(z0, z1))) → c15(NEGRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndspos(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndspos(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndsneg(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndsneg(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c16(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c16(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c16(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c16(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c16(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c16(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c16(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c16(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(cons2(z0, z1), x1)) → c16(CONS(cons2(z0, active(z1)), x1), ACTIVE(cons2(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
K tuples:none
Defined Rule Symbols:
active, 2ndspos, cons2, rcons, posrecip, 2ndsneg, negrecip, s, cons, from, pi, plus, times, square, proper
Defined Pair Symbols:
ACTIVE, S, POSRECIP, NEGRECIP, CONS, CONS2, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP
Compound Symbols:
c12, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c63, c64, c65, c67, c68, c70, c71, c72, c73, c74, c75, c76, c77, c78, c79, c, c7, c9, c11, c1, c13, c14, c15, c16
(19) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
ACTIVE(
cons2(
z0,
z1)) →
c17(
CONS2(
z0,
active(
z1)),
ACTIVE(
z1)) by
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, 2ndsneg(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(0, z0))) → c17(CONS2(x0, mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(cons2(x0, plus(s(z0), z1))) → c17(CONS2(x0, mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons2(x0, times(0, z0))) → c17(CONS2(x0, mark(0)), ACTIVE(times(0, z0)))
ACTIVE(cons2(x0, times(s(z0), z1))) → c17(CONS2(x0, mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(cons2(x0, s(z0))) → c17(CONS2(x0, s(active(z0))), ACTIVE(s(z0)))
ACTIVE(cons2(x0, posrecip(z0))) → c17(CONS2(x0, posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(cons2(x0, negrecip(z0))) → c17(CONS2(x0, negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(cons2(x0, cons(z0, z1))) → c17(CONS2(x0, cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(cons2(x0, cons2(z0, z1))) → c17(CONS2(x0, cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, from(active(z0))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, square(active(z0))), ACTIVE(square(z0)))
(20) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(2ndspos(0, z0)) → mark(rnil)
active(2ndspos(s(z0), cons(z1, z2))) → mark(2ndspos(s(z0), cons2(z1, z2)))
active(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(z1, z2))) → mark(2ndsneg(s(z0), cons2(z1, z2)))
active(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
active(pi(z0)) → mark(2ndspos(z0, from(0)))
active(plus(0, z0)) → mark(z0)
active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
active(times(0, z0)) → mark(0)
active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
active(square(z0)) → mark(times(z0, z0))
active(s(z0)) → s(active(z0))
active(posrecip(z0)) → posrecip(active(z0))
active(negrecip(z0)) → negrecip(active(z0))
active(cons(z0, z1)) → cons(active(z0), z1)
active(cons2(z0, z1)) → cons2(z0, active(z1))
active(rcons(z0, z1)) → rcons(active(z0), z1)
active(rcons(z0, z1)) → rcons(z0, active(z1))
active(from(z0)) → from(active(z0))
active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
active(pi(z0)) → pi(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(times(z0, z1)) → times(active(z0), z1)
active(times(z0, z1)) → times(z0, active(z1))
active(square(z0)) → square(active(z0))
2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
cons2(z0, mark(z1)) → mark(cons2(z0, z1))
cons2(ok(z0), ok(z1)) → ok(cons2(z0, z1))
rcons(mark(z0), z1) → mark(rcons(z0, z1))
rcons(z0, mark(z1)) → mark(rcons(z0, z1))
rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
posrecip(ok(z0)) → ok(posrecip(z0))
posrecip(mark(z0)) → mark(posrecip(z0))
2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
negrecip(ok(z0)) → ok(negrecip(z0))
negrecip(mark(z0)) → mark(negrecip(z0))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
cons(mark(z0), z1) → mark(cons(z0, z1))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
from(mark(z0)) → mark(from(z0))
from(ok(z0)) → ok(from(z0))
pi(mark(z0)) → mark(pi(z0))
pi(ok(z0)) → ok(pi(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
times(mark(z0), z1) → mark(times(z0, z1))
times(ok(z0), ok(z1)) → ok(times(z0, z1))
times(z0, mark(z1)) → mark(times(z0, z1))
square(mark(z0)) → mark(square(z0))
square(ok(z0)) → ok(square(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(posrecip(z0)) → posrecip(proper(z0))
proper(negrecip(z0)) → negrecip(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(cons2(z0, z1)) → cons2(proper(z0), proper(z1))
proper(rnil) → ok(rnil)
proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
proper(pi(z0)) → pi(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(times(z0, z1)) → times(proper(z0), proper(z1))
proper(square(z0)) → square(proper(z0))
Tuples:
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(from(z0)) → c20(FROM(active(z0)), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(pi(z0)) → c25(PI(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
ACTIVE(square(z0)) → c30(SQUARE(active(z0)), ACTIVE(z0))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
PROPER(s(z0)) → c63(S(proper(z0)), PROPER(z0))
PROPER(posrecip(z0)) → c64(POSRECIP(proper(z0)), PROPER(z0))
PROPER(negrecip(z0)) → c65(NEGRECIP(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c67(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(cons2(z0, z1)) → c68(CONS2(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(rcons(z0, z1)) → c70(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c71(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c72(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c73(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c74(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c75(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c76(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c77(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c78(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c79(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c9(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(2NDSPOS(s(z0), cons2(z1, z2)))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(2NDSNEG(s(z0), cons2(z1, z2)))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c13(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, z2)))) → c13(S(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(s(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, z2)))) → c13(S(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(s(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c13(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c13(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c13(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c13(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c13(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c13(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c13(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c13(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(cons2(z0, z1))) → c13(S(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c13(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c13(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c13(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c14(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c14(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c14(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c14(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c14(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c14(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c14(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c14(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(cons2(z0, z1))) → c14(POSRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c15(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c15(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c15(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c15(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c15(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c15(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c15(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c15(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(cons2(z0, z1))) → c15(NEGRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndspos(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndspos(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndsneg(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndsneg(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c16(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c16(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c16(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c16(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c16(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c16(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c16(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c16(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(cons2(z0, z1), x1)) → c16(CONS(cons2(z0, active(z1)), x1), ACTIVE(cons2(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, 2ndsneg(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(0, z0))) → c17(CONS2(x0, mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(cons2(x0, plus(s(z0), z1))) → c17(CONS2(x0, mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons2(x0, times(0, z0))) → c17(CONS2(x0, mark(0)), ACTIVE(times(0, z0)))
ACTIVE(cons2(x0, times(s(z0), z1))) → c17(CONS2(x0, mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(cons2(x0, s(z0))) → c17(CONS2(x0, s(active(z0))), ACTIVE(s(z0)))
ACTIVE(cons2(x0, posrecip(z0))) → c17(CONS2(x0, posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(cons2(x0, negrecip(z0))) → c17(CONS2(x0, negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(cons2(x0, cons(z0, z1))) → c17(CONS2(x0, cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(cons2(x0, cons2(z0, z1))) → c17(CONS2(x0, cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, from(active(z0))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, square(active(z0))), ACTIVE(square(z0)))
S tuples:
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(from(z0)) → c20(FROM(active(z0)), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(pi(z0)) → c25(PI(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
ACTIVE(square(z0)) → c30(SQUARE(active(z0)), ACTIVE(z0))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
PROPER(s(z0)) → c63(S(proper(z0)), PROPER(z0))
PROPER(posrecip(z0)) → c64(POSRECIP(proper(z0)), PROPER(z0))
PROPER(negrecip(z0)) → c65(NEGRECIP(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c67(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(cons2(z0, z1)) → c68(CONS2(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(rcons(z0, z1)) → c70(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c71(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c72(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c73(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c74(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c75(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c76(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c77(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c78(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c79(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c9(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(2NDSPOS(s(z0), cons2(z1, z2)))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(2NDSNEG(s(z0), cons2(z1, z2)))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c13(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, z2)))) → c13(S(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(s(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, z2)))) → c13(S(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(s(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c13(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c13(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c13(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c13(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c13(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c13(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c13(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c13(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(cons2(z0, z1))) → c13(S(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c13(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c13(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c13(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c14(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c14(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c14(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c14(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c14(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c14(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c14(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c14(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(cons2(z0, z1))) → c14(POSRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c15(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c15(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c15(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c15(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c15(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c15(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c15(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c15(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(cons2(z0, z1))) → c15(NEGRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndspos(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndspos(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndsneg(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndsneg(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c16(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c16(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c16(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c16(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c16(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c16(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c16(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c16(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(cons2(z0, z1), x1)) → c16(CONS(cons2(z0, active(z1)), x1), ACTIVE(cons2(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, 2ndsneg(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(0, z0))) → c17(CONS2(x0, mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(cons2(x0, plus(s(z0), z1))) → c17(CONS2(x0, mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons2(x0, times(0, z0))) → c17(CONS2(x0, mark(0)), ACTIVE(times(0, z0)))
ACTIVE(cons2(x0, times(s(z0), z1))) → c17(CONS2(x0, mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(cons2(x0, s(z0))) → c17(CONS2(x0, s(active(z0))), ACTIVE(s(z0)))
ACTIVE(cons2(x0, posrecip(z0))) → c17(CONS2(x0, posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(cons2(x0, negrecip(z0))) → c17(CONS2(x0, negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(cons2(x0, cons(z0, z1))) → c17(CONS2(x0, cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(cons2(x0, cons2(z0, z1))) → c17(CONS2(x0, cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, from(active(z0))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, square(active(z0))), ACTIVE(square(z0)))
K tuples:none
Defined Rule Symbols:
active, 2ndspos, cons2, rcons, posrecip, 2ndsneg, negrecip, s, cons, from, pi, plus, times, square, proper
Defined Pair Symbols:
ACTIVE, S, POSRECIP, NEGRECIP, CONS, CONS2, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP
Compound Symbols:
c12, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c63, c64, c65, c67, c68, c70, c71, c72, c73, c74, c75, c76, c77, c78, c79, c, c7, c9, c11, c1, c13, c14, c15, c16, c17
(21) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
ACTIVE(
from(
z0)) →
c20(
FROM(
active(
z0)),
ACTIVE(
z0)) by
ACTIVE(from(from(z0))) → c20(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(from(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(from(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c20(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c20(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c20(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c20(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c20(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c20(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c20(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c20(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c20(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c20(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(cons2(z0, z1))) → c20(FROM(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c20(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c20(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c20(FROM(square(active(z0))), ACTIVE(square(z0)))
(22) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(2ndspos(0, z0)) → mark(rnil)
active(2ndspos(s(z0), cons(z1, z2))) → mark(2ndspos(s(z0), cons2(z1, z2)))
active(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(z1, z2))) → mark(2ndsneg(s(z0), cons2(z1, z2)))
active(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
active(pi(z0)) → mark(2ndspos(z0, from(0)))
active(plus(0, z0)) → mark(z0)
active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
active(times(0, z0)) → mark(0)
active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
active(square(z0)) → mark(times(z0, z0))
active(s(z0)) → s(active(z0))
active(posrecip(z0)) → posrecip(active(z0))
active(negrecip(z0)) → negrecip(active(z0))
active(cons(z0, z1)) → cons(active(z0), z1)
active(cons2(z0, z1)) → cons2(z0, active(z1))
active(rcons(z0, z1)) → rcons(active(z0), z1)
active(rcons(z0, z1)) → rcons(z0, active(z1))
active(from(z0)) → from(active(z0))
active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
active(pi(z0)) → pi(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(times(z0, z1)) → times(active(z0), z1)
active(times(z0, z1)) → times(z0, active(z1))
active(square(z0)) → square(active(z0))
2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
cons2(z0, mark(z1)) → mark(cons2(z0, z1))
cons2(ok(z0), ok(z1)) → ok(cons2(z0, z1))
rcons(mark(z0), z1) → mark(rcons(z0, z1))
rcons(z0, mark(z1)) → mark(rcons(z0, z1))
rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
posrecip(ok(z0)) → ok(posrecip(z0))
posrecip(mark(z0)) → mark(posrecip(z0))
2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
negrecip(ok(z0)) → ok(negrecip(z0))
negrecip(mark(z0)) → mark(negrecip(z0))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
cons(mark(z0), z1) → mark(cons(z0, z1))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
from(mark(z0)) → mark(from(z0))
from(ok(z0)) → ok(from(z0))
pi(mark(z0)) → mark(pi(z0))
pi(ok(z0)) → ok(pi(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
times(mark(z0), z1) → mark(times(z0, z1))
times(ok(z0), ok(z1)) → ok(times(z0, z1))
times(z0, mark(z1)) → mark(times(z0, z1))
square(mark(z0)) → mark(square(z0))
square(ok(z0)) → ok(square(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(posrecip(z0)) → posrecip(proper(z0))
proper(negrecip(z0)) → negrecip(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(cons2(z0, z1)) → cons2(proper(z0), proper(z1))
proper(rnil) → ok(rnil)
proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
proper(pi(z0)) → pi(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(times(z0, z1)) → times(proper(z0), proper(z1))
proper(square(z0)) → square(proper(z0))
Tuples:
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(pi(z0)) → c25(PI(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
ACTIVE(square(z0)) → c30(SQUARE(active(z0)), ACTIVE(z0))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
PROPER(s(z0)) → c63(S(proper(z0)), PROPER(z0))
PROPER(posrecip(z0)) → c64(POSRECIP(proper(z0)), PROPER(z0))
PROPER(negrecip(z0)) → c65(NEGRECIP(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c67(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(cons2(z0, z1)) → c68(CONS2(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(rcons(z0, z1)) → c70(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c71(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c72(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c73(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c74(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c75(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c76(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c77(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c78(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c79(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c9(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(2NDSPOS(s(z0), cons2(z1, z2)))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(2NDSNEG(s(z0), cons2(z1, z2)))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c13(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, z2)))) → c13(S(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(s(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, z2)))) → c13(S(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(s(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c13(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c13(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c13(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c13(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c13(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c13(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c13(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c13(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(cons2(z0, z1))) → c13(S(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c13(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c13(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c13(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c14(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c14(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c14(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c14(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c14(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c14(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c14(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c14(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(cons2(z0, z1))) → c14(POSRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c15(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c15(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c15(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c15(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c15(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c15(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c15(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c15(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(cons2(z0, z1))) → c15(NEGRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndspos(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndspos(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndsneg(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndsneg(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c16(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c16(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c16(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c16(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c16(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c16(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c16(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c16(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(cons2(z0, z1), x1)) → c16(CONS(cons2(z0, active(z1)), x1), ACTIVE(cons2(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, 2ndsneg(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(0, z0))) → c17(CONS2(x0, mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(cons2(x0, plus(s(z0), z1))) → c17(CONS2(x0, mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons2(x0, times(0, z0))) → c17(CONS2(x0, mark(0)), ACTIVE(times(0, z0)))
ACTIVE(cons2(x0, times(s(z0), z1))) → c17(CONS2(x0, mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(cons2(x0, s(z0))) → c17(CONS2(x0, s(active(z0))), ACTIVE(s(z0)))
ACTIVE(cons2(x0, posrecip(z0))) → c17(CONS2(x0, posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(cons2(x0, negrecip(z0))) → c17(CONS2(x0, negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(cons2(x0, cons(z0, z1))) → c17(CONS2(x0, cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(cons2(x0, cons2(z0, z1))) → c17(CONS2(x0, cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, from(active(z0))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, square(active(z0))), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c20(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(from(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(from(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c20(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c20(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c20(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c20(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c20(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c20(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c20(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c20(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c20(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c20(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(cons2(z0, z1))) → c20(FROM(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c20(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c20(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c20(FROM(square(active(z0))), ACTIVE(square(z0)))
S tuples:
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(pi(z0)) → c25(PI(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
ACTIVE(square(z0)) → c30(SQUARE(active(z0)), ACTIVE(z0))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
PROPER(s(z0)) → c63(S(proper(z0)), PROPER(z0))
PROPER(posrecip(z0)) → c64(POSRECIP(proper(z0)), PROPER(z0))
PROPER(negrecip(z0)) → c65(NEGRECIP(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c67(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(cons2(z0, z1)) → c68(CONS2(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(rcons(z0, z1)) → c70(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c71(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c72(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c73(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c74(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c75(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c76(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c77(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c78(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c79(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c9(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(2NDSPOS(s(z0), cons2(z1, z2)))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(2NDSNEG(s(z0), cons2(z1, z2)))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c13(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, z2)))) → c13(S(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(s(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, z2)))) → c13(S(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(s(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c13(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c13(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c13(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c13(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c13(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c13(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c13(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c13(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(cons2(z0, z1))) → c13(S(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c13(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c13(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c13(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c14(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c14(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c14(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c14(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c14(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c14(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c14(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c14(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(cons2(z0, z1))) → c14(POSRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c15(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c15(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c15(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c15(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c15(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c15(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c15(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c15(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(cons2(z0, z1))) → c15(NEGRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndspos(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndspos(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndsneg(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndsneg(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c16(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c16(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c16(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c16(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c16(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c16(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c16(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c16(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(cons2(z0, z1), x1)) → c16(CONS(cons2(z0, active(z1)), x1), ACTIVE(cons2(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, 2ndsneg(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(0, z0))) → c17(CONS2(x0, mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(cons2(x0, plus(s(z0), z1))) → c17(CONS2(x0, mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons2(x0, times(0, z0))) → c17(CONS2(x0, mark(0)), ACTIVE(times(0, z0)))
ACTIVE(cons2(x0, times(s(z0), z1))) → c17(CONS2(x0, mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(cons2(x0, s(z0))) → c17(CONS2(x0, s(active(z0))), ACTIVE(s(z0)))
ACTIVE(cons2(x0, posrecip(z0))) → c17(CONS2(x0, posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(cons2(x0, negrecip(z0))) → c17(CONS2(x0, negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(cons2(x0, cons(z0, z1))) → c17(CONS2(x0, cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(cons2(x0, cons2(z0, z1))) → c17(CONS2(x0, cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, from(active(z0))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, square(active(z0))), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c20(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(from(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(from(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c20(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c20(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c20(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c20(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c20(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c20(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c20(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c20(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c20(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c20(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(cons2(z0, z1))) → c20(FROM(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c20(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c20(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c20(FROM(square(active(z0))), ACTIVE(square(z0)))
K tuples:none
Defined Rule Symbols:
active, 2ndspos, cons2, rcons, posrecip, 2ndsneg, negrecip, s, cons, from, pi, plus, times, square, proper
Defined Pair Symbols:
ACTIVE, S, POSRECIP, NEGRECIP, CONS, CONS2, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP
Compound Symbols:
c12, c18, c19, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c63, c64, c65, c67, c68, c70, c71, c72, c73, c74, c75, c76, c77, c78, c79, c, c7, c9, c11, c1, c13, c14, c15, c16, c17, c20
(23) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
ACTIVE(
pi(
z0)) →
c25(
PI(
active(
z0)),
ACTIVE(
z0)) by
ACTIVE(pi(from(z0))) → c25(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c25(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c25(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c25(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c25(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c25(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c25(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c25(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c25(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c25(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c25(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(cons2(z0, z1))) → c25(PI(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c25(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c25(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c25(PI(square(active(z0))), ACTIVE(square(z0)))
(24) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(2ndspos(0, z0)) → mark(rnil)
active(2ndspos(s(z0), cons(z1, z2))) → mark(2ndspos(s(z0), cons2(z1, z2)))
active(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(z1, z2))) → mark(2ndsneg(s(z0), cons2(z1, z2)))
active(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
active(pi(z0)) → mark(2ndspos(z0, from(0)))
active(plus(0, z0)) → mark(z0)
active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
active(times(0, z0)) → mark(0)
active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
active(square(z0)) → mark(times(z0, z0))
active(s(z0)) → s(active(z0))
active(posrecip(z0)) → posrecip(active(z0))
active(negrecip(z0)) → negrecip(active(z0))
active(cons(z0, z1)) → cons(active(z0), z1)
active(cons2(z0, z1)) → cons2(z0, active(z1))
active(rcons(z0, z1)) → rcons(active(z0), z1)
active(rcons(z0, z1)) → rcons(z0, active(z1))
active(from(z0)) → from(active(z0))
active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
active(pi(z0)) → pi(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(times(z0, z1)) → times(active(z0), z1)
active(times(z0, z1)) → times(z0, active(z1))
active(square(z0)) → square(active(z0))
2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
cons2(z0, mark(z1)) → mark(cons2(z0, z1))
cons2(ok(z0), ok(z1)) → ok(cons2(z0, z1))
rcons(mark(z0), z1) → mark(rcons(z0, z1))
rcons(z0, mark(z1)) → mark(rcons(z0, z1))
rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
posrecip(ok(z0)) → ok(posrecip(z0))
posrecip(mark(z0)) → mark(posrecip(z0))
2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
negrecip(ok(z0)) → ok(negrecip(z0))
negrecip(mark(z0)) → mark(negrecip(z0))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
cons(mark(z0), z1) → mark(cons(z0, z1))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
from(mark(z0)) → mark(from(z0))
from(ok(z0)) → ok(from(z0))
pi(mark(z0)) → mark(pi(z0))
pi(ok(z0)) → ok(pi(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
times(mark(z0), z1) → mark(times(z0, z1))
times(ok(z0), ok(z1)) → ok(times(z0, z1))
times(z0, mark(z1)) → mark(times(z0, z1))
square(mark(z0)) → mark(square(z0))
square(ok(z0)) → ok(square(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(posrecip(z0)) → posrecip(proper(z0))
proper(negrecip(z0)) → negrecip(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(cons2(z0, z1)) → cons2(proper(z0), proper(z1))
proper(rnil) → ok(rnil)
proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
proper(pi(z0)) → pi(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(times(z0, z1)) → times(proper(z0), proper(z1))
proper(square(z0)) → square(proper(z0))
Tuples:
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
ACTIVE(square(z0)) → c30(SQUARE(active(z0)), ACTIVE(z0))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
PROPER(s(z0)) → c63(S(proper(z0)), PROPER(z0))
PROPER(posrecip(z0)) → c64(POSRECIP(proper(z0)), PROPER(z0))
PROPER(negrecip(z0)) → c65(NEGRECIP(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c67(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(cons2(z0, z1)) → c68(CONS2(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(rcons(z0, z1)) → c70(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c71(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c72(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c73(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c74(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c75(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c76(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c77(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c78(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c79(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c9(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(2NDSPOS(s(z0), cons2(z1, z2)))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(2NDSNEG(s(z0), cons2(z1, z2)))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c13(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, z2)))) → c13(S(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(s(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, z2)))) → c13(S(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(s(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c13(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c13(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c13(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c13(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c13(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c13(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c13(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c13(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(cons2(z0, z1))) → c13(S(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c13(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c13(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c13(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c14(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c14(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c14(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c14(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c14(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c14(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c14(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c14(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(cons2(z0, z1))) → c14(POSRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c15(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c15(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c15(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c15(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c15(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c15(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c15(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c15(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(cons2(z0, z1))) → c15(NEGRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndspos(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndspos(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndsneg(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndsneg(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c16(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c16(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c16(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c16(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c16(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c16(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c16(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c16(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(cons2(z0, z1), x1)) → c16(CONS(cons2(z0, active(z1)), x1), ACTIVE(cons2(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, 2ndsneg(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(0, z0))) → c17(CONS2(x0, mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(cons2(x0, plus(s(z0), z1))) → c17(CONS2(x0, mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons2(x0, times(0, z0))) → c17(CONS2(x0, mark(0)), ACTIVE(times(0, z0)))
ACTIVE(cons2(x0, times(s(z0), z1))) → c17(CONS2(x0, mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(cons2(x0, s(z0))) → c17(CONS2(x0, s(active(z0))), ACTIVE(s(z0)))
ACTIVE(cons2(x0, posrecip(z0))) → c17(CONS2(x0, posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(cons2(x0, negrecip(z0))) → c17(CONS2(x0, negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(cons2(x0, cons(z0, z1))) → c17(CONS2(x0, cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(cons2(x0, cons2(z0, z1))) → c17(CONS2(x0, cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, from(active(z0))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, square(active(z0))), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c20(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(from(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(from(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c20(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c20(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c20(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c20(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c20(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c20(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c20(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c20(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c20(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c20(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(cons2(z0, z1))) → c20(FROM(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c20(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c20(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c20(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c25(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c25(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c25(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c25(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c25(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c25(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c25(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c25(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c25(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c25(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c25(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(cons2(z0, z1))) → c25(PI(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c25(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c25(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c25(PI(square(active(z0))), ACTIVE(square(z0)))
S tuples:
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
ACTIVE(square(z0)) → c30(SQUARE(active(z0)), ACTIVE(z0))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
PROPER(s(z0)) → c63(S(proper(z0)), PROPER(z0))
PROPER(posrecip(z0)) → c64(POSRECIP(proper(z0)), PROPER(z0))
PROPER(negrecip(z0)) → c65(NEGRECIP(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c67(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(cons2(z0, z1)) → c68(CONS2(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(rcons(z0, z1)) → c70(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c71(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c72(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c73(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c74(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c75(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c76(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c77(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c78(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c79(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c9(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(2NDSPOS(s(z0), cons2(z1, z2)))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(2NDSNEG(s(z0), cons2(z1, z2)))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c13(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, z2)))) → c13(S(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(s(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, z2)))) → c13(S(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(s(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c13(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c13(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c13(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c13(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c13(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c13(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c13(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c13(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(cons2(z0, z1))) → c13(S(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c13(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c13(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c13(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c14(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c14(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c14(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c14(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c14(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c14(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c14(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c14(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(cons2(z0, z1))) → c14(POSRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c15(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c15(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c15(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c15(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c15(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c15(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c15(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c15(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(cons2(z0, z1))) → c15(NEGRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndspos(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndspos(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndsneg(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndsneg(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c16(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c16(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c16(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c16(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c16(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c16(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c16(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c16(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(cons2(z0, z1), x1)) → c16(CONS(cons2(z0, active(z1)), x1), ACTIVE(cons2(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, 2ndsneg(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(0, z0))) → c17(CONS2(x0, mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(cons2(x0, plus(s(z0), z1))) → c17(CONS2(x0, mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons2(x0, times(0, z0))) → c17(CONS2(x0, mark(0)), ACTIVE(times(0, z0)))
ACTIVE(cons2(x0, times(s(z0), z1))) → c17(CONS2(x0, mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(cons2(x0, s(z0))) → c17(CONS2(x0, s(active(z0))), ACTIVE(s(z0)))
ACTIVE(cons2(x0, posrecip(z0))) → c17(CONS2(x0, posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(cons2(x0, negrecip(z0))) → c17(CONS2(x0, negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(cons2(x0, cons(z0, z1))) → c17(CONS2(x0, cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(cons2(x0, cons2(z0, z1))) → c17(CONS2(x0, cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, from(active(z0))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, square(active(z0))), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c20(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(from(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(from(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c20(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c20(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c20(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c20(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c20(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c20(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c20(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c20(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c20(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c20(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(cons2(z0, z1))) → c20(FROM(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c20(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c20(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c20(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c25(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c25(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c25(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c25(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c25(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c25(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c25(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c25(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c25(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c25(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c25(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(cons2(z0, z1))) → c25(PI(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c25(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c25(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c25(PI(square(active(z0))), ACTIVE(square(z0)))
K tuples:none
Defined Rule Symbols:
active, 2ndspos, cons2, rcons, posrecip, 2ndsneg, negrecip, s, cons, from, pi, plus, times, square, proper
Defined Pair Symbols:
ACTIVE, S, POSRECIP, NEGRECIP, CONS, CONS2, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP
Compound Symbols:
c12, c18, c19, c21, c22, c23, c24, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c63, c64, c65, c67, c68, c70, c71, c72, c73, c74, c75, c76, c77, c78, c79, c, c7, c9, c11, c1, c13, c14, c15, c16, c17, c20, c25
(25) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
ACTIVE(
square(
z0)) →
c30(
SQUARE(
active(
z0)),
ACTIVE(
z0)) by
ACTIVE(square(from(z0))) → c30(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(square(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(square(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c30(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c30(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c30(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c30(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c30(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c30(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c30(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c30(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c30(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(cons2(z0, z1))) → c30(SQUARE(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c30(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c30(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(square(active(z0))), ACTIVE(square(z0)))
(26) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(2ndspos(0, z0)) → mark(rnil)
active(2ndspos(s(z0), cons(z1, z2))) → mark(2ndspos(s(z0), cons2(z1, z2)))
active(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(z1, z2))) → mark(2ndsneg(s(z0), cons2(z1, z2)))
active(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
active(pi(z0)) → mark(2ndspos(z0, from(0)))
active(plus(0, z0)) → mark(z0)
active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
active(times(0, z0)) → mark(0)
active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
active(square(z0)) → mark(times(z0, z0))
active(s(z0)) → s(active(z0))
active(posrecip(z0)) → posrecip(active(z0))
active(negrecip(z0)) → negrecip(active(z0))
active(cons(z0, z1)) → cons(active(z0), z1)
active(cons2(z0, z1)) → cons2(z0, active(z1))
active(rcons(z0, z1)) → rcons(active(z0), z1)
active(rcons(z0, z1)) → rcons(z0, active(z1))
active(from(z0)) → from(active(z0))
active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
active(pi(z0)) → pi(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(times(z0, z1)) → times(active(z0), z1)
active(times(z0, z1)) → times(z0, active(z1))
active(square(z0)) → square(active(z0))
2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
cons2(z0, mark(z1)) → mark(cons2(z0, z1))
cons2(ok(z0), ok(z1)) → ok(cons2(z0, z1))
rcons(mark(z0), z1) → mark(rcons(z0, z1))
rcons(z0, mark(z1)) → mark(rcons(z0, z1))
rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
posrecip(ok(z0)) → ok(posrecip(z0))
posrecip(mark(z0)) → mark(posrecip(z0))
2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
negrecip(ok(z0)) → ok(negrecip(z0))
negrecip(mark(z0)) → mark(negrecip(z0))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
cons(mark(z0), z1) → mark(cons(z0, z1))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
from(mark(z0)) → mark(from(z0))
from(ok(z0)) → ok(from(z0))
pi(mark(z0)) → mark(pi(z0))
pi(ok(z0)) → ok(pi(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
times(mark(z0), z1) → mark(times(z0, z1))
times(ok(z0), ok(z1)) → ok(times(z0, z1))
times(z0, mark(z1)) → mark(times(z0, z1))
square(mark(z0)) → mark(square(z0))
square(ok(z0)) → ok(square(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(posrecip(z0)) → posrecip(proper(z0))
proper(negrecip(z0)) → negrecip(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(cons2(z0, z1)) → cons2(proper(z0), proper(z1))
proper(rnil) → ok(rnil)
proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
proper(pi(z0)) → pi(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(times(z0, z1)) → times(proper(z0), proper(z1))
proper(square(z0)) → square(proper(z0))
Tuples:
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
PROPER(s(z0)) → c63(S(proper(z0)), PROPER(z0))
PROPER(posrecip(z0)) → c64(POSRECIP(proper(z0)), PROPER(z0))
PROPER(negrecip(z0)) → c65(NEGRECIP(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c67(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(cons2(z0, z1)) → c68(CONS2(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(rcons(z0, z1)) → c70(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c71(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c72(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c73(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c74(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c75(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c76(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c77(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c78(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c79(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c9(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(2NDSPOS(s(z0), cons2(z1, z2)))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(2NDSNEG(s(z0), cons2(z1, z2)))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c13(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, z2)))) → c13(S(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(s(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, z2)))) → c13(S(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(s(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c13(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c13(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c13(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c13(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c13(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c13(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c13(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c13(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(cons2(z0, z1))) → c13(S(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c13(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c13(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c13(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c14(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c14(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c14(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c14(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c14(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c14(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c14(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c14(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(cons2(z0, z1))) → c14(POSRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c15(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c15(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c15(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c15(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c15(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c15(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c15(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c15(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(cons2(z0, z1))) → c15(NEGRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndspos(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndspos(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndsneg(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndsneg(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c16(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c16(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c16(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c16(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c16(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c16(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c16(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c16(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(cons2(z0, z1), x1)) → c16(CONS(cons2(z0, active(z1)), x1), ACTIVE(cons2(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, 2ndsneg(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(0, z0))) → c17(CONS2(x0, mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(cons2(x0, plus(s(z0), z1))) → c17(CONS2(x0, mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons2(x0, times(0, z0))) → c17(CONS2(x0, mark(0)), ACTIVE(times(0, z0)))
ACTIVE(cons2(x0, times(s(z0), z1))) → c17(CONS2(x0, mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(cons2(x0, s(z0))) → c17(CONS2(x0, s(active(z0))), ACTIVE(s(z0)))
ACTIVE(cons2(x0, posrecip(z0))) → c17(CONS2(x0, posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(cons2(x0, negrecip(z0))) → c17(CONS2(x0, negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(cons2(x0, cons(z0, z1))) → c17(CONS2(x0, cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(cons2(x0, cons2(z0, z1))) → c17(CONS2(x0, cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, from(active(z0))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, square(active(z0))), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c20(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(from(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(from(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c20(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c20(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c20(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c20(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c20(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c20(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c20(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c20(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c20(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c20(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(cons2(z0, z1))) → c20(FROM(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c20(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c20(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c20(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c25(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c25(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c25(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c25(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c25(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c25(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c25(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c25(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c25(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c25(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c25(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(cons2(z0, z1))) → c25(PI(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c25(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c25(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c25(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c30(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(square(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(square(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c30(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c30(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c30(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c30(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c30(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c30(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c30(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c30(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c30(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(cons2(z0, z1))) → c30(SQUARE(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c30(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c30(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(square(active(z0))), ACTIVE(square(z0)))
S tuples:
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
PROPER(s(z0)) → c63(S(proper(z0)), PROPER(z0))
PROPER(posrecip(z0)) → c64(POSRECIP(proper(z0)), PROPER(z0))
PROPER(negrecip(z0)) → c65(NEGRECIP(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c67(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(cons2(z0, z1)) → c68(CONS2(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(rcons(z0, z1)) → c70(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c71(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c72(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c73(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c74(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c75(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c76(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c77(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c78(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c79(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c9(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(2NDSPOS(s(z0), cons2(z1, z2)))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(2NDSNEG(s(z0), cons2(z1, z2)))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c13(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, z2)))) → c13(S(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(s(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, z2)))) → c13(S(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(s(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c13(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c13(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c13(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c13(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c13(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c13(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c13(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c13(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(cons2(z0, z1))) → c13(S(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c13(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c13(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c13(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c14(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c14(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c14(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c14(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c14(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c14(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c14(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c14(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(cons2(z0, z1))) → c14(POSRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c15(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c15(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c15(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c15(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c15(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c15(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c15(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c15(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(cons2(z0, z1))) → c15(NEGRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndspos(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndspos(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndsneg(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndsneg(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c16(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c16(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c16(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c16(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c16(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c16(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c16(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c16(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(cons2(z0, z1), x1)) → c16(CONS(cons2(z0, active(z1)), x1), ACTIVE(cons2(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, 2ndsneg(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(0, z0))) → c17(CONS2(x0, mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(cons2(x0, plus(s(z0), z1))) → c17(CONS2(x0, mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons2(x0, times(0, z0))) → c17(CONS2(x0, mark(0)), ACTIVE(times(0, z0)))
ACTIVE(cons2(x0, times(s(z0), z1))) → c17(CONS2(x0, mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(cons2(x0, s(z0))) → c17(CONS2(x0, s(active(z0))), ACTIVE(s(z0)))
ACTIVE(cons2(x0, posrecip(z0))) → c17(CONS2(x0, posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(cons2(x0, negrecip(z0))) → c17(CONS2(x0, negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(cons2(x0, cons(z0, z1))) → c17(CONS2(x0, cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(cons2(x0, cons2(z0, z1))) → c17(CONS2(x0, cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, from(active(z0))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, square(active(z0))), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c20(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(from(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(from(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c20(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c20(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c20(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c20(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c20(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c20(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c20(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c20(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c20(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c20(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(cons2(z0, z1))) → c20(FROM(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c20(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c20(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c20(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c25(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c25(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c25(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c25(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c25(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c25(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c25(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c25(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c25(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c25(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c25(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(cons2(z0, z1))) → c25(PI(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c25(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c25(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c25(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c30(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(square(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(square(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c30(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c30(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c30(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c30(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c30(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c30(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c30(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c30(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c30(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(cons2(z0, z1))) → c30(SQUARE(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c30(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c30(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(square(active(z0))), ACTIVE(square(z0)))
K tuples:none
Defined Rule Symbols:
active, 2ndspos, cons2, rcons, posrecip, 2ndsneg, negrecip, s, cons, from, pi, plus, times, square, proper
Defined Pair Symbols:
ACTIVE, S, POSRECIP, NEGRECIP, CONS, CONS2, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP
Compound Symbols:
c12, c18, c19, c21, c22, c23, c24, c26, c27, c28, c29, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c63, c64, c65, c67, c68, c70, c71, c72, c73, c74, c75, c76, c77, c78, c79, c, c7, c9, c11, c1, c13, c14, c15, c16, c17, c20, c25, c30
(27) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
PROPER(
s(
z0)) →
c63(
S(
proper(
z0)),
PROPER(
z0)) by
PROPER(s(0)) → c63(S(ok(0)), PROPER(0))
PROPER(s(s(z0))) → c63(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c63(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c63(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(nil)) → c63(S(ok(nil)), PROPER(nil))
PROPER(s(cons(z0, z1))) → c63(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(cons2(z0, z1))) → c63(S(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(s(rnil)) → c63(S(ok(rnil)), PROPER(rnil))
PROPER(s(rcons(z0, z1))) → c63(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c63(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c63(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c63(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c63(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c63(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c63(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c63(S(square(proper(z0))), PROPER(square(z0)))
(28) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(2ndspos(0, z0)) → mark(rnil)
active(2ndspos(s(z0), cons(z1, z2))) → mark(2ndspos(s(z0), cons2(z1, z2)))
active(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(z1, z2))) → mark(2ndsneg(s(z0), cons2(z1, z2)))
active(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
active(pi(z0)) → mark(2ndspos(z0, from(0)))
active(plus(0, z0)) → mark(z0)
active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
active(times(0, z0)) → mark(0)
active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
active(square(z0)) → mark(times(z0, z0))
active(s(z0)) → s(active(z0))
active(posrecip(z0)) → posrecip(active(z0))
active(negrecip(z0)) → negrecip(active(z0))
active(cons(z0, z1)) → cons(active(z0), z1)
active(cons2(z0, z1)) → cons2(z0, active(z1))
active(rcons(z0, z1)) → rcons(active(z0), z1)
active(rcons(z0, z1)) → rcons(z0, active(z1))
active(from(z0)) → from(active(z0))
active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
active(pi(z0)) → pi(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(times(z0, z1)) → times(active(z0), z1)
active(times(z0, z1)) → times(z0, active(z1))
active(square(z0)) → square(active(z0))
2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
cons2(z0, mark(z1)) → mark(cons2(z0, z1))
cons2(ok(z0), ok(z1)) → ok(cons2(z0, z1))
rcons(mark(z0), z1) → mark(rcons(z0, z1))
rcons(z0, mark(z1)) → mark(rcons(z0, z1))
rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
posrecip(ok(z0)) → ok(posrecip(z0))
posrecip(mark(z0)) → mark(posrecip(z0))
2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
negrecip(ok(z0)) → ok(negrecip(z0))
negrecip(mark(z0)) → mark(negrecip(z0))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
cons(mark(z0), z1) → mark(cons(z0, z1))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
from(mark(z0)) → mark(from(z0))
from(ok(z0)) → ok(from(z0))
pi(mark(z0)) → mark(pi(z0))
pi(ok(z0)) → ok(pi(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
times(mark(z0), z1) → mark(times(z0, z1))
times(ok(z0), ok(z1)) → ok(times(z0, z1))
times(z0, mark(z1)) → mark(times(z0, z1))
square(mark(z0)) → mark(square(z0))
square(ok(z0)) → ok(square(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(posrecip(z0)) → posrecip(proper(z0))
proper(negrecip(z0)) → negrecip(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(cons2(z0, z1)) → cons2(proper(z0), proper(z1))
proper(rnil) → ok(rnil)
proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
proper(pi(z0)) → pi(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(times(z0, z1)) → times(proper(z0), proper(z1))
proper(square(z0)) → square(proper(z0))
Tuples:
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
PROPER(posrecip(z0)) → c64(POSRECIP(proper(z0)), PROPER(z0))
PROPER(negrecip(z0)) → c65(NEGRECIP(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c67(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(cons2(z0, z1)) → c68(CONS2(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(rcons(z0, z1)) → c70(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c71(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c72(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c73(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c74(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c75(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c76(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c77(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c78(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c79(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c9(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(2NDSPOS(s(z0), cons2(z1, z2)))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(2NDSNEG(s(z0), cons2(z1, z2)))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c13(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, z2)))) → c13(S(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(s(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, z2)))) → c13(S(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(s(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c13(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c13(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c13(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c13(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c13(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c13(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c13(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c13(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(cons2(z0, z1))) → c13(S(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c13(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c13(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c13(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c14(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c14(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c14(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c14(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c14(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c14(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c14(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c14(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(cons2(z0, z1))) → c14(POSRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c15(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c15(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c15(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c15(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c15(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c15(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c15(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c15(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(cons2(z0, z1))) → c15(NEGRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndspos(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndspos(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndsneg(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndsneg(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c16(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c16(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c16(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c16(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c16(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c16(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c16(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c16(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(cons2(z0, z1), x1)) → c16(CONS(cons2(z0, active(z1)), x1), ACTIVE(cons2(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, 2ndsneg(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(0, z0))) → c17(CONS2(x0, mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(cons2(x0, plus(s(z0), z1))) → c17(CONS2(x0, mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons2(x0, times(0, z0))) → c17(CONS2(x0, mark(0)), ACTIVE(times(0, z0)))
ACTIVE(cons2(x0, times(s(z0), z1))) → c17(CONS2(x0, mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(cons2(x0, s(z0))) → c17(CONS2(x0, s(active(z0))), ACTIVE(s(z0)))
ACTIVE(cons2(x0, posrecip(z0))) → c17(CONS2(x0, posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(cons2(x0, negrecip(z0))) → c17(CONS2(x0, negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(cons2(x0, cons(z0, z1))) → c17(CONS2(x0, cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(cons2(x0, cons2(z0, z1))) → c17(CONS2(x0, cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, from(active(z0))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, square(active(z0))), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c20(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(from(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(from(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c20(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c20(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c20(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c20(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c20(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c20(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c20(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c20(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c20(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c20(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(cons2(z0, z1))) → c20(FROM(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c20(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c20(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c20(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c25(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c25(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c25(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c25(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c25(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c25(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c25(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c25(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c25(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c25(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c25(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(cons2(z0, z1))) → c25(PI(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c25(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c25(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c25(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c30(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(square(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(square(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c30(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c30(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c30(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c30(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c30(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c30(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c30(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c30(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c30(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(cons2(z0, z1))) → c30(SQUARE(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c30(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c30(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(0)) → c63(S(ok(0)), PROPER(0))
PROPER(s(s(z0))) → c63(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c63(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c63(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(nil)) → c63(S(ok(nil)), PROPER(nil))
PROPER(s(cons(z0, z1))) → c63(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(cons2(z0, z1))) → c63(S(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(s(rnil)) → c63(S(ok(rnil)), PROPER(rnil))
PROPER(s(rcons(z0, z1))) → c63(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c63(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c63(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c63(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c63(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c63(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c63(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c63(S(square(proper(z0))), PROPER(square(z0)))
S tuples:
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
PROPER(posrecip(z0)) → c64(POSRECIP(proper(z0)), PROPER(z0))
PROPER(negrecip(z0)) → c65(NEGRECIP(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c67(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(cons2(z0, z1)) → c68(CONS2(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(rcons(z0, z1)) → c70(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c71(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c72(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c73(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c74(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c75(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c76(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c77(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c78(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c79(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c9(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(2NDSPOS(s(z0), cons2(z1, z2)))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(2NDSNEG(s(z0), cons2(z1, z2)))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c13(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, z2)))) → c13(S(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(s(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, z2)))) → c13(S(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(s(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c13(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c13(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c13(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c13(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c13(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c13(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c13(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c13(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(cons2(z0, z1))) → c13(S(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c13(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c13(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c13(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c14(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c14(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c14(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c14(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c14(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c14(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c14(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c14(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(cons2(z0, z1))) → c14(POSRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c15(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c15(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c15(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c15(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c15(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c15(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c15(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c15(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(cons2(z0, z1))) → c15(NEGRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndspos(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndspos(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndsneg(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndsneg(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c16(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c16(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c16(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c16(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c16(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c16(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c16(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c16(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(cons2(z0, z1), x1)) → c16(CONS(cons2(z0, active(z1)), x1), ACTIVE(cons2(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, 2ndsneg(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(0, z0))) → c17(CONS2(x0, mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(cons2(x0, plus(s(z0), z1))) → c17(CONS2(x0, mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons2(x0, times(0, z0))) → c17(CONS2(x0, mark(0)), ACTIVE(times(0, z0)))
ACTIVE(cons2(x0, times(s(z0), z1))) → c17(CONS2(x0, mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(cons2(x0, s(z0))) → c17(CONS2(x0, s(active(z0))), ACTIVE(s(z0)))
ACTIVE(cons2(x0, posrecip(z0))) → c17(CONS2(x0, posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(cons2(x0, negrecip(z0))) → c17(CONS2(x0, negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(cons2(x0, cons(z0, z1))) → c17(CONS2(x0, cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(cons2(x0, cons2(z0, z1))) → c17(CONS2(x0, cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, from(active(z0))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, square(active(z0))), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c20(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(from(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(from(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c20(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c20(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c20(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c20(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c20(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c20(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c20(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c20(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c20(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c20(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(cons2(z0, z1))) → c20(FROM(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c20(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c20(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c20(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c25(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c25(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c25(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c25(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c25(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c25(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c25(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c25(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c25(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c25(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c25(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(cons2(z0, z1))) → c25(PI(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c25(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c25(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c25(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c30(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(square(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(square(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c30(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c30(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c30(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c30(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c30(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c30(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c30(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c30(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c30(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(cons2(z0, z1))) → c30(SQUARE(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c30(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c30(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(0)) → c63(S(ok(0)), PROPER(0))
PROPER(s(s(z0))) → c63(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c63(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c63(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(nil)) → c63(S(ok(nil)), PROPER(nil))
PROPER(s(cons(z0, z1))) → c63(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(cons2(z0, z1))) → c63(S(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(s(rnil)) → c63(S(ok(rnil)), PROPER(rnil))
PROPER(s(rcons(z0, z1))) → c63(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c63(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c63(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c63(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c63(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c63(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c63(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c63(S(square(proper(z0))), PROPER(square(z0)))
K tuples:none
Defined Rule Symbols:
active, 2ndspos, cons2, rcons, posrecip, 2ndsneg, negrecip, s, cons, from, pi, plus, times, square, proper
Defined Pair Symbols:
ACTIVE, S, POSRECIP, NEGRECIP, CONS, CONS2, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP
Compound Symbols:
c12, c18, c19, c21, c22, c23, c24, c26, c27, c28, c29, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c64, c65, c67, c68, c70, c71, c72, c73, c74, c75, c76, c77, c78, c79, c, c7, c9, c11, c1, c13, c14, c15, c16, c17, c20, c25, c30, c63
(29) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 3 trailing tuple parts
(30) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(2ndspos(0, z0)) → mark(rnil)
active(2ndspos(s(z0), cons(z1, z2))) → mark(2ndspos(s(z0), cons2(z1, z2)))
active(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(z1, z2))) → mark(2ndsneg(s(z0), cons2(z1, z2)))
active(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
active(pi(z0)) → mark(2ndspos(z0, from(0)))
active(plus(0, z0)) → mark(z0)
active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
active(times(0, z0)) → mark(0)
active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
active(square(z0)) → mark(times(z0, z0))
active(s(z0)) → s(active(z0))
active(posrecip(z0)) → posrecip(active(z0))
active(negrecip(z0)) → negrecip(active(z0))
active(cons(z0, z1)) → cons(active(z0), z1)
active(cons2(z0, z1)) → cons2(z0, active(z1))
active(rcons(z0, z1)) → rcons(active(z0), z1)
active(rcons(z0, z1)) → rcons(z0, active(z1))
active(from(z0)) → from(active(z0))
active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
active(pi(z0)) → pi(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(times(z0, z1)) → times(active(z0), z1)
active(times(z0, z1)) → times(z0, active(z1))
active(square(z0)) → square(active(z0))
2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
cons2(z0, mark(z1)) → mark(cons2(z0, z1))
cons2(ok(z0), ok(z1)) → ok(cons2(z0, z1))
rcons(mark(z0), z1) → mark(rcons(z0, z1))
rcons(z0, mark(z1)) → mark(rcons(z0, z1))
rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
posrecip(ok(z0)) → ok(posrecip(z0))
posrecip(mark(z0)) → mark(posrecip(z0))
2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
negrecip(ok(z0)) → ok(negrecip(z0))
negrecip(mark(z0)) → mark(negrecip(z0))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
cons(mark(z0), z1) → mark(cons(z0, z1))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
from(mark(z0)) → mark(from(z0))
from(ok(z0)) → ok(from(z0))
pi(mark(z0)) → mark(pi(z0))
pi(ok(z0)) → ok(pi(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
times(mark(z0), z1) → mark(times(z0, z1))
times(ok(z0), ok(z1)) → ok(times(z0, z1))
times(z0, mark(z1)) → mark(times(z0, z1))
square(mark(z0)) → mark(square(z0))
square(ok(z0)) → ok(square(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(posrecip(z0)) → posrecip(proper(z0))
proper(negrecip(z0)) → negrecip(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(cons2(z0, z1)) → cons2(proper(z0), proper(z1))
proper(rnil) → ok(rnil)
proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
proper(pi(z0)) → pi(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(times(z0, z1)) → times(proper(z0), proper(z1))
proper(square(z0)) → square(proper(z0))
Tuples:
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
PROPER(posrecip(z0)) → c64(POSRECIP(proper(z0)), PROPER(z0))
PROPER(negrecip(z0)) → c65(NEGRECIP(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c67(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(cons2(z0, z1)) → c68(CONS2(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(rcons(z0, z1)) → c70(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c71(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c72(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c73(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c74(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c75(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c76(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c77(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c78(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c79(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c9(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(2NDSPOS(s(z0), cons2(z1, z2)))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(2NDSNEG(s(z0), cons2(z1, z2)))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c13(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, z2)))) → c13(S(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(s(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, z2)))) → c13(S(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(s(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c13(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c13(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c13(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c13(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c13(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c13(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c13(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c13(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(cons2(z0, z1))) → c13(S(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c13(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c13(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c13(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c14(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c14(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c14(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c14(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c14(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c14(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c14(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c14(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(cons2(z0, z1))) → c14(POSRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c15(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c15(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c15(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c15(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c15(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c15(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c15(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c15(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(cons2(z0, z1))) → c15(NEGRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndspos(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndspos(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndsneg(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndsneg(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c16(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c16(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c16(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c16(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c16(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c16(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c16(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c16(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(cons2(z0, z1), x1)) → c16(CONS(cons2(z0, active(z1)), x1), ACTIVE(cons2(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, 2ndsneg(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(0, z0))) → c17(CONS2(x0, mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(cons2(x0, plus(s(z0), z1))) → c17(CONS2(x0, mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons2(x0, times(0, z0))) → c17(CONS2(x0, mark(0)), ACTIVE(times(0, z0)))
ACTIVE(cons2(x0, times(s(z0), z1))) → c17(CONS2(x0, mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(cons2(x0, s(z0))) → c17(CONS2(x0, s(active(z0))), ACTIVE(s(z0)))
ACTIVE(cons2(x0, posrecip(z0))) → c17(CONS2(x0, posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(cons2(x0, negrecip(z0))) → c17(CONS2(x0, negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(cons2(x0, cons(z0, z1))) → c17(CONS2(x0, cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(cons2(x0, cons2(z0, z1))) → c17(CONS2(x0, cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, from(active(z0))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, square(active(z0))), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c20(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(from(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(from(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c20(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c20(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c20(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c20(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c20(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c20(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c20(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c20(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c20(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c20(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(cons2(z0, z1))) → c20(FROM(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c20(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c20(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c20(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c25(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c25(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c25(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c25(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c25(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c25(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c25(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c25(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c25(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c25(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c25(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(cons2(z0, z1))) → c25(PI(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c25(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c25(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c25(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c30(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(square(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(square(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c30(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c30(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c30(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c30(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c30(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c30(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c30(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c30(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c30(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(cons2(z0, z1))) → c30(SQUARE(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c30(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c30(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c63(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c63(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c63(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c63(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(cons2(z0, z1))) → c63(S(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(s(rcons(z0, z1))) → c63(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c63(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c63(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c63(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c63(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c63(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c63(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c63(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c63(S(ok(0)))
PROPER(s(nil)) → c63(S(ok(nil)))
PROPER(s(rnil)) → c63(S(ok(rnil)))
S tuples:
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
PROPER(posrecip(z0)) → c64(POSRECIP(proper(z0)), PROPER(z0))
PROPER(negrecip(z0)) → c65(NEGRECIP(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c67(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(cons2(z0, z1)) → c68(CONS2(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(rcons(z0, z1)) → c70(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c71(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c72(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c73(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c74(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c75(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c76(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c77(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c78(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c79(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c9(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(2NDSPOS(s(z0), cons2(z1, z2)))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(2NDSNEG(s(z0), cons2(z1, z2)))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c13(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, z2)))) → c13(S(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(s(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, z2)))) → c13(S(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(s(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c13(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c13(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c13(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c13(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c13(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c13(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c13(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c13(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(cons2(z0, z1))) → c13(S(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c13(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c13(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c13(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c14(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c14(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c14(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c14(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c14(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c14(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c14(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c14(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(cons2(z0, z1))) → c14(POSRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c15(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c15(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c15(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c15(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c15(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c15(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c15(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c15(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(cons2(z0, z1))) → c15(NEGRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndspos(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndspos(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndsneg(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndsneg(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c16(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c16(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c16(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c16(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c16(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c16(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c16(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c16(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(cons2(z0, z1), x1)) → c16(CONS(cons2(z0, active(z1)), x1), ACTIVE(cons2(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, 2ndsneg(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(0, z0))) → c17(CONS2(x0, mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(cons2(x0, plus(s(z0), z1))) → c17(CONS2(x0, mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons2(x0, times(0, z0))) → c17(CONS2(x0, mark(0)), ACTIVE(times(0, z0)))
ACTIVE(cons2(x0, times(s(z0), z1))) → c17(CONS2(x0, mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(cons2(x0, s(z0))) → c17(CONS2(x0, s(active(z0))), ACTIVE(s(z0)))
ACTIVE(cons2(x0, posrecip(z0))) → c17(CONS2(x0, posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(cons2(x0, negrecip(z0))) → c17(CONS2(x0, negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(cons2(x0, cons(z0, z1))) → c17(CONS2(x0, cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(cons2(x0, cons2(z0, z1))) → c17(CONS2(x0, cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, from(active(z0))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, square(active(z0))), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c20(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(from(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(from(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c20(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c20(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c20(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c20(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c20(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c20(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c20(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c20(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c20(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c20(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(cons2(z0, z1))) → c20(FROM(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c20(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c20(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c20(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c25(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c25(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c25(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c25(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c25(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c25(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c25(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c25(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c25(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c25(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c25(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(cons2(z0, z1))) → c25(PI(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c25(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c25(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c25(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c30(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(square(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(square(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c30(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c30(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c30(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c30(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c30(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c30(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c30(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c30(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c30(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(cons2(z0, z1))) → c30(SQUARE(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c30(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c30(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c63(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c63(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c63(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c63(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(cons2(z0, z1))) → c63(S(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(s(rcons(z0, z1))) → c63(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c63(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c63(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c63(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c63(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c63(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c63(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c63(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c63(S(ok(0)))
PROPER(s(nil)) → c63(S(ok(nil)))
PROPER(s(rnil)) → c63(S(ok(rnil)))
K tuples:none
Defined Rule Symbols:
active, 2ndspos, cons2, rcons, posrecip, 2ndsneg, negrecip, s, cons, from, pi, plus, times, square, proper
Defined Pair Symbols:
ACTIVE, S, POSRECIP, NEGRECIP, CONS, CONS2, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP
Compound Symbols:
c12, c18, c19, c21, c22, c23, c24, c26, c27, c28, c29, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c64, c65, c67, c68, c70, c71, c72, c73, c74, c75, c76, c77, c78, c79, c, c7, c9, c11, c1, c13, c14, c15, c16, c17, c20, c25, c30, c63, c63
(31) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
PROPER(
posrecip(
z0)) →
c64(
POSRECIP(
proper(
z0)),
PROPER(
z0)) by
PROPER(posrecip(0)) → c64(POSRECIP(ok(0)), PROPER(0))
PROPER(posrecip(s(z0))) → c64(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c64(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c64(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(nil)) → c64(POSRECIP(ok(nil)), PROPER(nil))
PROPER(posrecip(cons(z0, z1))) → c64(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(cons2(z0, z1))) → c64(POSRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(posrecip(rnil)) → c64(POSRECIP(ok(rnil)), PROPER(rnil))
PROPER(posrecip(rcons(z0, z1))) → c64(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c64(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c64(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c64(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c64(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c64(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c64(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c64(POSRECIP(square(proper(z0))), PROPER(square(z0)))
(32) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(2ndspos(0, z0)) → mark(rnil)
active(2ndspos(s(z0), cons(z1, z2))) → mark(2ndspos(s(z0), cons2(z1, z2)))
active(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(z1, z2))) → mark(2ndsneg(s(z0), cons2(z1, z2)))
active(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
active(pi(z0)) → mark(2ndspos(z0, from(0)))
active(plus(0, z0)) → mark(z0)
active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
active(times(0, z0)) → mark(0)
active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
active(square(z0)) → mark(times(z0, z0))
active(s(z0)) → s(active(z0))
active(posrecip(z0)) → posrecip(active(z0))
active(negrecip(z0)) → negrecip(active(z0))
active(cons(z0, z1)) → cons(active(z0), z1)
active(cons2(z0, z1)) → cons2(z0, active(z1))
active(rcons(z0, z1)) → rcons(active(z0), z1)
active(rcons(z0, z1)) → rcons(z0, active(z1))
active(from(z0)) → from(active(z0))
active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
active(pi(z0)) → pi(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(times(z0, z1)) → times(active(z0), z1)
active(times(z0, z1)) → times(z0, active(z1))
active(square(z0)) → square(active(z0))
2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
cons2(z0, mark(z1)) → mark(cons2(z0, z1))
cons2(ok(z0), ok(z1)) → ok(cons2(z0, z1))
rcons(mark(z0), z1) → mark(rcons(z0, z1))
rcons(z0, mark(z1)) → mark(rcons(z0, z1))
rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
posrecip(ok(z0)) → ok(posrecip(z0))
posrecip(mark(z0)) → mark(posrecip(z0))
2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
negrecip(ok(z0)) → ok(negrecip(z0))
negrecip(mark(z0)) → mark(negrecip(z0))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
cons(mark(z0), z1) → mark(cons(z0, z1))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
from(mark(z0)) → mark(from(z0))
from(ok(z0)) → ok(from(z0))
pi(mark(z0)) → mark(pi(z0))
pi(ok(z0)) → ok(pi(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
times(mark(z0), z1) → mark(times(z0, z1))
times(ok(z0), ok(z1)) → ok(times(z0, z1))
times(z0, mark(z1)) → mark(times(z0, z1))
square(mark(z0)) → mark(square(z0))
square(ok(z0)) → ok(square(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(posrecip(z0)) → posrecip(proper(z0))
proper(negrecip(z0)) → negrecip(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(cons2(z0, z1)) → cons2(proper(z0), proper(z1))
proper(rnil) → ok(rnil)
proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
proper(pi(z0)) → pi(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(times(z0, z1)) → times(proper(z0), proper(z1))
proper(square(z0)) → square(proper(z0))
Tuples:
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
PROPER(negrecip(z0)) → c65(NEGRECIP(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c67(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(cons2(z0, z1)) → c68(CONS2(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(rcons(z0, z1)) → c70(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c71(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c72(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c73(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c74(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c75(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c76(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c77(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c78(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c79(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c9(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(2NDSPOS(s(z0), cons2(z1, z2)))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(2NDSNEG(s(z0), cons2(z1, z2)))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c13(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, z2)))) → c13(S(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(s(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, z2)))) → c13(S(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(s(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c13(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c13(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c13(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c13(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c13(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c13(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c13(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c13(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(cons2(z0, z1))) → c13(S(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c13(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c13(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c13(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c14(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c14(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c14(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c14(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c14(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c14(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c14(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c14(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(cons2(z0, z1))) → c14(POSRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c15(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c15(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c15(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c15(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c15(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c15(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c15(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c15(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(cons2(z0, z1))) → c15(NEGRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndspos(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndspos(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndsneg(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndsneg(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c16(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c16(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c16(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c16(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c16(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c16(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c16(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c16(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(cons2(z0, z1), x1)) → c16(CONS(cons2(z0, active(z1)), x1), ACTIVE(cons2(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, 2ndsneg(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(0, z0))) → c17(CONS2(x0, mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(cons2(x0, plus(s(z0), z1))) → c17(CONS2(x0, mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons2(x0, times(0, z0))) → c17(CONS2(x0, mark(0)), ACTIVE(times(0, z0)))
ACTIVE(cons2(x0, times(s(z0), z1))) → c17(CONS2(x0, mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(cons2(x0, s(z0))) → c17(CONS2(x0, s(active(z0))), ACTIVE(s(z0)))
ACTIVE(cons2(x0, posrecip(z0))) → c17(CONS2(x0, posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(cons2(x0, negrecip(z0))) → c17(CONS2(x0, negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(cons2(x0, cons(z0, z1))) → c17(CONS2(x0, cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(cons2(x0, cons2(z0, z1))) → c17(CONS2(x0, cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, from(active(z0))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, square(active(z0))), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c20(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(from(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(from(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c20(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c20(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c20(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c20(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c20(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c20(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c20(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c20(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c20(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c20(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(cons2(z0, z1))) → c20(FROM(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c20(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c20(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c20(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c25(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c25(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c25(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c25(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c25(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c25(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c25(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c25(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c25(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c25(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c25(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(cons2(z0, z1))) → c25(PI(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c25(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c25(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c25(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c30(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(square(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(square(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c30(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c30(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c30(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c30(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c30(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c30(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c30(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c30(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c30(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(cons2(z0, z1))) → c30(SQUARE(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c30(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c30(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c63(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c63(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c63(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c63(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(cons2(z0, z1))) → c63(S(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(s(rcons(z0, z1))) → c63(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c63(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c63(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c63(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c63(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c63(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c63(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c63(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c63(S(ok(0)))
PROPER(s(nil)) → c63(S(ok(nil)))
PROPER(s(rnil)) → c63(S(ok(rnil)))
PROPER(posrecip(0)) → c64(POSRECIP(ok(0)), PROPER(0))
PROPER(posrecip(s(z0))) → c64(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c64(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c64(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(nil)) → c64(POSRECIP(ok(nil)), PROPER(nil))
PROPER(posrecip(cons(z0, z1))) → c64(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(cons2(z0, z1))) → c64(POSRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(posrecip(rnil)) → c64(POSRECIP(ok(rnil)), PROPER(rnil))
PROPER(posrecip(rcons(z0, z1))) → c64(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c64(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c64(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c64(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c64(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c64(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c64(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c64(POSRECIP(square(proper(z0))), PROPER(square(z0)))
S tuples:
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
PROPER(negrecip(z0)) → c65(NEGRECIP(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c67(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(cons2(z0, z1)) → c68(CONS2(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(rcons(z0, z1)) → c70(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c71(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c72(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c73(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c74(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c75(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c76(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c77(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c78(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c79(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c9(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(2NDSPOS(s(z0), cons2(z1, z2)))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(2NDSNEG(s(z0), cons2(z1, z2)))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c13(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, z2)))) → c13(S(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(s(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, z2)))) → c13(S(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(s(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c13(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c13(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c13(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c13(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c13(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c13(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c13(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c13(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(cons2(z0, z1))) → c13(S(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c13(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c13(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c13(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c14(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c14(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c14(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c14(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c14(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c14(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c14(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c14(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(cons2(z0, z1))) → c14(POSRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c15(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c15(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c15(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c15(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c15(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c15(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c15(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c15(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(cons2(z0, z1))) → c15(NEGRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndspos(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndspos(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndsneg(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndsneg(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c16(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c16(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c16(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c16(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c16(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c16(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c16(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c16(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(cons2(z0, z1), x1)) → c16(CONS(cons2(z0, active(z1)), x1), ACTIVE(cons2(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, 2ndsneg(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(0, z0))) → c17(CONS2(x0, mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(cons2(x0, plus(s(z0), z1))) → c17(CONS2(x0, mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons2(x0, times(0, z0))) → c17(CONS2(x0, mark(0)), ACTIVE(times(0, z0)))
ACTIVE(cons2(x0, times(s(z0), z1))) → c17(CONS2(x0, mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(cons2(x0, s(z0))) → c17(CONS2(x0, s(active(z0))), ACTIVE(s(z0)))
ACTIVE(cons2(x0, posrecip(z0))) → c17(CONS2(x0, posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(cons2(x0, negrecip(z0))) → c17(CONS2(x0, negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(cons2(x0, cons(z0, z1))) → c17(CONS2(x0, cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(cons2(x0, cons2(z0, z1))) → c17(CONS2(x0, cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, from(active(z0))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, square(active(z0))), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c20(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(from(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(from(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c20(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c20(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c20(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c20(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c20(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c20(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c20(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c20(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c20(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c20(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(cons2(z0, z1))) → c20(FROM(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c20(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c20(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c20(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c25(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c25(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c25(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c25(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c25(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c25(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c25(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c25(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c25(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c25(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c25(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(cons2(z0, z1))) → c25(PI(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c25(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c25(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c25(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c30(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(square(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(square(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c30(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c30(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c30(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c30(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c30(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c30(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c30(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c30(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c30(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(cons2(z0, z1))) → c30(SQUARE(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c30(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c30(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c63(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c63(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c63(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c63(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(cons2(z0, z1))) → c63(S(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(s(rcons(z0, z1))) → c63(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c63(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c63(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c63(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c63(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c63(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c63(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c63(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c63(S(ok(0)))
PROPER(s(nil)) → c63(S(ok(nil)))
PROPER(s(rnil)) → c63(S(ok(rnil)))
PROPER(posrecip(0)) → c64(POSRECIP(ok(0)), PROPER(0))
PROPER(posrecip(s(z0))) → c64(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c64(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c64(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(nil)) → c64(POSRECIP(ok(nil)), PROPER(nil))
PROPER(posrecip(cons(z0, z1))) → c64(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(cons2(z0, z1))) → c64(POSRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(posrecip(rnil)) → c64(POSRECIP(ok(rnil)), PROPER(rnil))
PROPER(posrecip(rcons(z0, z1))) → c64(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c64(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c64(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c64(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c64(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c64(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c64(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c64(POSRECIP(square(proper(z0))), PROPER(square(z0)))
K tuples:none
Defined Rule Symbols:
active, 2ndspos, cons2, rcons, posrecip, 2ndsneg, negrecip, s, cons, from, pi, plus, times, square, proper
Defined Pair Symbols:
ACTIVE, S, POSRECIP, NEGRECIP, CONS, CONS2, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP
Compound Symbols:
c12, c18, c19, c21, c22, c23, c24, c26, c27, c28, c29, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c65, c67, c68, c70, c71, c72, c73, c74, c75, c76, c77, c78, c79, c, c7, c9, c11, c1, c13, c14, c15, c16, c17, c20, c25, c30, c63, c63, c64
(33) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 3 trailing tuple parts
(34) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(2ndspos(0, z0)) → mark(rnil)
active(2ndspos(s(z0), cons(z1, z2))) → mark(2ndspos(s(z0), cons2(z1, z2)))
active(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(z1, z2))) → mark(2ndsneg(s(z0), cons2(z1, z2)))
active(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
active(pi(z0)) → mark(2ndspos(z0, from(0)))
active(plus(0, z0)) → mark(z0)
active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
active(times(0, z0)) → mark(0)
active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
active(square(z0)) → mark(times(z0, z0))
active(s(z0)) → s(active(z0))
active(posrecip(z0)) → posrecip(active(z0))
active(negrecip(z0)) → negrecip(active(z0))
active(cons(z0, z1)) → cons(active(z0), z1)
active(cons2(z0, z1)) → cons2(z0, active(z1))
active(rcons(z0, z1)) → rcons(active(z0), z1)
active(rcons(z0, z1)) → rcons(z0, active(z1))
active(from(z0)) → from(active(z0))
active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
active(pi(z0)) → pi(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(times(z0, z1)) → times(active(z0), z1)
active(times(z0, z1)) → times(z0, active(z1))
active(square(z0)) → square(active(z0))
2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
cons2(z0, mark(z1)) → mark(cons2(z0, z1))
cons2(ok(z0), ok(z1)) → ok(cons2(z0, z1))
rcons(mark(z0), z1) → mark(rcons(z0, z1))
rcons(z0, mark(z1)) → mark(rcons(z0, z1))
rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
posrecip(ok(z0)) → ok(posrecip(z0))
posrecip(mark(z0)) → mark(posrecip(z0))
2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
negrecip(ok(z0)) → ok(negrecip(z0))
negrecip(mark(z0)) → mark(negrecip(z0))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
cons(mark(z0), z1) → mark(cons(z0, z1))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
from(mark(z0)) → mark(from(z0))
from(ok(z0)) → ok(from(z0))
pi(mark(z0)) → mark(pi(z0))
pi(ok(z0)) → ok(pi(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
times(mark(z0), z1) → mark(times(z0, z1))
times(ok(z0), ok(z1)) → ok(times(z0, z1))
times(z0, mark(z1)) → mark(times(z0, z1))
square(mark(z0)) → mark(square(z0))
square(ok(z0)) → ok(square(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(posrecip(z0)) → posrecip(proper(z0))
proper(negrecip(z0)) → negrecip(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(cons2(z0, z1)) → cons2(proper(z0), proper(z1))
proper(rnil) → ok(rnil)
proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
proper(pi(z0)) → pi(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(times(z0, z1)) → times(proper(z0), proper(z1))
proper(square(z0)) → square(proper(z0))
Tuples:
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
PROPER(negrecip(z0)) → c65(NEGRECIP(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c67(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(cons2(z0, z1)) → c68(CONS2(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(rcons(z0, z1)) → c70(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c71(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c72(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c73(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c74(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c75(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c76(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c77(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c78(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c79(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c9(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(2NDSPOS(s(z0), cons2(z1, z2)))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(2NDSNEG(s(z0), cons2(z1, z2)))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c13(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, z2)))) → c13(S(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(s(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, z2)))) → c13(S(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(s(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c13(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c13(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c13(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c13(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c13(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c13(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c13(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c13(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(cons2(z0, z1))) → c13(S(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c13(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c13(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c13(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c14(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c14(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c14(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c14(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c14(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c14(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c14(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c14(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(cons2(z0, z1))) → c14(POSRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c15(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c15(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c15(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c15(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c15(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c15(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c15(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c15(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(cons2(z0, z1))) → c15(NEGRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndspos(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndspos(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndsneg(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndsneg(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c16(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c16(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c16(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c16(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c16(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c16(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c16(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c16(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(cons2(z0, z1), x1)) → c16(CONS(cons2(z0, active(z1)), x1), ACTIVE(cons2(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, 2ndsneg(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(0, z0))) → c17(CONS2(x0, mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(cons2(x0, plus(s(z0), z1))) → c17(CONS2(x0, mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons2(x0, times(0, z0))) → c17(CONS2(x0, mark(0)), ACTIVE(times(0, z0)))
ACTIVE(cons2(x0, times(s(z0), z1))) → c17(CONS2(x0, mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(cons2(x0, s(z0))) → c17(CONS2(x0, s(active(z0))), ACTIVE(s(z0)))
ACTIVE(cons2(x0, posrecip(z0))) → c17(CONS2(x0, posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(cons2(x0, negrecip(z0))) → c17(CONS2(x0, negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(cons2(x0, cons(z0, z1))) → c17(CONS2(x0, cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(cons2(x0, cons2(z0, z1))) → c17(CONS2(x0, cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, from(active(z0))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, square(active(z0))), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c20(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(from(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(from(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c20(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c20(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c20(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c20(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c20(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c20(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c20(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c20(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c20(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c20(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(cons2(z0, z1))) → c20(FROM(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c20(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c20(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c20(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c25(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c25(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c25(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c25(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c25(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c25(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c25(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c25(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c25(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c25(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c25(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(cons2(z0, z1))) → c25(PI(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c25(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c25(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c25(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c30(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(square(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(square(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c30(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c30(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c30(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c30(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c30(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c30(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c30(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c30(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c30(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(cons2(z0, z1))) → c30(SQUARE(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c30(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c30(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c63(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c63(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c63(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c63(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(cons2(z0, z1))) → c63(S(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(s(rcons(z0, z1))) → c63(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c63(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c63(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c63(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c63(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c63(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c63(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c63(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c63(S(ok(0)))
PROPER(s(nil)) → c63(S(ok(nil)))
PROPER(s(rnil)) → c63(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c64(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c64(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c64(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c64(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(cons2(z0, z1))) → c64(POSRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c64(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c64(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c64(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c64(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c64(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c64(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c64(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c64(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c64(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c64(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c64(POSRECIP(ok(rnil)))
S tuples:
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
PROPER(negrecip(z0)) → c65(NEGRECIP(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c67(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(cons2(z0, z1)) → c68(CONS2(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(rcons(z0, z1)) → c70(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c71(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c72(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c73(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c74(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c75(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c76(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c77(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c78(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c79(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c9(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(2NDSPOS(s(z0), cons2(z1, z2)))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(2NDSNEG(s(z0), cons2(z1, z2)))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c13(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, z2)))) → c13(S(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(s(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, z2)))) → c13(S(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(s(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c13(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c13(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c13(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c13(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c13(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c13(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c13(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c13(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(cons2(z0, z1))) → c13(S(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c13(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c13(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c13(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c14(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c14(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c14(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c14(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c14(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c14(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c14(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c14(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(cons2(z0, z1))) → c14(POSRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c15(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c15(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c15(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c15(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c15(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c15(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c15(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c15(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(cons2(z0, z1))) → c15(NEGRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndspos(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndspos(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndsneg(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndsneg(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c16(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c16(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c16(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c16(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c16(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c16(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c16(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c16(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(cons2(z0, z1), x1)) → c16(CONS(cons2(z0, active(z1)), x1), ACTIVE(cons2(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, 2ndsneg(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(0, z0))) → c17(CONS2(x0, mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(cons2(x0, plus(s(z0), z1))) → c17(CONS2(x0, mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons2(x0, times(0, z0))) → c17(CONS2(x0, mark(0)), ACTIVE(times(0, z0)))
ACTIVE(cons2(x0, times(s(z0), z1))) → c17(CONS2(x0, mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(cons2(x0, s(z0))) → c17(CONS2(x0, s(active(z0))), ACTIVE(s(z0)))
ACTIVE(cons2(x0, posrecip(z0))) → c17(CONS2(x0, posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(cons2(x0, negrecip(z0))) → c17(CONS2(x0, negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(cons2(x0, cons(z0, z1))) → c17(CONS2(x0, cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(cons2(x0, cons2(z0, z1))) → c17(CONS2(x0, cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, from(active(z0))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, square(active(z0))), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c20(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(from(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(from(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c20(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c20(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c20(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c20(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c20(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c20(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c20(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c20(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c20(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c20(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(cons2(z0, z1))) → c20(FROM(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c20(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c20(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c20(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c25(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c25(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c25(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c25(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c25(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c25(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c25(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c25(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c25(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c25(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c25(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(cons2(z0, z1))) → c25(PI(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c25(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c25(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c25(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c30(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(square(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(square(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c30(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c30(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c30(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c30(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c30(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c30(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c30(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c30(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c30(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(cons2(z0, z1))) → c30(SQUARE(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c30(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c30(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c63(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c63(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c63(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c63(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(cons2(z0, z1))) → c63(S(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(s(rcons(z0, z1))) → c63(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c63(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c63(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c63(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c63(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c63(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c63(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c63(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c63(S(ok(0)))
PROPER(s(nil)) → c63(S(ok(nil)))
PROPER(s(rnil)) → c63(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c64(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c64(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c64(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c64(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(cons2(z0, z1))) → c64(POSRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c64(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c64(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c64(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c64(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c64(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c64(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c64(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c64(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c64(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c64(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c64(POSRECIP(ok(rnil)))
K tuples:none
Defined Rule Symbols:
active, 2ndspos, cons2, rcons, posrecip, 2ndsneg, negrecip, s, cons, from, pi, plus, times, square, proper
Defined Pair Symbols:
ACTIVE, S, POSRECIP, NEGRECIP, CONS, CONS2, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP
Compound Symbols:
c12, c18, c19, c21, c22, c23, c24, c26, c27, c28, c29, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c65, c67, c68, c70, c71, c72, c73, c74, c75, c76, c77, c78, c79, c, c7, c9, c11, c1, c13, c14, c15, c16, c17, c20, c25, c30, c63, c63, c64, c64
(35) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
PROPER(
negrecip(
z0)) →
c65(
NEGRECIP(
proper(
z0)),
PROPER(
z0)) by
PROPER(negrecip(0)) → c65(NEGRECIP(ok(0)), PROPER(0))
PROPER(negrecip(s(z0))) → c65(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c65(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c65(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(nil)) → c65(NEGRECIP(ok(nil)), PROPER(nil))
PROPER(negrecip(cons(z0, z1))) → c65(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(cons2(z0, z1))) → c65(NEGRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(negrecip(rnil)) → c65(NEGRECIP(ok(rnil)), PROPER(rnil))
PROPER(negrecip(rcons(z0, z1))) → c65(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c65(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c65(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c65(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c65(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c65(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c65(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c65(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
(36) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(2ndspos(0, z0)) → mark(rnil)
active(2ndspos(s(z0), cons(z1, z2))) → mark(2ndspos(s(z0), cons2(z1, z2)))
active(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(z1, z2))) → mark(2ndsneg(s(z0), cons2(z1, z2)))
active(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
active(pi(z0)) → mark(2ndspos(z0, from(0)))
active(plus(0, z0)) → mark(z0)
active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
active(times(0, z0)) → mark(0)
active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
active(square(z0)) → mark(times(z0, z0))
active(s(z0)) → s(active(z0))
active(posrecip(z0)) → posrecip(active(z0))
active(negrecip(z0)) → negrecip(active(z0))
active(cons(z0, z1)) → cons(active(z0), z1)
active(cons2(z0, z1)) → cons2(z0, active(z1))
active(rcons(z0, z1)) → rcons(active(z0), z1)
active(rcons(z0, z1)) → rcons(z0, active(z1))
active(from(z0)) → from(active(z0))
active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
active(pi(z0)) → pi(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(times(z0, z1)) → times(active(z0), z1)
active(times(z0, z1)) → times(z0, active(z1))
active(square(z0)) → square(active(z0))
2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
cons2(z0, mark(z1)) → mark(cons2(z0, z1))
cons2(ok(z0), ok(z1)) → ok(cons2(z0, z1))
rcons(mark(z0), z1) → mark(rcons(z0, z1))
rcons(z0, mark(z1)) → mark(rcons(z0, z1))
rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
posrecip(ok(z0)) → ok(posrecip(z0))
posrecip(mark(z0)) → mark(posrecip(z0))
2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
negrecip(ok(z0)) → ok(negrecip(z0))
negrecip(mark(z0)) → mark(negrecip(z0))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
cons(mark(z0), z1) → mark(cons(z0, z1))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
from(mark(z0)) → mark(from(z0))
from(ok(z0)) → ok(from(z0))
pi(mark(z0)) → mark(pi(z0))
pi(ok(z0)) → ok(pi(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
times(mark(z0), z1) → mark(times(z0, z1))
times(ok(z0), ok(z1)) → ok(times(z0, z1))
times(z0, mark(z1)) → mark(times(z0, z1))
square(mark(z0)) → mark(square(z0))
square(ok(z0)) → ok(square(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(posrecip(z0)) → posrecip(proper(z0))
proper(negrecip(z0)) → negrecip(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(cons2(z0, z1)) → cons2(proper(z0), proper(z1))
proper(rnil) → ok(rnil)
proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
proper(pi(z0)) → pi(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(times(z0, z1)) → times(proper(z0), proper(z1))
proper(square(z0)) → square(proper(z0))
Tuples:
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
PROPER(cons(z0, z1)) → c67(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(cons2(z0, z1)) → c68(CONS2(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(rcons(z0, z1)) → c70(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c71(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c72(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c73(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c74(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c75(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c76(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c77(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c78(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c79(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c9(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(2NDSPOS(s(z0), cons2(z1, z2)))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(2NDSNEG(s(z0), cons2(z1, z2)))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c13(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, z2)))) → c13(S(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(s(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, z2)))) → c13(S(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(s(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c13(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c13(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c13(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c13(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c13(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c13(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c13(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c13(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(cons2(z0, z1))) → c13(S(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c13(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c13(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c13(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c14(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c14(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c14(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c14(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c14(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c14(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c14(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c14(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(cons2(z0, z1))) → c14(POSRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c15(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c15(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c15(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c15(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c15(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c15(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c15(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c15(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(cons2(z0, z1))) → c15(NEGRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndspos(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndspos(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndsneg(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndsneg(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c16(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c16(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c16(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c16(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c16(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c16(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c16(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c16(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(cons2(z0, z1), x1)) → c16(CONS(cons2(z0, active(z1)), x1), ACTIVE(cons2(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, 2ndsneg(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(0, z0))) → c17(CONS2(x0, mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(cons2(x0, plus(s(z0), z1))) → c17(CONS2(x0, mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons2(x0, times(0, z0))) → c17(CONS2(x0, mark(0)), ACTIVE(times(0, z0)))
ACTIVE(cons2(x0, times(s(z0), z1))) → c17(CONS2(x0, mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(cons2(x0, s(z0))) → c17(CONS2(x0, s(active(z0))), ACTIVE(s(z0)))
ACTIVE(cons2(x0, posrecip(z0))) → c17(CONS2(x0, posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(cons2(x0, negrecip(z0))) → c17(CONS2(x0, negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(cons2(x0, cons(z0, z1))) → c17(CONS2(x0, cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(cons2(x0, cons2(z0, z1))) → c17(CONS2(x0, cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, from(active(z0))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, square(active(z0))), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c20(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(from(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(from(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c20(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c20(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c20(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c20(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c20(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c20(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c20(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c20(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c20(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c20(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(cons2(z0, z1))) → c20(FROM(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c20(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c20(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c20(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c25(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c25(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c25(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c25(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c25(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c25(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c25(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c25(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c25(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c25(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c25(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(cons2(z0, z1))) → c25(PI(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c25(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c25(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c25(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c30(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(square(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(square(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c30(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c30(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c30(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c30(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c30(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c30(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c30(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c30(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c30(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(cons2(z0, z1))) → c30(SQUARE(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c30(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c30(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c63(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c63(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c63(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c63(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(cons2(z0, z1))) → c63(S(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(s(rcons(z0, z1))) → c63(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c63(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c63(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c63(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c63(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c63(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c63(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c63(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c63(S(ok(0)))
PROPER(s(nil)) → c63(S(ok(nil)))
PROPER(s(rnil)) → c63(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c64(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c64(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c64(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c64(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(cons2(z0, z1))) → c64(POSRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c64(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c64(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c64(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c64(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c64(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c64(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c64(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c64(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c64(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c64(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c64(POSRECIP(ok(rnil)))
PROPER(negrecip(0)) → c65(NEGRECIP(ok(0)), PROPER(0))
PROPER(negrecip(s(z0))) → c65(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c65(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c65(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(nil)) → c65(NEGRECIP(ok(nil)), PROPER(nil))
PROPER(negrecip(cons(z0, z1))) → c65(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(cons2(z0, z1))) → c65(NEGRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(negrecip(rnil)) → c65(NEGRECIP(ok(rnil)), PROPER(rnil))
PROPER(negrecip(rcons(z0, z1))) → c65(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c65(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c65(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c65(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c65(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c65(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c65(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c65(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
S tuples:
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
PROPER(cons(z0, z1)) → c67(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(cons2(z0, z1)) → c68(CONS2(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(rcons(z0, z1)) → c70(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c71(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c72(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c73(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c74(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c75(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c76(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c77(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c78(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c79(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c9(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(2NDSPOS(s(z0), cons2(z1, z2)))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(2NDSNEG(s(z0), cons2(z1, z2)))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c13(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, z2)))) → c13(S(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(s(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, z2)))) → c13(S(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(s(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c13(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c13(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c13(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c13(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c13(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c13(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c13(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c13(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(cons2(z0, z1))) → c13(S(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c13(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c13(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c13(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c14(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c14(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c14(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c14(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c14(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c14(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c14(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c14(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(cons2(z0, z1))) → c14(POSRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c15(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c15(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c15(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c15(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c15(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c15(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c15(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c15(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(cons2(z0, z1))) → c15(NEGRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndspos(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndspos(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndsneg(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndsneg(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c16(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c16(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c16(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c16(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c16(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c16(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c16(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c16(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(cons2(z0, z1), x1)) → c16(CONS(cons2(z0, active(z1)), x1), ACTIVE(cons2(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, 2ndsneg(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(0, z0))) → c17(CONS2(x0, mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(cons2(x0, plus(s(z0), z1))) → c17(CONS2(x0, mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons2(x0, times(0, z0))) → c17(CONS2(x0, mark(0)), ACTIVE(times(0, z0)))
ACTIVE(cons2(x0, times(s(z0), z1))) → c17(CONS2(x0, mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(cons2(x0, s(z0))) → c17(CONS2(x0, s(active(z0))), ACTIVE(s(z0)))
ACTIVE(cons2(x0, posrecip(z0))) → c17(CONS2(x0, posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(cons2(x0, negrecip(z0))) → c17(CONS2(x0, negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(cons2(x0, cons(z0, z1))) → c17(CONS2(x0, cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(cons2(x0, cons2(z0, z1))) → c17(CONS2(x0, cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, from(active(z0))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, square(active(z0))), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c20(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(from(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(from(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c20(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c20(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c20(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c20(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c20(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c20(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c20(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c20(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c20(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c20(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(cons2(z0, z1))) → c20(FROM(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c20(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c20(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c20(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c25(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c25(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c25(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c25(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c25(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c25(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c25(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c25(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c25(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c25(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c25(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(cons2(z0, z1))) → c25(PI(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c25(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c25(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c25(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c30(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(square(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(square(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c30(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c30(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c30(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c30(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c30(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c30(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c30(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c30(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c30(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(cons2(z0, z1))) → c30(SQUARE(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c30(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c30(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c63(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c63(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c63(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c63(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(cons2(z0, z1))) → c63(S(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(s(rcons(z0, z1))) → c63(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c63(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c63(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c63(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c63(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c63(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c63(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c63(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c63(S(ok(0)))
PROPER(s(nil)) → c63(S(ok(nil)))
PROPER(s(rnil)) → c63(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c64(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c64(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c64(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c64(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(cons2(z0, z1))) → c64(POSRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c64(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c64(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c64(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c64(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c64(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c64(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c64(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c64(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c64(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c64(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c64(POSRECIP(ok(rnil)))
PROPER(negrecip(0)) → c65(NEGRECIP(ok(0)), PROPER(0))
PROPER(negrecip(s(z0))) → c65(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c65(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c65(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(nil)) → c65(NEGRECIP(ok(nil)), PROPER(nil))
PROPER(negrecip(cons(z0, z1))) → c65(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(cons2(z0, z1))) → c65(NEGRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(negrecip(rnil)) → c65(NEGRECIP(ok(rnil)), PROPER(rnil))
PROPER(negrecip(rcons(z0, z1))) → c65(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c65(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c65(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c65(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c65(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c65(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c65(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c65(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
K tuples:none
Defined Rule Symbols:
active, 2ndspos, cons2, rcons, posrecip, 2ndsneg, negrecip, s, cons, from, pi, plus, times, square, proper
Defined Pair Symbols:
ACTIVE, S, POSRECIP, NEGRECIP, CONS, CONS2, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP
Compound Symbols:
c12, c18, c19, c21, c22, c23, c24, c26, c27, c28, c29, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c67, c68, c70, c71, c72, c73, c74, c75, c76, c77, c78, c79, c, c7, c9, c11, c1, c13, c14, c15, c16, c17, c20, c25, c30, c63, c63, c64, c64, c65
(37) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 3 trailing tuple parts
(38) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(2ndspos(0, z0)) → mark(rnil)
active(2ndspos(s(z0), cons(z1, z2))) → mark(2ndspos(s(z0), cons2(z1, z2)))
active(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(z1, z2))) → mark(2ndsneg(s(z0), cons2(z1, z2)))
active(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
active(pi(z0)) → mark(2ndspos(z0, from(0)))
active(plus(0, z0)) → mark(z0)
active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
active(times(0, z0)) → mark(0)
active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
active(square(z0)) → mark(times(z0, z0))
active(s(z0)) → s(active(z0))
active(posrecip(z0)) → posrecip(active(z0))
active(negrecip(z0)) → negrecip(active(z0))
active(cons(z0, z1)) → cons(active(z0), z1)
active(cons2(z0, z1)) → cons2(z0, active(z1))
active(rcons(z0, z1)) → rcons(active(z0), z1)
active(rcons(z0, z1)) → rcons(z0, active(z1))
active(from(z0)) → from(active(z0))
active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
active(pi(z0)) → pi(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(times(z0, z1)) → times(active(z0), z1)
active(times(z0, z1)) → times(z0, active(z1))
active(square(z0)) → square(active(z0))
2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
cons2(z0, mark(z1)) → mark(cons2(z0, z1))
cons2(ok(z0), ok(z1)) → ok(cons2(z0, z1))
rcons(mark(z0), z1) → mark(rcons(z0, z1))
rcons(z0, mark(z1)) → mark(rcons(z0, z1))
rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
posrecip(ok(z0)) → ok(posrecip(z0))
posrecip(mark(z0)) → mark(posrecip(z0))
2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
negrecip(ok(z0)) → ok(negrecip(z0))
negrecip(mark(z0)) → mark(negrecip(z0))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
cons(mark(z0), z1) → mark(cons(z0, z1))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
from(mark(z0)) → mark(from(z0))
from(ok(z0)) → ok(from(z0))
pi(mark(z0)) → mark(pi(z0))
pi(ok(z0)) → ok(pi(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
times(mark(z0), z1) → mark(times(z0, z1))
times(ok(z0), ok(z1)) → ok(times(z0, z1))
times(z0, mark(z1)) → mark(times(z0, z1))
square(mark(z0)) → mark(square(z0))
square(ok(z0)) → ok(square(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(posrecip(z0)) → posrecip(proper(z0))
proper(negrecip(z0)) → negrecip(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(cons2(z0, z1)) → cons2(proper(z0), proper(z1))
proper(rnil) → ok(rnil)
proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
proper(pi(z0)) → pi(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(times(z0, z1)) → times(proper(z0), proper(z1))
proper(square(z0)) → square(proper(z0))
Tuples:
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
PROPER(cons(z0, z1)) → c67(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(cons2(z0, z1)) → c68(CONS2(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(rcons(z0, z1)) → c70(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c71(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c72(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c73(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c74(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c75(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c76(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c77(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c78(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c79(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c9(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(2NDSPOS(s(z0), cons2(z1, z2)))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(2NDSNEG(s(z0), cons2(z1, z2)))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c13(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, z2)))) → c13(S(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(s(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, z2)))) → c13(S(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(s(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c13(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c13(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c13(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c13(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c13(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c13(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c13(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c13(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(cons2(z0, z1))) → c13(S(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c13(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c13(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c13(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c14(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c14(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c14(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c14(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c14(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c14(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c14(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c14(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(cons2(z0, z1))) → c14(POSRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c15(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c15(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c15(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c15(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c15(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c15(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c15(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c15(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(cons2(z0, z1))) → c15(NEGRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndspos(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndspos(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndsneg(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndsneg(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c16(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c16(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c16(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c16(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c16(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c16(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c16(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c16(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(cons2(z0, z1), x1)) → c16(CONS(cons2(z0, active(z1)), x1), ACTIVE(cons2(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, 2ndsneg(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(0, z0))) → c17(CONS2(x0, mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(cons2(x0, plus(s(z0), z1))) → c17(CONS2(x0, mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons2(x0, times(0, z0))) → c17(CONS2(x0, mark(0)), ACTIVE(times(0, z0)))
ACTIVE(cons2(x0, times(s(z0), z1))) → c17(CONS2(x0, mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(cons2(x0, s(z0))) → c17(CONS2(x0, s(active(z0))), ACTIVE(s(z0)))
ACTIVE(cons2(x0, posrecip(z0))) → c17(CONS2(x0, posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(cons2(x0, negrecip(z0))) → c17(CONS2(x0, negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(cons2(x0, cons(z0, z1))) → c17(CONS2(x0, cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(cons2(x0, cons2(z0, z1))) → c17(CONS2(x0, cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, from(active(z0))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, square(active(z0))), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c20(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(from(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(from(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c20(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c20(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c20(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c20(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c20(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c20(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c20(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c20(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c20(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c20(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(cons2(z0, z1))) → c20(FROM(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c20(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c20(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c20(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c25(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c25(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c25(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c25(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c25(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c25(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c25(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c25(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c25(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c25(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c25(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(cons2(z0, z1))) → c25(PI(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c25(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c25(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c25(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c30(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(square(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(square(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c30(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c30(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c30(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c30(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c30(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c30(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c30(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c30(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c30(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(cons2(z0, z1))) → c30(SQUARE(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c30(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c30(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c63(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c63(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c63(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c63(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(cons2(z0, z1))) → c63(S(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(s(rcons(z0, z1))) → c63(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c63(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c63(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c63(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c63(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c63(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c63(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c63(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c63(S(ok(0)))
PROPER(s(nil)) → c63(S(ok(nil)))
PROPER(s(rnil)) → c63(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c64(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c64(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c64(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c64(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(cons2(z0, z1))) → c64(POSRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c64(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c64(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c64(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c64(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c64(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c64(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c64(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c64(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c64(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c64(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c64(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c65(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c65(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c65(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c65(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(cons2(z0, z1))) → c65(NEGRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c65(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c65(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c65(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c65(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c65(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c65(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c65(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c65(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c65(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c65(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c65(NEGRECIP(ok(rnil)))
S tuples:
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
PROPER(cons(z0, z1)) → c67(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(cons2(z0, z1)) → c68(CONS2(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(rcons(z0, z1)) → c70(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c71(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c72(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c73(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c74(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c75(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c76(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c77(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c78(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c79(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c9(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(2NDSPOS(s(z0), cons2(z1, z2)))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(2NDSNEG(s(z0), cons2(z1, z2)))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c13(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, z2)))) → c13(S(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(s(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, z2)))) → c13(S(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(s(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c13(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c13(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c13(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c13(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c13(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c13(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c13(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c13(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(cons2(z0, z1))) → c13(S(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c13(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c13(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c13(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c14(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c14(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c14(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c14(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c14(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c14(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c14(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c14(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(cons2(z0, z1))) → c14(POSRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c15(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c15(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c15(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c15(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c15(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c15(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c15(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c15(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(cons2(z0, z1))) → c15(NEGRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndspos(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndspos(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndsneg(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndsneg(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c16(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c16(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c16(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c16(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c16(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c16(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c16(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c16(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(cons2(z0, z1), x1)) → c16(CONS(cons2(z0, active(z1)), x1), ACTIVE(cons2(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, 2ndsneg(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(0, z0))) → c17(CONS2(x0, mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(cons2(x0, plus(s(z0), z1))) → c17(CONS2(x0, mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons2(x0, times(0, z0))) → c17(CONS2(x0, mark(0)), ACTIVE(times(0, z0)))
ACTIVE(cons2(x0, times(s(z0), z1))) → c17(CONS2(x0, mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(cons2(x0, s(z0))) → c17(CONS2(x0, s(active(z0))), ACTIVE(s(z0)))
ACTIVE(cons2(x0, posrecip(z0))) → c17(CONS2(x0, posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(cons2(x0, negrecip(z0))) → c17(CONS2(x0, negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(cons2(x0, cons(z0, z1))) → c17(CONS2(x0, cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(cons2(x0, cons2(z0, z1))) → c17(CONS2(x0, cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, from(active(z0))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, square(active(z0))), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c20(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(from(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(from(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c20(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c20(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c20(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c20(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c20(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c20(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c20(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c20(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c20(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c20(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(cons2(z0, z1))) → c20(FROM(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c20(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c20(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c20(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c25(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c25(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c25(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c25(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c25(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c25(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c25(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c25(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c25(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c25(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c25(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(cons2(z0, z1))) → c25(PI(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c25(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c25(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c25(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c30(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(square(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(square(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c30(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c30(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c30(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c30(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c30(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c30(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c30(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c30(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c30(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(cons2(z0, z1))) → c30(SQUARE(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c30(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c30(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c63(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c63(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c63(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c63(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(cons2(z0, z1))) → c63(S(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(s(rcons(z0, z1))) → c63(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c63(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c63(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c63(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c63(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c63(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c63(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c63(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c63(S(ok(0)))
PROPER(s(nil)) → c63(S(ok(nil)))
PROPER(s(rnil)) → c63(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c64(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c64(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c64(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c64(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(cons2(z0, z1))) → c64(POSRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c64(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c64(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c64(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c64(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c64(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c64(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c64(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c64(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c64(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c64(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c64(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c65(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c65(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c65(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c65(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(cons2(z0, z1))) → c65(NEGRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c65(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c65(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c65(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c65(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c65(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c65(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c65(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c65(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c65(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c65(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c65(NEGRECIP(ok(rnil)))
K tuples:none
Defined Rule Symbols:
active, 2ndspos, cons2, rcons, posrecip, 2ndsneg, negrecip, s, cons, from, pi, plus, times, square, proper
Defined Pair Symbols:
ACTIVE, S, POSRECIP, NEGRECIP, CONS, CONS2, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP
Compound Symbols:
c12, c18, c19, c21, c22, c23, c24, c26, c27, c28, c29, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c67, c68, c70, c71, c72, c73, c74, c75, c76, c77, c78, c79, c, c7, c9, c11, c1, c13, c14, c15, c16, c17, c20, c25, c30, c63, c63, c64, c64, c65, c65
(39) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
PROPER(
cons(
z0,
z1)) →
c67(
CONS(
proper(
z0),
proper(
z1)),
PROPER(
z0),
PROPER(
z1)) by
PROPER(cons(x0, 0)) → c67(CONS(proper(x0), ok(0)), PROPER(x0), PROPER(0))
PROPER(cons(x0, s(z0))) → c67(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c67(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c67(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, nil)) → c67(CONS(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
PROPER(cons(x0, cons(z0, z1))) → c67(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, cons2(z0, z1))) → c67(CONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons(x0, rnil)) → c67(CONS(proper(x0), ok(rnil)), PROPER(x0), PROPER(rnil))
PROPER(cons(x0, rcons(z0, z1))) → c67(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c67(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c67(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c67(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c67(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c67(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c67(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c67(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(0, x1)) → c67(CONS(ok(0), proper(x1)), PROPER(0), PROPER(x1))
PROPER(cons(s(z0), x1)) → c67(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c67(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c67(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(nil, x1)) → c67(CONS(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c67(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(cons2(z0, z1), x1)) → c67(CONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c67(CONS(ok(rnil), proper(x1)), PROPER(rnil), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c67(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c67(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c67(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c67(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c67(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c67(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c67(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c67(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
(40) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(2ndspos(0, z0)) → mark(rnil)
active(2ndspos(s(z0), cons(z1, z2))) → mark(2ndspos(s(z0), cons2(z1, z2)))
active(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(z1, z2))) → mark(2ndsneg(s(z0), cons2(z1, z2)))
active(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
active(pi(z0)) → mark(2ndspos(z0, from(0)))
active(plus(0, z0)) → mark(z0)
active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
active(times(0, z0)) → mark(0)
active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
active(square(z0)) → mark(times(z0, z0))
active(s(z0)) → s(active(z0))
active(posrecip(z0)) → posrecip(active(z0))
active(negrecip(z0)) → negrecip(active(z0))
active(cons(z0, z1)) → cons(active(z0), z1)
active(cons2(z0, z1)) → cons2(z0, active(z1))
active(rcons(z0, z1)) → rcons(active(z0), z1)
active(rcons(z0, z1)) → rcons(z0, active(z1))
active(from(z0)) → from(active(z0))
active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
active(pi(z0)) → pi(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(times(z0, z1)) → times(active(z0), z1)
active(times(z0, z1)) → times(z0, active(z1))
active(square(z0)) → square(active(z0))
2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
cons2(z0, mark(z1)) → mark(cons2(z0, z1))
cons2(ok(z0), ok(z1)) → ok(cons2(z0, z1))
rcons(mark(z0), z1) → mark(rcons(z0, z1))
rcons(z0, mark(z1)) → mark(rcons(z0, z1))
rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
posrecip(ok(z0)) → ok(posrecip(z0))
posrecip(mark(z0)) → mark(posrecip(z0))
2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
negrecip(ok(z0)) → ok(negrecip(z0))
negrecip(mark(z0)) → mark(negrecip(z0))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
cons(mark(z0), z1) → mark(cons(z0, z1))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
from(mark(z0)) → mark(from(z0))
from(ok(z0)) → ok(from(z0))
pi(mark(z0)) → mark(pi(z0))
pi(ok(z0)) → ok(pi(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
times(mark(z0), z1) → mark(times(z0, z1))
times(ok(z0), ok(z1)) → ok(times(z0, z1))
times(z0, mark(z1)) → mark(times(z0, z1))
square(mark(z0)) → mark(square(z0))
square(ok(z0)) → ok(square(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(posrecip(z0)) → posrecip(proper(z0))
proper(negrecip(z0)) → negrecip(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(cons2(z0, z1)) → cons2(proper(z0), proper(z1))
proper(rnil) → ok(rnil)
proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
proper(pi(z0)) → pi(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(times(z0, z1)) → times(proper(z0), proper(z1))
proper(square(z0)) → square(proper(z0))
Tuples:
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
PROPER(cons2(z0, z1)) → c68(CONS2(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(rcons(z0, z1)) → c70(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c71(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c72(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c73(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c74(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c75(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c76(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c77(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c78(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c79(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c9(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(2NDSPOS(s(z0), cons2(z1, z2)))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(2NDSNEG(s(z0), cons2(z1, z2)))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c13(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, z2)))) → c13(S(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(s(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, z2)))) → c13(S(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(s(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c13(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c13(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c13(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c13(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c13(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c13(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c13(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c13(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(cons2(z0, z1))) → c13(S(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c13(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c13(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c13(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c14(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c14(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c14(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c14(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c14(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c14(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c14(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c14(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(cons2(z0, z1))) → c14(POSRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c15(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c15(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c15(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c15(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c15(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c15(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c15(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c15(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(cons2(z0, z1))) → c15(NEGRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndspos(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndspos(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndsneg(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndsneg(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c16(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c16(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c16(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c16(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c16(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c16(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c16(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c16(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(cons2(z0, z1), x1)) → c16(CONS(cons2(z0, active(z1)), x1), ACTIVE(cons2(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, 2ndsneg(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(0, z0))) → c17(CONS2(x0, mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(cons2(x0, plus(s(z0), z1))) → c17(CONS2(x0, mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons2(x0, times(0, z0))) → c17(CONS2(x0, mark(0)), ACTIVE(times(0, z0)))
ACTIVE(cons2(x0, times(s(z0), z1))) → c17(CONS2(x0, mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(cons2(x0, s(z0))) → c17(CONS2(x0, s(active(z0))), ACTIVE(s(z0)))
ACTIVE(cons2(x0, posrecip(z0))) → c17(CONS2(x0, posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(cons2(x0, negrecip(z0))) → c17(CONS2(x0, negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(cons2(x0, cons(z0, z1))) → c17(CONS2(x0, cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(cons2(x0, cons2(z0, z1))) → c17(CONS2(x0, cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, from(active(z0))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, square(active(z0))), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c20(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(from(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(from(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c20(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c20(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c20(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c20(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c20(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c20(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c20(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c20(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c20(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c20(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(cons2(z0, z1))) → c20(FROM(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c20(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c20(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c20(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c25(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c25(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c25(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c25(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c25(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c25(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c25(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c25(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c25(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c25(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c25(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(cons2(z0, z1))) → c25(PI(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c25(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c25(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c25(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c30(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(square(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(square(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c30(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c30(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c30(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c30(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c30(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c30(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c30(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c30(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c30(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(cons2(z0, z1))) → c30(SQUARE(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c30(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c30(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c63(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c63(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c63(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c63(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(cons2(z0, z1))) → c63(S(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(s(rcons(z0, z1))) → c63(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c63(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c63(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c63(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c63(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c63(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c63(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c63(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c63(S(ok(0)))
PROPER(s(nil)) → c63(S(ok(nil)))
PROPER(s(rnil)) → c63(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c64(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c64(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c64(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c64(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(cons2(z0, z1))) → c64(POSRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c64(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c64(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c64(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c64(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c64(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c64(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c64(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c64(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c64(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c64(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c64(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c65(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c65(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c65(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c65(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(cons2(z0, z1))) → c65(NEGRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c65(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c65(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c65(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c65(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c65(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c65(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c65(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c65(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c65(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c65(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c65(NEGRECIP(ok(rnil)))
PROPER(cons(x0, 0)) → c67(CONS(proper(x0), ok(0)), PROPER(x0), PROPER(0))
PROPER(cons(x0, s(z0))) → c67(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c67(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c67(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, nil)) → c67(CONS(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
PROPER(cons(x0, cons(z0, z1))) → c67(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, cons2(z0, z1))) → c67(CONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons(x0, rnil)) → c67(CONS(proper(x0), ok(rnil)), PROPER(x0), PROPER(rnil))
PROPER(cons(x0, rcons(z0, z1))) → c67(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c67(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c67(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c67(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c67(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c67(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c67(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c67(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(0, x1)) → c67(CONS(ok(0), proper(x1)), PROPER(0), PROPER(x1))
PROPER(cons(s(z0), x1)) → c67(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c67(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c67(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(nil, x1)) → c67(CONS(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c67(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(cons2(z0, z1), x1)) → c67(CONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c67(CONS(ok(rnil), proper(x1)), PROPER(rnil), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c67(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c67(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c67(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c67(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c67(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c67(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c67(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c67(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
S tuples:
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
PROPER(cons2(z0, z1)) → c68(CONS2(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(rcons(z0, z1)) → c70(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c71(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c72(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c73(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c74(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c75(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c76(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c77(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c78(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c79(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c9(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(2NDSPOS(s(z0), cons2(z1, z2)))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(2NDSNEG(s(z0), cons2(z1, z2)))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c13(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, z2)))) → c13(S(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(s(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, z2)))) → c13(S(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(s(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c13(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c13(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c13(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c13(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c13(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c13(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c13(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c13(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(cons2(z0, z1))) → c13(S(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c13(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c13(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c13(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c14(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c14(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c14(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c14(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c14(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c14(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c14(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c14(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(cons2(z0, z1))) → c14(POSRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c15(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c15(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c15(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c15(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c15(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c15(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c15(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c15(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(cons2(z0, z1))) → c15(NEGRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndspos(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndspos(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndsneg(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndsneg(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c16(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c16(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c16(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c16(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c16(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c16(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c16(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c16(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(cons2(z0, z1), x1)) → c16(CONS(cons2(z0, active(z1)), x1), ACTIVE(cons2(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, 2ndsneg(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(0, z0))) → c17(CONS2(x0, mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(cons2(x0, plus(s(z0), z1))) → c17(CONS2(x0, mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons2(x0, times(0, z0))) → c17(CONS2(x0, mark(0)), ACTIVE(times(0, z0)))
ACTIVE(cons2(x0, times(s(z0), z1))) → c17(CONS2(x0, mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(cons2(x0, s(z0))) → c17(CONS2(x0, s(active(z0))), ACTIVE(s(z0)))
ACTIVE(cons2(x0, posrecip(z0))) → c17(CONS2(x0, posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(cons2(x0, negrecip(z0))) → c17(CONS2(x0, negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(cons2(x0, cons(z0, z1))) → c17(CONS2(x0, cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(cons2(x0, cons2(z0, z1))) → c17(CONS2(x0, cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, from(active(z0))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, square(active(z0))), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c20(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(from(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(from(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c20(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c20(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c20(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c20(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c20(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c20(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c20(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c20(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c20(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c20(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(cons2(z0, z1))) → c20(FROM(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c20(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c20(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c20(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c25(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c25(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c25(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c25(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c25(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c25(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c25(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c25(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c25(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c25(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c25(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(cons2(z0, z1))) → c25(PI(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c25(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c25(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c25(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c30(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(square(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(square(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c30(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c30(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c30(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c30(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c30(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c30(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c30(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c30(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c30(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(cons2(z0, z1))) → c30(SQUARE(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c30(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c30(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c63(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c63(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c63(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c63(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(cons2(z0, z1))) → c63(S(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(s(rcons(z0, z1))) → c63(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c63(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c63(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c63(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c63(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c63(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c63(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c63(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c63(S(ok(0)))
PROPER(s(nil)) → c63(S(ok(nil)))
PROPER(s(rnil)) → c63(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c64(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c64(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c64(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c64(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(cons2(z0, z1))) → c64(POSRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c64(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c64(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c64(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c64(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c64(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c64(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c64(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c64(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c64(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c64(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c64(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c65(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c65(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c65(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c65(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(cons2(z0, z1))) → c65(NEGRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c65(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c65(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c65(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c65(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c65(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c65(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c65(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c65(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c65(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c65(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c65(NEGRECIP(ok(rnil)))
PROPER(cons(x0, 0)) → c67(CONS(proper(x0), ok(0)), PROPER(x0), PROPER(0))
PROPER(cons(x0, s(z0))) → c67(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c67(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c67(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, nil)) → c67(CONS(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
PROPER(cons(x0, cons(z0, z1))) → c67(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, cons2(z0, z1))) → c67(CONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons(x0, rnil)) → c67(CONS(proper(x0), ok(rnil)), PROPER(x0), PROPER(rnil))
PROPER(cons(x0, rcons(z0, z1))) → c67(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c67(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c67(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c67(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c67(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c67(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c67(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c67(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(0, x1)) → c67(CONS(ok(0), proper(x1)), PROPER(0), PROPER(x1))
PROPER(cons(s(z0), x1)) → c67(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c67(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c67(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(nil, x1)) → c67(CONS(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c67(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(cons2(z0, z1), x1)) → c67(CONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c67(CONS(ok(rnil), proper(x1)), PROPER(rnil), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c67(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c67(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c67(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c67(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c67(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c67(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c67(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c67(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
K tuples:none
Defined Rule Symbols:
active, 2ndspos, cons2, rcons, posrecip, 2ndsneg, negrecip, s, cons, from, pi, plus, times, square, proper
Defined Pair Symbols:
ACTIVE, S, POSRECIP, NEGRECIP, CONS, CONS2, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP
Compound Symbols:
c12, c18, c19, c21, c22, c23, c24, c26, c27, c28, c29, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c68, c70, c71, c72, c73, c74, c75, c76, c77, c78, c79, c, c7, c9, c11, c1, c13, c14, c15, c16, c17, c20, c25, c30, c63, c63, c64, c64, c65, c65, c67
(41) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 6 trailing tuple parts
(42) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(2ndspos(0, z0)) → mark(rnil)
active(2ndspos(s(z0), cons(z1, z2))) → mark(2ndspos(s(z0), cons2(z1, z2)))
active(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(z1, z2))) → mark(2ndsneg(s(z0), cons2(z1, z2)))
active(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
active(pi(z0)) → mark(2ndspos(z0, from(0)))
active(plus(0, z0)) → mark(z0)
active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
active(times(0, z0)) → mark(0)
active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
active(square(z0)) → mark(times(z0, z0))
active(s(z0)) → s(active(z0))
active(posrecip(z0)) → posrecip(active(z0))
active(negrecip(z0)) → negrecip(active(z0))
active(cons(z0, z1)) → cons(active(z0), z1)
active(cons2(z0, z1)) → cons2(z0, active(z1))
active(rcons(z0, z1)) → rcons(active(z0), z1)
active(rcons(z0, z1)) → rcons(z0, active(z1))
active(from(z0)) → from(active(z0))
active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
active(pi(z0)) → pi(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(times(z0, z1)) → times(active(z0), z1)
active(times(z0, z1)) → times(z0, active(z1))
active(square(z0)) → square(active(z0))
2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
cons2(z0, mark(z1)) → mark(cons2(z0, z1))
cons2(ok(z0), ok(z1)) → ok(cons2(z0, z1))
rcons(mark(z0), z1) → mark(rcons(z0, z1))
rcons(z0, mark(z1)) → mark(rcons(z0, z1))
rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
posrecip(ok(z0)) → ok(posrecip(z0))
posrecip(mark(z0)) → mark(posrecip(z0))
2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
negrecip(ok(z0)) → ok(negrecip(z0))
negrecip(mark(z0)) → mark(negrecip(z0))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
cons(mark(z0), z1) → mark(cons(z0, z1))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
from(mark(z0)) → mark(from(z0))
from(ok(z0)) → ok(from(z0))
pi(mark(z0)) → mark(pi(z0))
pi(ok(z0)) → ok(pi(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
times(mark(z0), z1) → mark(times(z0, z1))
times(ok(z0), ok(z1)) → ok(times(z0, z1))
times(z0, mark(z1)) → mark(times(z0, z1))
square(mark(z0)) → mark(square(z0))
square(ok(z0)) → ok(square(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(posrecip(z0)) → posrecip(proper(z0))
proper(negrecip(z0)) → negrecip(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(cons2(z0, z1)) → cons2(proper(z0), proper(z1))
proper(rnil) → ok(rnil)
proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
proper(pi(z0)) → pi(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(times(z0, z1)) → times(proper(z0), proper(z1))
proper(square(z0)) → square(proper(z0))
Tuples:
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
PROPER(cons2(z0, z1)) → c68(CONS2(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(rcons(z0, z1)) → c70(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c71(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c72(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c73(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c74(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c75(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c76(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c77(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c78(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c79(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c9(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(2NDSPOS(s(z0), cons2(z1, z2)))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(2NDSNEG(s(z0), cons2(z1, z2)))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c13(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, z2)))) → c13(S(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(s(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, z2)))) → c13(S(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(s(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c13(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c13(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c13(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c13(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c13(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c13(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c13(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c13(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(cons2(z0, z1))) → c13(S(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c13(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c13(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c13(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c14(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c14(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c14(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c14(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c14(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c14(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c14(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c14(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(cons2(z0, z1))) → c14(POSRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c15(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c15(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c15(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c15(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c15(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c15(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c15(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c15(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(cons2(z0, z1))) → c15(NEGRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndspos(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndspos(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndsneg(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndsneg(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c16(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c16(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c16(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c16(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c16(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c16(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c16(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c16(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(cons2(z0, z1), x1)) → c16(CONS(cons2(z0, active(z1)), x1), ACTIVE(cons2(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, 2ndsneg(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(0, z0))) → c17(CONS2(x0, mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(cons2(x0, plus(s(z0), z1))) → c17(CONS2(x0, mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons2(x0, times(0, z0))) → c17(CONS2(x0, mark(0)), ACTIVE(times(0, z0)))
ACTIVE(cons2(x0, times(s(z0), z1))) → c17(CONS2(x0, mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(cons2(x0, s(z0))) → c17(CONS2(x0, s(active(z0))), ACTIVE(s(z0)))
ACTIVE(cons2(x0, posrecip(z0))) → c17(CONS2(x0, posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(cons2(x0, negrecip(z0))) → c17(CONS2(x0, negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(cons2(x0, cons(z0, z1))) → c17(CONS2(x0, cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(cons2(x0, cons2(z0, z1))) → c17(CONS2(x0, cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, from(active(z0))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, square(active(z0))), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c20(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(from(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(from(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c20(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c20(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c20(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c20(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c20(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c20(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c20(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c20(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c20(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c20(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(cons2(z0, z1))) → c20(FROM(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c20(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c20(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c20(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c25(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c25(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c25(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c25(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c25(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c25(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c25(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c25(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c25(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c25(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c25(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(cons2(z0, z1))) → c25(PI(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c25(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c25(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c25(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c30(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(square(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(square(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c30(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c30(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c30(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c30(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c30(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c30(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c30(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c30(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c30(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(cons2(z0, z1))) → c30(SQUARE(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c30(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c30(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c63(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c63(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c63(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c63(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(cons2(z0, z1))) → c63(S(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(s(rcons(z0, z1))) → c63(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c63(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c63(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c63(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c63(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c63(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c63(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c63(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c63(S(ok(0)))
PROPER(s(nil)) → c63(S(ok(nil)))
PROPER(s(rnil)) → c63(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c64(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c64(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c64(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c64(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(cons2(z0, z1))) → c64(POSRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c64(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c64(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c64(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c64(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c64(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c64(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c64(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c64(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c64(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c64(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c64(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c65(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c65(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c65(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c65(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(cons2(z0, z1))) → c65(NEGRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c65(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c65(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c65(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c65(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c65(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c65(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c65(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c65(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c65(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c65(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c65(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c67(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c67(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c67(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c67(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, cons2(z0, z1))) → c67(CONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c67(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c67(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c67(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c67(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c67(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c67(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c67(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c67(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c67(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c67(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c67(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c67(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(cons2(z0, z1), x1)) → c67(CONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c67(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c67(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c67(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c67(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c67(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c67(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c67(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c67(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c67(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c67(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c67(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c67(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c67(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c67(CONS(ok(rnil), proper(x1)), PROPER(x1))
S tuples:
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
PROPER(cons2(z0, z1)) → c68(CONS2(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(rcons(z0, z1)) → c70(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c71(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c72(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c73(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c74(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c75(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c76(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c77(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c78(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c79(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c9(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(2NDSPOS(s(z0), cons2(z1, z2)))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(2NDSNEG(s(z0), cons2(z1, z2)))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c13(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, z2)))) → c13(S(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(s(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, z2)))) → c13(S(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(s(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c13(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c13(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c13(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c13(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c13(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c13(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c13(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c13(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(cons2(z0, z1))) → c13(S(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c13(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c13(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c13(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c14(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c14(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c14(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c14(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c14(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c14(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c14(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c14(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(cons2(z0, z1))) → c14(POSRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c15(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c15(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c15(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c15(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c15(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c15(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c15(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c15(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(cons2(z0, z1))) → c15(NEGRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndspos(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndspos(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndsneg(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndsneg(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c16(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c16(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c16(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c16(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c16(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c16(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c16(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c16(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(cons2(z0, z1), x1)) → c16(CONS(cons2(z0, active(z1)), x1), ACTIVE(cons2(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, 2ndsneg(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(0, z0))) → c17(CONS2(x0, mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(cons2(x0, plus(s(z0), z1))) → c17(CONS2(x0, mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons2(x0, times(0, z0))) → c17(CONS2(x0, mark(0)), ACTIVE(times(0, z0)))
ACTIVE(cons2(x0, times(s(z0), z1))) → c17(CONS2(x0, mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(cons2(x0, s(z0))) → c17(CONS2(x0, s(active(z0))), ACTIVE(s(z0)))
ACTIVE(cons2(x0, posrecip(z0))) → c17(CONS2(x0, posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(cons2(x0, negrecip(z0))) → c17(CONS2(x0, negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(cons2(x0, cons(z0, z1))) → c17(CONS2(x0, cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(cons2(x0, cons2(z0, z1))) → c17(CONS2(x0, cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, from(active(z0))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, square(active(z0))), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c20(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(from(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(from(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c20(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c20(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c20(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c20(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c20(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c20(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c20(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c20(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c20(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c20(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(cons2(z0, z1))) → c20(FROM(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c20(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c20(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c20(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c25(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c25(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c25(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c25(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c25(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c25(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c25(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c25(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c25(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c25(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c25(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(cons2(z0, z1))) → c25(PI(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c25(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c25(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c25(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c30(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(square(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(square(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c30(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c30(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c30(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c30(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c30(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c30(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c30(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c30(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c30(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(cons2(z0, z1))) → c30(SQUARE(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c30(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c30(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c63(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c63(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c63(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c63(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(cons2(z0, z1))) → c63(S(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(s(rcons(z0, z1))) → c63(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c63(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c63(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c63(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c63(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c63(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c63(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c63(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c63(S(ok(0)))
PROPER(s(nil)) → c63(S(ok(nil)))
PROPER(s(rnil)) → c63(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c64(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c64(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c64(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c64(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(cons2(z0, z1))) → c64(POSRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c64(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c64(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c64(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c64(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c64(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c64(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c64(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c64(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c64(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c64(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c64(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c65(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c65(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c65(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c65(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(cons2(z0, z1))) → c65(NEGRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c65(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c65(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c65(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c65(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c65(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c65(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c65(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c65(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c65(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c65(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c65(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c67(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c67(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c67(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c67(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, cons2(z0, z1))) → c67(CONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c67(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c67(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c67(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c67(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c67(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c67(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c67(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c67(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c67(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c67(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c67(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c67(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(cons2(z0, z1), x1)) → c67(CONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c67(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c67(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c67(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c67(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c67(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c67(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c67(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c67(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c67(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c67(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c67(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c67(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c67(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c67(CONS(ok(rnil), proper(x1)), PROPER(x1))
K tuples:none
Defined Rule Symbols:
active, 2ndspos, cons2, rcons, posrecip, 2ndsneg, negrecip, s, cons, from, pi, plus, times, square, proper
Defined Pair Symbols:
ACTIVE, S, POSRECIP, NEGRECIP, CONS, CONS2, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP
Compound Symbols:
c12, c18, c19, c21, c22, c23, c24, c26, c27, c28, c29, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c68, c70, c71, c72, c73, c74, c75, c76, c77, c78, c79, c, c7, c9, c11, c1, c13, c14, c15, c16, c17, c20, c25, c30, c63, c63, c64, c64, c65, c65, c67, c67
(43) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
PROPER(
cons2(
z0,
z1)) →
c68(
CONS2(
proper(
z0),
proper(
z1)),
PROPER(
z0),
PROPER(
z1)) by
PROPER(cons2(x0, 0)) → c68(CONS2(proper(x0), ok(0)), PROPER(x0), PROPER(0))
PROPER(cons2(x0, s(z0))) → c68(CONS2(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons2(x0, posrecip(z0))) → c68(CONS2(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons2(x0, negrecip(z0))) → c68(CONS2(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons2(x0, nil)) → c68(CONS2(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
PROPER(cons2(x0, cons(z0, z1))) → c68(CONS2(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons2(x0, cons2(z0, z1))) → c68(CONS2(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons2(x0, rnil)) → c68(CONS2(proper(x0), ok(rnil)), PROPER(x0), PROPER(rnil))
PROPER(cons2(x0, rcons(z0, z1))) → c68(CONS2(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons2(x0, from(z0))) → c68(CONS2(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons2(x0, 2ndspos(z0, z1))) → c68(CONS2(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons2(x0, 2ndsneg(z0, z1))) → c68(CONS2(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons2(x0, pi(z0))) → c68(CONS2(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons2(x0, plus(z0, z1))) → c68(CONS2(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons2(x0, times(z0, z1))) → c68(CONS2(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons2(x0, square(z0))) → c68(CONS2(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons2(0, x1)) → c68(CONS2(ok(0), proper(x1)), PROPER(0), PROPER(x1))
PROPER(cons2(s(z0), x1)) → c68(CONS2(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons2(posrecip(z0), x1)) → c68(CONS2(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons2(negrecip(z0), x1)) → c68(CONS2(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons2(nil, x1)) → c68(CONS2(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
PROPER(cons2(cons(z0, z1), x1)) → c68(CONS2(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons2(cons2(z0, z1), x1)) → c68(CONS2(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons2(rnil, x1)) → c68(CONS2(ok(rnil), proper(x1)), PROPER(rnil), PROPER(x1))
PROPER(cons2(rcons(z0, z1), x1)) → c68(CONS2(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons2(from(z0), x1)) → c68(CONS2(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons2(2ndspos(z0, z1), x1)) → c68(CONS2(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons2(2ndsneg(z0, z1), x1)) → c68(CONS2(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons2(pi(z0), x1)) → c68(CONS2(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons2(plus(z0, z1), x1)) → c68(CONS2(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons2(times(z0, z1), x1)) → c68(CONS2(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons2(square(z0), x1)) → c68(CONS2(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
(44) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(2ndspos(0, z0)) → mark(rnil)
active(2ndspos(s(z0), cons(z1, z2))) → mark(2ndspos(s(z0), cons2(z1, z2)))
active(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(z1, z2))) → mark(2ndsneg(s(z0), cons2(z1, z2)))
active(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
active(pi(z0)) → mark(2ndspos(z0, from(0)))
active(plus(0, z0)) → mark(z0)
active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
active(times(0, z0)) → mark(0)
active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
active(square(z0)) → mark(times(z0, z0))
active(s(z0)) → s(active(z0))
active(posrecip(z0)) → posrecip(active(z0))
active(negrecip(z0)) → negrecip(active(z0))
active(cons(z0, z1)) → cons(active(z0), z1)
active(cons2(z0, z1)) → cons2(z0, active(z1))
active(rcons(z0, z1)) → rcons(active(z0), z1)
active(rcons(z0, z1)) → rcons(z0, active(z1))
active(from(z0)) → from(active(z0))
active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
active(pi(z0)) → pi(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(times(z0, z1)) → times(active(z0), z1)
active(times(z0, z1)) → times(z0, active(z1))
active(square(z0)) → square(active(z0))
2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
cons2(z0, mark(z1)) → mark(cons2(z0, z1))
cons2(ok(z0), ok(z1)) → ok(cons2(z0, z1))
rcons(mark(z0), z1) → mark(rcons(z0, z1))
rcons(z0, mark(z1)) → mark(rcons(z0, z1))
rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
posrecip(ok(z0)) → ok(posrecip(z0))
posrecip(mark(z0)) → mark(posrecip(z0))
2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
negrecip(ok(z0)) → ok(negrecip(z0))
negrecip(mark(z0)) → mark(negrecip(z0))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
cons(mark(z0), z1) → mark(cons(z0, z1))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
from(mark(z0)) → mark(from(z0))
from(ok(z0)) → ok(from(z0))
pi(mark(z0)) → mark(pi(z0))
pi(ok(z0)) → ok(pi(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
times(mark(z0), z1) → mark(times(z0, z1))
times(ok(z0), ok(z1)) → ok(times(z0, z1))
times(z0, mark(z1)) → mark(times(z0, z1))
square(mark(z0)) → mark(square(z0))
square(ok(z0)) → ok(square(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(posrecip(z0)) → posrecip(proper(z0))
proper(negrecip(z0)) → negrecip(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(cons2(z0, z1)) → cons2(proper(z0), proper(z1))
proper(rnil) → ok(rnil)
proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
proper(pi(z0)) → pi(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(times(z0, z1)) → times(proper(z0), proper(z1))
proper(square(z0)) → square(proper(z0))
Tuples:
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
PROPER(rcons(z0, z1)) → c70(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c71(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c72(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c73(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c74(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c75(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c76(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c77(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c78(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c79(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c9(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(2NDSPOS(s(z0), cons2(z1, z2)))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(2NDSNEG(s(z0), cons2(z1, z2)))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c13(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, z2)))) → c13(S(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(s(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, z2)))) → c13(S(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(s(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c13(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c13(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c13(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c13(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c13(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c13(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c13(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c13(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(cons2(z0, z1))) → c13(S(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c13(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c13(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c13(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c14(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c14(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c14(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c14(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c14(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c14(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c14(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c14(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(cons2(z0, z1))) → c14(POSRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c15(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c15(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c15(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c15(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c15(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c15(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c15(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c15(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(cons2(z0, z1))) → c15(NEGRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndspos(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndspos(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndsneg(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndsneg(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c16(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c16(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c16(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c16(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c16(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c16(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c16(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c16(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(cons2(z0, z1), x1)) → c16(CONS(cons2(z0, active(z1)), x1), ACTIVE(cons2(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, 2ndsneg(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(0, z0))) → c17(CONS2(x0, mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(cons2(x0, plus(s(z0), z1))) → c17(CONS2(x0, mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons2(x0, times(0, z0))) → c17(CONS2(x0, mark(0)), ACTIVE(times(0, z0)))
ACTIVE(cons2(x0, times(s(z0), z1))) → c17(CONS2(x0, mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(cons2(x0, s(z0))) → c17(CONS2(x0, s(active(z0))), ACTIVE(s(z0)))
ACTIVE(cons2(x0, posrecip(z0))) → c17(CONS2(x0, posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(cons2(x0, negrecip(z0))) → c17(CONS2(x0, negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(cons2(x0, cons(z0, z1))) → c17(CONS2(x0, cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(cons2(x0, cons2(z0, z1))) → c17(CONS2(x0, cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, from(active(z0))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, square(active(z0))), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c20(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(from(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(from(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c20(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c20(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c20(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c20(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c20(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c20(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c20(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c20(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c20(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c20(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(cons2(z0, z1))) → c20(FROM(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c20(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c20(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c20(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c25(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c25(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c25(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c25(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c25(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c25(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c25(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c25(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c25(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c25(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c25(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(cons2(z0, z1))) → c25(PI(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c25(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c25(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c25(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c30(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(square(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(square(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c30(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c30(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c30(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c30(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c30(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c30(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c30(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c30(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c30(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(cons2(z0, z1))) → c30(SQUARE(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c30(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c30(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c63(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c63(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c63(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c63(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(cons2(z0, z1))) → c63(S(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(s(rcons(z0, z1))) → c63(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c63(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c63(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c63(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c63(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c63(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c63(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c63(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c63(S(ok(0)))
PROPER(s(nil)) → c63(S(ok(nil)))
PROPER(s(rnil)) → c63(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c64(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c64(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c64(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c64(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(cons2(z0, z1))) → c64(POSRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c64(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c64(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c64(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c64(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c64(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c64(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c64(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c64(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c64(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c64(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c64(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c65(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c65(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c65(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c65(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(cons2(z0, z1))) → c65(NEGRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c65(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c65(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c65(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c65(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c65(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c65(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c65(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c65(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c65(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c65(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c65(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c67(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c67(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c67(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c67(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, cons2(z0, z1))) → c67(CONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c67(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c67(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c67(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c67(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c67(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c67(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c67(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c67(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c67(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c67(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c67(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c67(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(cons2(z0, z1), x1)) → c67(CONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c67(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c67(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c67(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c67(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c67(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c67(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c67(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c67(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c67(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c67(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c67(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c67(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c67(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c67(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(cons2(x0, 0)) → c68(CONS2(proper(x0), ok(0)), PROPER(x0), PROPER(0))
PROPER(cons2(x0, s(z0))) → c68(CONS2(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons2(x0, posrecip(z0))) → c68(CONS2(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons2(x0, negrecip(z0))) → c68(CONS2(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons2(x0, nil)) → c68(CONS2(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
PROPER(cons2(x0, cons(z0, z1))) → c68(CONS2(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons2(x0, cons2(z0, z1))) → c68(CONS2(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons2(x0, rnil)) → c68(CONS2(proper(x0), ok(rnil)), PROPER(x0), PROPER(rnil))
PROPER(cons2(x0, rcons(z0, z1))) → c68(CONS2(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons2(x0, from(z0))) → c68(CONS2(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons2(x0, 2ndspos(z0, z1))) → c68(CONS2(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons2(x0, 2ndsneg(z0, z1))) → c68(CONS2(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons2(x0, pi(z0))) → c68(CONS2(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons2(x0, plus(z0, z1))) → c68(CONS2(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons2(x0, times(z0, z1))) → c68(CONS2(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons2(x0, square(z0))) → c68(CONS2(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons2(0, x1)) → c68(CONS2(ok(0), proper(x1)), PROPER(0), PROPER(x1))
PROPER(cons2(s(z0), x1)) → c68(CONS2(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons2(posrecip(z0), x1)) → c68(CONS2(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons2(negrecip(z0), x1)) → c68(CONS2(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons2(nil, x1)) → c68(CONS2(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
PROPER(cons2(cons(z0, z1), x1)) → c68(CONS2(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons2(cons2(z0, z1), x1)) → c68(CONS2(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons2(rnil, x1)) → c68(CONS2(ok(rnil), proper(x1)), PROPER(rnil), PROPER(x1))
PROPER(cons2(rcons(z0, z1), x1)) → c68(CONS2(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons2(from(z0), x1)) → c68(CONS2(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons2(2ndspos(z0, z1), x1)) → c68(CONS2(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons2(2ndsneg(z0, z1), x1)) → c68(CONS2(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons2(pi(z0), x1)) → c68(CONS2(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons2(plus(z0, z1), x1)) → c68(CONS2(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons2(times(z0, z1), x1)) → c68(CONS2(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons2(square(z0), x1)) → c68(CONS2(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
S tuples:
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
PROPER(rcons(z0, z1)) → c70(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c71(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c72(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c73(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c74(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c75(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c76(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c77(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c78(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c79(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c9(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(2NDSPOS(s(z0), cons2(z1, z2)))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(2NDSNEG(s(z0), cons2(z1, z2)))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c13(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, z2)))) → c13(S(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(s(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, z2)))) → c13(S(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(s(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c13(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c13(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c13(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c13(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c13(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c13(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c13(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c13(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(cons2(z0, z1))) → c13(S(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c13(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c13(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c13(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c14(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c14(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c14(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c14(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c14(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c14(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c14(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c14(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(cons2(z0, z1))) → c14(POSRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c15(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c15(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c15(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c15(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c15(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c15(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c15(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c15(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(cons2(z0, z1))) → c15(NEGRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndspos(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndspos(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndsneg(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndsneg(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c16(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c16(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c16(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c16(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c16(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c16(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c16(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c16(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(cons2(z0, z1), x1)) → c16(CONS(cons2(z0, active(z1)), x1), ACTIVE(cons2(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, 2ndsneg(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(0, z0))) → c17(CONS2(x0, mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(cons2(x0, plus(s(z0), z1))) → c17(CONS2(x0, mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons2(x0, times(0, z0))) → c17(CONS2(x0, mark(0)), ACTIVE(times(0, z0)))
ACTIVE(cons2(x0, times(s(z0), z1))) → c17(CONS2(x0, mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(cons2(x0, s(z0))) → c17(CONS2(x0, s(active(z0))), ACTIVE(s(z0)))
ACTIVE(cons2(x0, posrecip(z0))) → c17(CONS2(x0, posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(cons2(x0, negrecip(z0))) → c17(CONS2(x0, negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(cons2(x0, cons(z0, z1))) → c17(CONS2(x0, cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(cons2(x0, cons2(z0, z1))) → c17(CONS2(x0, cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, from(active(z0))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, square(active(z0))), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c20(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(from(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(from(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c20(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c20(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c20(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c20(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c20(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c20(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c20(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c20(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c20(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c20(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(cons2(z0, z1))) → c20(FROM(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c20(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c20(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c20(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c25(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c25(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c25(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c25(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c25(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c25(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c25(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c25(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c25(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c25(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c25(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(cons2(z0, z1))) → c25(PI(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c25(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c25(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c25(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c30(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(square(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(square(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c30(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c30(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c30(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c30(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c30(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c30(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c30(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c30(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c30(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(cons2(z0, z1))) → c30(SQUARE(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c30(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c30(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c63(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c63(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c63(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c63(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(cons2(z0, z1))) → c63(S(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(s(rcons(z0, z1))) → c63(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c63(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c63(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c63(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c63(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c63(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c63(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c63(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c63(S(ok(0)))
PROPER(s(nil)) → c63(S(ok(nil)))
PROPER(s(rnil)) → c63(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c64(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c64(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c64(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c64(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(cons2(z0, z1))) → c64(POSRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c64(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c64(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c64(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c64(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c64(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c64(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c64(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c64(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c64(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c64(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c64(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c65(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c65(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c65(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c65(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(cons2(z0, z1))) → c65(NEGRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c65(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c65(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c65(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c65(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c65(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c65(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c65(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c65(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c65(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c65(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c65(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c67(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c67(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c67(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c67(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, cons2(z0, z1))) → c67(CONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c67(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c67(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c67(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c67(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c67(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c67(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c67(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c67(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c67(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c67(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c67(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c67(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(cons2(z0, z1), x1)) → c67(CONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c67(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c67(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c67(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c67(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c67(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c67(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c67(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c67(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c67(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c67(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c67(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c67(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c67(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c67(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(cons2(x0, 0)) → c68(CONS2(proper(x0), ok(0)), PROPER(x0), PROPER(0))
PROPER(cons2(x0, s(z0))) → c68(CONS2(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons2(x0, posrecip(z0))) → c68(CONS2(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons2(x0, negrecip(z0))) → c68(CONS2(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons2(x0, nil)) → c68(CONS2(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
PROPER(cons2(x0, cons(z0, z1))) → c68(CONS2(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons2(x0, cons2(z0, z1))) → c68(CONS2(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons2(x0, rnil)) → c68(CONS2(proper(x0), ok(rnil)), PROPER(x0), PROPER(rnil))
PROPER(cons2(x0, rcons(z0, z1))) → c68(CONS2(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons2(x0, from(z0))) → c68(CONS2(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons2(x0, 2ndspos(z0, z1))) → c68(CONS2(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons2(x0, 2ndsneg(z0, z1))) → c68(CONS2(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons2(x0, pi(z0))) → c68(CONS2(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons2(x0, plus(z0, z1))) → c68(CONS2(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons2(x0, times(z0, z1))) → c68(CONS2(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons2(x0, square(z0))) → c68(CONS2(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons2(0, x1)) → c68(CONS2(ok(0), proper(x1)), PROPER(0), PROPER(x1))
PROPER(cons2(s(z0), x1)) → c68(CONS2(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons2(posrecip(z0), x1)) → c68(CONS2(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons2(negrecip(z0), x1)) → c68(CONS2(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons2(nil, x1)) → c68(CONS2(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
PROPER(cons2(cons(z0, z1), x1)) → c68(CONS2(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons2(cons2(z0, z1), x1)) → c68(CONS2(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons2(rnil, x1)) → c68(CONS2(ok(rnil), proper(x1)), PROPER(rnil), PROPER(x1))
PROPER(cons2(rcons(z0, z1), x1)) → c68(CONS2(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons2(from(z0), x1)) → c68(CONS2(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons2(2ndspos(z0, z1), x1)) → c68(CONS2(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons2(2ndsneg(z0, z1), x1)) → c68(CONS2(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons2(pi(z0), x1)) → c68(CONS2(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons2(plus(z0, z1), x1)) → c68(CONS2(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons2(times(z0, z1), x1)) → c68(CONS2(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons2(square(z0), x1)) → c68(CONS2(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
K tuples:none
Defined Rule Symbols:
active, 2ndspos, cons2, rcons, posrecip, 2ndsneg, negrecip, s, cons, from, pi, plus, times, square, proper
Defined Pair Symbols:
ACTIVE, S, POSRECIP, NEGRECIP, CONS, CONS2, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP
Compound Symbols:
c12, c18, c19, c21, c22, c23, c24, c26, c27, c28, c29, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c70, c71, c72, c73, c74, c75, c76, c77, c78, c79, c, c7, c9, c11, c1, c13, c14, c15, c16, c17, c20, c25, c30, c63, c63, c64, c64, c65, c65, c67, c67, c68
(45) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 6 trailing tuple parts
(46) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(2ndspos(0, z0)) → mark(rnil)
active(2ndspos(s(z0), cons(z1, z2))) → mark(2ndspos(s(z0), cons2(z1, z2)))
active(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(z1, z2))) → mark(2ndsneg(s(z0), cons2(z1, z2)))
active(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
active(pi(z0)) → mark(2ndspos(z0, from(0)))
active(plus(0, z0)) → mark(z0)
active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
active(times(0, z0)) → mark(0)
active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
active(square(z0)) → mark(times(z0, z0))
active(s(z0)) → s(active(z0))
active(posrecip(z0)) → posrecip(active(z0))
active(negrecip(z0)) → negrecip(active(z0))
active(cons(z0, z1)) → cons(active(z0), z1)
active(cons2(z0, z1)) → cons2(z0, active(z1))
active(rcons(z0, z1)) → rcons(active(z0), z1)
active(rcons(z0, z1)) → rcons(z0, active(z1))
active(from(z0)) → from(active(z0))
active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
active(pi(z0)) → pi(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(times(z0, z1)) → times(active(z0), z1)
active(times(z0, z1)) → times(z0, active(z1))
active(square(z0)) → square(active(z0))
2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
cons2(z0, mark(z1)) → mark(cons2(z0, z1))
cons2(ok(z0), ok(z1)) → ok(cons2(z0, z1))
rcons(mark(z0), z1) → mark(rcons(z0, z1))
rcons(z0, mark(z1)) → mark(rcons(z0, z1))
rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
posrecip(ok(z0)) → ok(posrecip(z0))
posrecip(mark(z0)) → mark(posrecip(z0))
2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
negrecip(ok(z0)) → ok(negrecip(z0))
negrecip(mark(z0)) → mark(negrecip(z0))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
cons(mark(z0), z1) → mark(cons(z0, z1))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
from(mark(z0)) → mark(from(z0))
from(ok(z0)) → ok(from(z0))
pi(mark(z0)) → mark(pi(z0))
pi(ok(z0)) → ok(pi(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
times(mark(z0), z1) → mark(times(z0, z1))
times(ok(z0), ok(z1)) → ok(times(z0, z1))
times(z0, mark(z1)) → mark(times(z0, z1))
square(mark(z0)) → mark(square(z0))
square(ok(z0)) → ok(square(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(posrecip(z0)) → posrecip(proper(z0))
proper(negrecip(z0)) → negrecip(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(cons2(z0, z1)) → cons2(proper(z0), proper(z1))
proper(rnil) → ok(rnil)
proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
proper(pi(z0)) → pi(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(times(z0, z1)) → times(proper(z0), proper(z1))
proper(square(z0)) → square(proper(z0))
Tuples:
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
PROPER(rcons(z0, z1)) → c70(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c71(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c72(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c73(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c74(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c75(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c76(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c77(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c78(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c79(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c9(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(2NDSPOS(s(z0), cons2(z1, z2)))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(2NDSNEG(s(z0), cons2(z1, z2)))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c13(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, z2)))) → c13(S(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(s(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, z2)))) → c13(S(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(s(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c13(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c13(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c13(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c13(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c13(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c13(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c13(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c13(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(cons2(z0, z1))) → c13(S(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c13(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c13(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c13(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c14(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c14(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c14(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c14(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c14(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c14(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c14(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c14(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(cons2(z0, z1))) → c14(POSRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c15(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c15(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c15(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c15(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c15(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c15(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c15(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c15(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(cons2(z0, z1))) → c15(NEGRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndspos(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndspos(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndsneg(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndsneg(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c16(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c16(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c16(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c16(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c16(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c16(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c16(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c16(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(cons2(z0, z1), x1)) → c16(CONS(cons2(z0, active(z1)), x1), ACTIVE(cons2(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, 2ndsneg(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(0, z0))) → c17(CONS2(x0, mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(cons2(x0, plus(s(z0), z1))) → c17(CONS2(x0, mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons2(x0, times(0, z0))) → c17(CONS2(x0, mark(0)), ACTIVE(times(0, z0)))
ACTIVE(cons2(x0, times(s(z0), z1))) → c17(CONS2(x0, mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(cons2(x0, s(z0))) → c17(CONS2(x0, s(active(z0))), ACTIVE(s(z0)))
ACTIVE(cons2(x0, posrecip(z0))) → c17(CONS2(x0, posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(cons2(x0, negrecip(z0))) → c17(CONS2(x0, negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(cons2(x0, cons(z0, z1))) → c17(CONS2(x0, cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(cons2(x0, cons2(z0, z1))) → c17(CONS2(x0, cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, from(active(z0))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, square(active(z0))), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c20(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(from(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(from(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c20(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c20(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c20(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c20(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c20(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c20(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c20(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c20(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c20(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c20(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(cons2(z0, z1))) → c20(FROM(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c20(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c20(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c20(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c25(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c25(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c25(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c25(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c25(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c25(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c25(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c25(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c25(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c25(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c25(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(cons2(z0, z1))) → c25(PI(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c25(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c25(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c25(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c30(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(square(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(square(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c30(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c30(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c30(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c30(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c30(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c30(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c30(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c30(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c30(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(cons2(z0, z1))) → c30(SQUARE(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c30(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c30(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c63(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c63(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c63(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c63(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(cons2(z0, z1))) → c63(S(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(s(rcons(z0, z1))) → c63(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c63(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c63(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c63(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c63(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c63(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c63(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c63(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c63(S(ok(0)))
PROPER(s(nil)) → c63(S(ok(nil)))
PROPER(s(rnil)) → c63(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c64(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c64(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c64(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c64(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(cons2(z0, z1))) → c64(POSRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c64(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c64(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c64(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c64(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c64(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c64(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c64(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c64(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c64(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c64(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c64(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c65(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c65(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c65(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c65(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(cons2(z0, z1))) → c65(NEGRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c65(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c65(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c65(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c65(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c65(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c65(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c65(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c65(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c65(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c65(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c65(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c67(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c67(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c67(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c67(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, cons2(z0, z1))) → c67(CONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c67(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c67(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c67(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c67(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c67(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c67(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c67(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c67(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c67(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c67(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c67(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c67(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(cons2(z0, z1), x1)) → c67(CONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c67(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c67(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c67(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c67(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c67(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c67(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c67(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c67(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c67(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c67(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c67(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c67(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c67(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c67(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(cons2(x0, s(z0))) → c68(CONS2(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons2(x0, posrecip(z0))) → c68(CONS2(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons2(x0, negrecip(z0))) → c68(CONS2(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons2(x0, cons(z0, z1))) → c68(CONS2(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons2(x0, cons2(z0, z1))) → c68(CONS2(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons2(x0, rcons(z0, z1))) → c68(CONS2(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons2(x0, from(z0))) → c68(CONS2(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons2(x0, 2ndspos(z0, z1))) → c68(CONS2(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons2(x0, 2ndsneg(z0, z1))) → c68(CONS2(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons2(x0, pi(z0))) → c68(CONS2(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons2(x0, plus(z0, z1))) → c68(CONS2(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons2(x0, times(z0, z1))) → c68(CONS2(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons2(x0, square(z0))) → c68(CONS2(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons2(s(z0), x1)) → c68(CONS2(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons2(posrecip(z0), x1)) → c68(CONS2(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons2(negrecip(z0), x1)) → c68(CONS2(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons2(cons(z0, z1), x1)) → c68(CONS2(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons2(cons2(z0, z1), x1)) → c68(CONS2(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons2(rcons(z0, z1), x1)) → c68(CONS2(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons2(from(z0), x1)) → c68(CONS2(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons2(2ndspos(z0, z1), x1)) → c68(CONS2(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons2(2ndsneg(z0, z1), x1)) → c68(CONS2(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons2(pi(z0), x1)) → c68(CONS2(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons2(plus(z0, z1), x1)) → c68(CONS2(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons2(times(z0, z1), x1)) → c68(CONS2(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons2(square(z0), x1)) → c68(CONS2(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons2(x0, 0)) → c68(CONS2(proper(x0), ok(0)), PROPER(x0))
PROPER(cons2(x0, nil)) → c68(CONS2(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons2(x0, rnil)) → c68(CONS2(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons2(0, x1)) → c68(CONS2(ok(0), proper(x1)), PROPER(x1))
PROPER(cons2(nil, x1)) → c68(CONS2(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons2(rnil, x1)) → c68(CONS2(ok(rnil), proper(x1)), PROPER(x1))
S tuples:
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
PROPER(rcons(z0, z1)) → c70(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c71(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c72(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c73(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c74(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c75(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c76(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c77(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c78(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c79(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c9(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(2NDSPOS(s(z0), cons2(z1, z2)))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(2NDSNEG(s(z0), cons2(z1, z2)))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c13(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, z2)))) → c13(S(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(s(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, z2)))) → c13(S(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(s(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c13(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c13(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c13(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c13(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c13(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c13(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c13(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c13(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(cons2(z0, z1))) → c13(S(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c13(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c13(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c13(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c14(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c14(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c14(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c14(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c14(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c14(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c14(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c14(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(cons2(z0, z1))) → c14(POSRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c15(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c15(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c15(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c15(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c15(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c15(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c15(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c15(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(cons2(z0, z1))) → c15(NEGRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndspos(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndspos(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndsneg(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndsneg(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c16(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c16(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c16(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c16(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c16(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c16(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c16(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c16(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(cons2(z0, z1), x1)) → c16(CONS(cons2(z0, active(z1)), x1), ACTIVE(cons2(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, 2ndsneg(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(0, z0))) → c17(CONS2(x0, mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(cons2(x0, plus(s(z0), z1))) → c17(CONS2(x0, mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons2(x0, times(0, z0))) → c17(CONS2(x0, mark(0)), ACTIVE(times(0, z0)))
ACTIVE(cons2(x0, times(s(z0), z1))) → c17(CONS2(x0, mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(cons2(x0, s(z0))) → c17(CONS2(x0, s(active(z0))), ACTIVE(s(z0)))
ACTIVE(cons2(x0, posrecip(z0))) → c17(CONS2(x0, posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(cons2(x0, negrecip(z0))) → c17(CONS2(x0, negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(cons2(x0, cons(z0, z1))) → c17(CONS2(x0, cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(cons2(x0, cons2(z0, z1))) → c17(CONS2(x0, cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, from(active(z0))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, square(active(z0))), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c20(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(from(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(from(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c20(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c20(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c20(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c20(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c20(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c20(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c20(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c20(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c20(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c20(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(cons2(z0, z1))) → c20(FROM(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c20(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c20(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c20(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c25(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c25(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c25(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c25(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c25(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c25(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c25(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c25(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c25(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c25(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c25(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(cons2(z0, z1))) → c25(PI(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c25(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c25(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c25(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c30(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(square(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(square(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c30(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c30(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c30(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c30(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c30(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c30(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c30(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c30(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c30(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(cons2(z0, z1))) → c30(SQUARE(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c30(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c30(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c63(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c63(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c63(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c63(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(cons2(z0, z1))) → c63(S(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(s(rcons(z0, z1))) → c63(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c63(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c63(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c63(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c63(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c63(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c63(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c63(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c63(S(ok(0)))
PROPER(s(nil)) → c63(S(ok(nil)))
PROPER(s(rnil)) → c63(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c64(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c64(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c64(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c64(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(cons2(z0, z1))) → c64(POSRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c64(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c64(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c64(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c64(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c64(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c64(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c64(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c64(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c64(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c64(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c64(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c65(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c65(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c65(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c65(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(cons2(z0, z1))) → c65(NEGRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c65(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c65(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c65(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c65(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c65(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c65(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c65(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c65(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c65(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c65(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c65(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c67(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c67(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c67(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c67(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, cons2(z0, z1))) → c67(CONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c67(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c67(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c67(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c67(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c67(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c67(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c67(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c67(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c67(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c67(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c67(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c67(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(cons2(z0, z1), x1)) → c67(CONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c67(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c67(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c67(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c67(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c67(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c67(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c67(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c67(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c67(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c67(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c67(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c67(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c67(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c67(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(cons2(x0, s(z0))) → c68(CONS2(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons2(x0, posrecip(z0))) → c68(CONS2(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons2(x0, negrecip(z0))) → c68(CONS2(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons2(x0, cons(z0, z1))) → c68(CONS2(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons2(x0, cons2(z0, z1))) → c68(CONS2(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons2(x0, rcons(z0, z1))) → c68(CONS2(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons2(x0, from(z0))) → c68(CONS2(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons2(x0, 2ndspos(z0, z1))) → c68(CONS2(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons2(x0, 2ndsneg(z0, z1))) → c68(CONS2(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons2(x0, pi(z0))) → c68(CONS2(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons2(x0, plus(z0, z1))) → c68(CONS2(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons2(x0, times(z0, z1))) → c68(CONS2(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons2(x0, square(z0))) → c68(CONS2(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons2(s(z0), x1)) → c68(CONS2(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons2(posrecip(z0), x1)) → c68(CONS2(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons2(negrecip(z0), x1)) → c68(CONS2(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons2(cons(z0, z1), x1)) → c68(CONS2(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons2(cons2(z0, z1), x1)) → c68(CONS2(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons2(rcons(z0, z1), x1)) → c68(CONS2(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons2(from(z0), x1)) → c68(CONS2(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons2(2ndspos(z0, z1), x1)) → c68(CONS2(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons2(2ndsneg(z0, z1), x1)) → c68(CONS2(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons2(pi(z0), x1)) → c68(CONS2(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons2(plus(z0, z1), x1)) → c68(CONS2(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons2(times(z0, z1), x1)) → c68(CONS2(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons2(square(z0), x1)) → c68(CONS2(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons2(x0, 0)) → c68(CONS2(proper(x0), ok(0)), PROPER(x0))
PROPER(cons2(x0, nil)) → c68(CONS2(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons2(x0, rnil)) → c68(CONS2(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons2(0, x1)) → c68(CONS2(ok(0), proper(x1)), PROPER(x1))
PROPER(cons2(nil, x1)) → c68(CONS2(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons2(rnil, x1)) → c68(CONS2(ok(rnil), proper(x1)), PROPER(x1))
K tuples:none
Defined Rule Symbols:
active, 2ndspos, cons2, rcons, posrecip, 2ndsneg, negrecip, s, cons, from, pi, plus, times, square, proper
Defined Pair Symbols:
ACTIVE, S, POSRECIP, NEGRECIP, CONS, CONS2, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP
Compound Symbols:
c12, c18, c19, c21, c22, c23, c24, c26, c27, c28, c29, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c70, c71, c72, c73, c74, c75, c76, c77, c78, c79, c, c7, c9, c11, c1, c13, c14, c15, c16, c17, c20, c25, c30, c63, c63, c64, c64, c65, c65, c67, c67, c68, c68
(47) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
PROPER(
rcons(
z0,
z1)) →
c70(
RCONS(
proper(
z0),
proper(
z1)),
PROPER(
z0),
PROPER(
z1)) by
PROPER(rcons(x0, 0)) → c70(RCONS(proper(x0), ok(0)), PROPER(x0), PROPER(0))
PROPER(rcons(x0, s(z0))) → c70(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c70(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c70(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, nil)) → c70(RCONS(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
PROPER(rcons(x0, cons(z0, z1))) → c70(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, cons2(z0, z1))) → c70(RCONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(rcons(x0, rnil)) → c70(RCONS(proper(x0), ok(rnil)), PROPER(x0), PROPER(rnil))
PROPER(rcons(x0, rcons(z0, z1))) → c70(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c70(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c70(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c70(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c70(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c70(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c70(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c70(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(0, x1)) → c70(RCONS(ok(0), proper(x1)), PROPER(0), PROPER(x1))
PROPER(rcons(s(z0), x1)) → c70(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c70(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c70(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(nil, x1)) → c70(RCONS(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c70(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(cons2(z0, z1), x1)) → c70(RCONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c70(RCONS(ok(rnil), proper(x1)), PROPER(rnil), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c70(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c70(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c70(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c70(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c70(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c70(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c70(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c70(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
(48) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(2ndspos(0, z0)) → mark(rnil)
active(2ndspos(s(z0), cons(z1, z2))) → mark(2ndspos(s(z0), cons2(z1, z2)))
active(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(z1, z2))) → mark(2ndsneg(s(z0), cons2(z1, z2)))
active(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
active(pi(z0)) → mark(2ndspos(z0, from(0)))
active(plus(0, z0)) → mark(z0)
active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
active(times(0, z0)) → mark(0)
active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
active(square(z0)) → mark(times(z0, z0))
active(s(z0)) → s(active(z0))
active(posrecip(z0)) → posrecip(active(z0))
active(negrecip(z0)) → negrecip(active(z0))
active(cons(z0, z1)) → cons(active(z0), z1)
active(cons2(z0, z1)) → cons2(z0, active(z1))
active(rcons(z0, z1)) → rcons(active(z0), z1)
active(rcons(z0, z1)) → rcons(z0, active(z1))
active(from(z0)) → from(active(z0))
active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
active(pi(z0)) → pi(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(times(z0, z1)) → times(active(z0), z1)
active(times(z0, z1)) → times(z0, active(z1))
active(square(z0)) → square(active(z0))
2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
cons2(z0, mark(z1)) → mark(cons2(z0, z1))
cons2(ok(z0), ok(z1)) → ok(cons2(z0, z1))
rcons(mark(z0), z1) → mark(rcons(z0, z1))
rcons(z0, mark(z1)) → mark(rcons(z0, z1))
rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
posrecip(ok(z0)) → ok(posrecip(z0))
posrecip(mark(z0)) → mark(posrecip(z0))
2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
negrecip(ok(z0)) → ok(negrecip(z0))
negrecip(mark(z0)) → mark(negrecip(z0))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
cons(mark(z0), z1) → mark(cons(z0, z1))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
from(mark(z0)) → mark(from(z0))
from(ok(z0)) → ok(from(z0))
pi(mark(z0)) → mark(pi(z0))
pi(ok(z0)) → ok(pi(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
times(mark(z0), z1) → mark(times(z0, z1))
times(ok(z0), ok(z1)) → ok(times(z0, z1))
times(z0, mark(z1)) → mark(times(z0, z1))
square(mark(z0)) → mark(square(z0))
square(ok(z0)) → ok(square(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(posrecip(z0)) → posrecip(proper(z0))
proper(negrecip(z0)) → negrecip(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(cons2(z0, z1)) → cons2(proper(z0), proper(z1))
proper(rnil) → ok(rnil)
proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
proper(pi(z0)) → pi(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(times(z0, z1)) → times(proper(z0), proper(z1))
proper(square(z0)) → square(proper(z0))
Tuples:
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
PROPER(from(z0)) → c71(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c72(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c73(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c74(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c75(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c76(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c77(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c78(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c79(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c9(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(2NDSPOS(s(z0), cons2(z1, z2)))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(2NDSNEG(s(z0), cons2(z1, z2)))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c13(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, z2)))) → c13(S(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(s(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, z2)))) → c13(S(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(s(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c13(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c13(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c13(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c13(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c13(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c13(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c13(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c13(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(cons2(z0, z1))) → c13(S(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c13(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c13(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c13(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c14(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c14(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c14(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c14(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c14(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c14(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c14(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c14(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(cons2(z0, z1))) → c14(POSRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c15(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c15(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c15(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c15(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c15(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c15(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c15(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c15(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(cons2(z0, z1))) → c15(NEGRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndspos(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndspos(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndsneg(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndsneg(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c16(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c16(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c16(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c16(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c16(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c16(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c16(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c16(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(cons2(z0, z1), x1)) → c16(CONS(cons2(z0, active(z1)), x1), ACTIVE(cons2(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, 2ndsneg(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(0, z0))) → c17(CONS2(x0, mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(cons2(x0, plus(s(z0), z1))) → c17(CONS2(x0, mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons2(x0, times(0, z0))) → c17(CONS2(x0, mark(0)), ACTIVE(times(0, z0)))
ACTIVE(cons2(x0, times(s(z0), z1))) → c17(CONS2(x0, mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(cons2(x0, s(z0))) → c17(CONS2(x0, s(active(z0))), ACTIVE(s(z0)))
ACTIVE(cons2(x0, posrecip(z0))) → c17(CONS2(x0, posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(cons2(x0, negrecip(z0))) → c17(CONS2(x0, negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(cons2(x0, cons(z0, z1))) → c17(CONS2(x0, cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(cons2(x0, cons2(z0, z1))) → c17(CONS2(x0, cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, from(active(z0))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, square(active(z0))), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c20(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(from(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(from(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c20(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c20(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c20(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c20(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c20(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c20(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c20(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c20(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c20(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c20(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(cons2(z0, z1))) → c20(FROM(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c20(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c20(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c20(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c25(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c25(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c25(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c25(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c25(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c25(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c25(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c25(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c25(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c25(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c25(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(cons2(z0, z1))) → c25(PI(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c25(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c25(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c25(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c30(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(square(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(square(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c30(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c30(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c30(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c30(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c30(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c30(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c30(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c30(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c30(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(cons2(z0, z1))) → c30(SQUARE(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c30(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c30(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c63(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c63(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c63(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c63(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(cons2(z0, z1))) → c63(S(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(s(rcons(z0, z1))) → c63(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c63(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c63(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c63(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c63(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c63(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c63(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c63(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c63(S(ok(0)))
PROPER(s(nil)) → c63(S(ok(nil)))
PROPER(s(rnil)) → c63(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c64(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c64(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c64(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c64(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(cons2(z0, z1))) → c64(POSRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c64(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c64(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c64(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c64(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c64(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c64(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c64(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c64(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c64(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c64(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c64(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c65(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c65(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c65(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c65(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(cons2(z0, z1))) → c65(NEGRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c65(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c65(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c65(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c65(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c65(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c65(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c65(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c65(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c65(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c65(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c65(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c67(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c67(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c67(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c67(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, cons2(z0, z1))) → c67(CONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c67(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c67(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c67(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c67(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c67(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c67(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c67(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c67(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c67(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c67(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c67(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c67(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(cons2(z0, z1), x1)) → c67(CONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c67(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c67(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c67(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c67(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c67(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c67(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c67(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c67(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c67(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c67(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c67(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c67(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c67(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c67(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(cons2(x0, s(z0))) → c68(CONS2(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons2(x0, posrecip(z0))) → c68(CONS2(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons2(x0, negrecip(z0))) → c68(CONS2(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons2(x0, cons(z0, z1))) → c68(CONS2(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons2(x0, cons2(z0, z1))) → c68(CONS2(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons2(x0, rcons(z0, z1))) → c68(CONS2(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons2(x0, from(z0))) → c68(CONS2(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons2(x0, 2ndspos(z0, z1))) → c68(CONS2(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons2(x0, 2ndsneg(z0, z1))) → c68(CONS2(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons2(x0, pi(z0))) → c68(CONS2(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons2(x0, plus(z0, z1))) → c68(CONS2(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons2(x0, times(z0, z1))) → c68(CONS2(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons2(x0, square(z0))) → c68(CONS2(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons2(s(z0), x1)) → c68(CONS2(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons2(posrecip(z0), x1)) → c68(CONS2(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons2(negrecip(z0), x1)) → c68(CONS2(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons2(cons(z0, z1), x1)) → c68(CONS2(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons2(cons2(z0, z1), x1)) → c68(CONS2(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons2(rcons(z0, z1), x1)) → c68(CONS2(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons2(from(z0), x1)) → c68(CONS2(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons2(2ndspos(z0, z1), x1)) → c68(CONS2(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons2(2ndsneg(z0, z1), x1)) → c68(CONS2(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons2(pi(z0), x1)) → c68(CONS2(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons2(plus(z0, z1), x1)) → c68(CONS2(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons2(times(z0, z1), x1)) → c68(CONS2(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons2(square(z0), x1)) → c68(CONS2(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons2(x0, 0)) → c68(CONS2(proper(x0), ok(0)), PROPER(x0))
PROPER(cons2(x0, nil)) → c68(CONS2(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons2(x0, rnil)) → c68(CONS2(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons2(0, x1)) → c68(CONS2(ok(0), proper(x1)), PROPER(x1))
PROPER(cons2(nil, x1)) → c68(CONS2(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons2(rnil, x1)) → c68(CONS2(ok(rnil), proper(x1)), PROPER(x1))
PROPER(rcons(x0, 0)) → c70(RCONS(proper(x0), ok(0)), PROPER(x0), PROPER(0))
PROPER(rcons(x0, s(z0))) → c70(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c70(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c70(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, nil)) → c70(RCONS(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
PROPER(rcons(x0, cons(z0, z1))) → c70(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, cons2(z0, z1))) → c70(RCONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(rcons(x0, rnil)) → c70(RCONS(proper(x0), ok(rnil)), PROPER(x0), PROPER(rnil))
PROPER(rcons(x0, rcons(z0, z1))) → c70(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c70(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c70(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c70(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c70(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c70(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c70(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c70(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(0, x1)) → c70(RCONS(ok(0), proper(x1)), PROPER(0), PROPER(x1))
PROPER(rcons(s(z0), x1)) → c70(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c70(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c70(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(nil, x1)) → c70(RCONS(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c70(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(cons2(z0, z1), x1)) → c70(RCONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c70(RCONS(ok(rnil), proper(x1)), PROPER(rnil), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c70(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c70(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c70(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c70(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c70(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c70(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c70(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c70(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
S tuples:
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
PROPER(from(z0)) → c71(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c72(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c73(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c74(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c75(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c76(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c77(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c78(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c79(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c9(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(2NDSPOS(s(z0), cons2(z1, z2)))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(2NDSNEG(s(z0), cons2(z1, z2)))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c13(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, z2)))) → c13(S(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(s(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, z2)))) → c13(S(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(s(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c13(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c13(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c13(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c13(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c13(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c13(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c13(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c13(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(cons2(z0, z1))) → c13(S(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c13(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c13(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c13(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c14(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c14(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c14(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c14(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c14(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c14(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c14(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c14(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(cons2(z0, z1))) → c14(POSRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c15(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c15(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c15(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c15(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c15(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c15(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c15(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c15(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(cons2(z0, z1))) → c15(NEGRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndspos(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndspos(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndsneg(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndsneg(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c16(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c16(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c16(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c16(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c16(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c16(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c16(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c16(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(cons2(z0, z1), x1)) → c16(CONS(cons2(z0, active(z1)), x1), ACTIVE(cons2(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, 2ndsneg(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(0, z0))) → c17(CONS2(x0, mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(cons2(x0, plus(s(z0), z1))) → c17(CONS2(x0, mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons2(x0, times(0, z0))) → c17(CONS2(x0, mark(0)), ACTIVE(times(0, z0)))
ACTIVE(cons2(x0, times(s(z0), z1))) → c17(CONS2(x0, mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(cons2(x0, s(z0))) → c17(CONS2(x0, s(active(z0))), ACTIVE(s(z0)))
ACTIVE(cons2(x0, posrecip(z0))) → c17(CONS2(x0, posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(cons2(x0, negrecip(z0))) → c17(CONS2(x0, negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(cons2(x0, cons(z0, z1))) → c17(CONS2(x0, cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(cons2(x0, cons2(z0, z1))) → c17(CONS2(x0, cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, from(active(z0))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, square(active(z0))), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c20(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(from(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(from(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c20(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c20(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c20(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c20(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c20(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c20(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c20(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c20(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c20(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c20(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(cons2(z0, z1))) → c20(FROM(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c20(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c20(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c20(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c25(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c25(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c25(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c25(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c25(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c25(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c25(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c25(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c25(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c25(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c25(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(cons2(z0, z1))) → c25(PI(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c25(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c25(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c25(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c30(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(square(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(square(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c30(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c30(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c30(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c30(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c30(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c30(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c30(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c30(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c30(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(cons2(z0, z1))) → c30(SQUARE(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c30(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c30(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c63(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c63(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c63(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c63(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(cons2(z0, z1))) → c63(S(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(s(rcons(z0, z1))) → c63(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c63(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c63(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c63(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c63(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c63(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c63(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c63(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c63(S(ok(0)))
PROPER(s(nil)) → c63(S(ok(nil)))
PROPER(s(rnil)) → c63(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c64(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c64(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c64(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c64(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(cons2(z0, z1))) → c64(POSRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c64(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c64(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c64(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c64(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c64(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c64(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c64(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c64(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c64(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c64(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c64(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c65(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c65(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c65(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c65(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(cons2(z0, z1))) → c65(NEGRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c65(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c65(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c65(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c65(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c65(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c65(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c65(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c65(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c65(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c65(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c65(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c67(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c67(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c67(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c67(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, cons2(z0, z1))) → c67(CONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c67(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c67(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c67(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c67(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c67(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c67(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c67(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c67(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c67(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c67(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c67(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c67(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(cons2(z0, z1), x1)) → c67(CONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c67(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c67(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c67(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c67(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c67(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c67(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c67(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c67(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c67(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c67(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c67(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c67(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c67(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c67(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(cons2(x0, s(z0))) → c68(CONS2(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons2(x0, posrecip(z0))) → c68(CONS2(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons2(x0, negrecip(z0))) → c68(CONS2(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons2(x0, cons(z0, z1))) → c68(CONS2(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons2(x0, cons2(z0, z1))) → c68(CONS2(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons2(x0, rcons(z0, z1))) → c68(CONS2(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons2(x0, from(z0))) → c68(CONS2(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons2(x0, 2ndspos(z0, z1))) → c68(CONS2(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons2(x0, 2ndsneg(z0, z1))) → c68(CONS2(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons2(x0, pi(z0))) → c68(CONS2(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons2(x0, plus(z0, z1))) → c68(CONS2(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons2(x0, times(z0, z1))) → c68(CONS2(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons2(x0, square(z0))) → c68(CONS2(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons2(s(z0), x1)) → c68(CONS2(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons2(posrecip(z0), x1)) → c68(CONS2(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons2(negrecip(z0), x1)) → c68(CONS2(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons2(cons(z0, z1), x1)) → c68(CONS2(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons2(cons2(z0, z1), x1)) → c68(CONS2(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons2(rcons(z0, z1), x1)) → c68(CONS2(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons2(from(z0), x1)) → c68(CONS2(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons2(2ndspos(z0, z1), x1)) → c68(CONS2(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons2(2ndsneg(z0, z1), x1)) → c68(CONS2(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons2(pi(z0), x1)) → c68(CONS2(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons2(plus(z0, z1), x1)) → c68(CONS2(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons2(times(z0, z1), x1)) → c68(CONS2(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons2(square(z0), x1)) → c68(CONS2(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons2(x0, 0)) → c68(CONS2(proper(x0), ok(0)), PROPER(x0))
PROPER(cons2(x0, nil)) → c68(CONS2(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons2(x0, rnil)) → c68(CONS2(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons2(0, x1)) → c68(CONS2(ok(0), proper(x1)), PROPER(x1))
PROPER(cons2(nil, x1)) → c68(CONS2(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons2(rnil, x1)) → c68(CONS2(ok(rnil), proper(x1)), PROPER(x1))
PROPER(rcons(x0, 0)) → c70(RCONS(proper(x0), ok(0)), PROPER(x0), PROPER(0))
PROPER(rcons(x0, s(z0))) → c70(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c70(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c70(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, nil)) → c70(RCONS(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
PROPER(rcons(x0, cons(z0, z1))) → c70(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, cons2(z0, z1))) → c70(RCONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(rcons(x0, rnil)) → c70(RCONS(proper(x0), ok(rnil)), PROPER(x0), PROPER(rnil))
PROPER(rcons(x0, rcons(z0, z1))) → c70(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c70(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c70(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c70(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c70(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c70(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c70(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c70(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(0, x1)) → c70(RCONS(ok(0), proper(x1)), PROPER(0), PROPER(x1))
PROPER(rcons(s(z0), x1)) → c70(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c70(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c70(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(nil, x1)) → c70(RCONS(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c70(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(cons2(z0, z1), x1)) → c70(RCONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c70(RCONS(ok(rnil), proper(x1)), PROPER(rnil), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c70(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c70(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c70(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c70(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c70(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c70(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c70(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c70(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
K tuples:none
Defined Rule Symbols:
active, 2ndspos, cons2, rcons, posrecip, 2ndsneg, negrecip, s, cons, from, pi, plus, times, square, proper
Defined Pair Symbols:
ACTIVE, S, POSRECIP, NEGRECIP, CONS, CONS2, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP
Compound Symbols:
c12, c18, c19, c21, c22, c23, c24, c26, c27, c28, c29, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c71, c72, c73, c74, c75, c76, c77, c78, c79, c, c7, c9, c11, c1, c13, c14, c15, c16, c17, c20, c25, c30, c63, c63, c64, c64, c65, c65, c67, c67, c68, c68, c70
(49) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 6 trailing tuple parts
(50) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(2ndspos(0, z0)) → mark(rnil)
active(2ndspos(s(z0), cons(z1, z2))) → mark(2ndspos(s(z0), cons2(z1, z2)))
active(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(z1, z2))) → mark(2ndsneg(s(z0), cons2(z1, z2)))
active(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
active(pi(z0)) → mark(2ndspos(z0, from(0)))
active(plus(0, z0)) → mark(z0)
active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
active(times(0, z0)) → mark(0)
active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
active(square(z0)) → mark(times(z0, z0))
active(s(z0)) → s(active(z0))
active(posrecip(z0)) → posrecip(active(z0))
active(negrecip(z0)) → negrecip(active(z0))
active(cons(z0, z1)) → cons(active(z0), z1)
active(cons2(z0, z1)) → cons2(z0, active(z1))
active(rcons(z0, z1)) → rcons(active(z0), z1)
active(rcons(z0, z1)) → rcons(z0, active(z1))
active(from(z0)) → from(active(z0))
active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
active(pi(z0)) → pi(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(times(z0, z1)) → times(active(z0), z1)
active(times(z0, z1)) → times(z0, active(z1))
active(square(z0)) → square(active(z0))
2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
cons2(z0, mark(z1)) → mark(cons2(z0, z1))
cons2(ok(z0), ok(z1)) → ok(cons2(z0, z1))
rcons(mark(z0), z1) → mark(rcons(z0, z1))
rcons(z0, mark(z1)) → mark(rcons(z0, z1))
rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
posrecip(ok(z0)) → ok(posrecip(z0))
posrecip(mark(z0)) → mark(posrecip(z0))
2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
negrecip(ok(z0)) → ok(negrecip(z0))
negrecip(mark(z0)) → mark(negrecip(z0))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
cons(mark(z0), z1) → mark(cons(z0, z1))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
from(mark(z0)) → mark(from(z0))
from(ok(z0)) → ok(from(z0))
pi(mark(z0)) → mark(pi(z0))
pi(ok(z0)) → ok(pi(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
times(mark(z0), z1) → mark(times(z0, z1))
times(ok(z0), ok(z1)) → ok(times(z0, z1))
times(z0, mark(z1)) → mark(times(z0, z1))
square(mark(z0)) → mark(square(z0))
square(ok(z0)) → ok(square(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(posrecip(z0)) → posrecip(proper(z0))
proper(negrecip(z0)) → negrecip(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(cons2(z0, z1)) → cons2(proper(z0), proper(z1))
proper(rnil) → ok(rnil)
proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
proper(pi(z0)) → pi(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(times(z0, z1)) → times(proper(z0), proper(z1))
proper(square(z0)) → square(proper(z0))
Tuples:
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
PROPER(from(z0)) → c71(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c72(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c73(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c74(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c75(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c76(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c77(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c78(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c79(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c9(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(2NDSPOS(s(z0), cons2(z1, z2)))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(2NDSNEG(s(z0), cons2(z1, z2)))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c13(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, z2)))) → c13(S(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(s(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, z2)))) → c13(S(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(s(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c13(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c13(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c13(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c13(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c13(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c13(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c13(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c13(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(cons2(z0, z1))) → c13(S(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c13(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c13(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c13(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c14(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c14(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c14(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c14(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c14(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c14(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c14(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c14(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(cons2(z0, z1))) → c14(POSRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c15(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c15(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c15(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c15(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c15(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c15(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c15(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c15(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(cons2(z0, z1))) → c15(NEGRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndspos(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndspos(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndsneg(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndsneg(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c16(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c16(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c16(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c16(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c16(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c16(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c16(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c16(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(cons2(z0, z1), x1)) → c16(CONS(cons2(z0, active(z1)), x1), ACTIVE(cons2(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, 2ndsneg(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(0, z0))) → c17(CONS2(x0, mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(cons2(x0, plus(s(z0), z1))) → c17(CONS2(x0, mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons2(x0, times(0, z0))) → c17(CONS2(x0, mark(0)), ACTIVE(times(0, z0)))
ACTIVE(cons2(x0, times(s(z0), z1))) → c17(CONS2(x0, mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(cons2(x0, s(z0))) → c17(CONS2(x0, s(active(z0))), ACTIVE(s(z0)))
ACTIVE(cons2(x0, posrecip(z0))) → c17(CONS2(x0, posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(cons2(x0, negrecip(z0))) → c17(CONS2(x0, negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(cons2(x0, cons(z0, z1))) → c17(CONS2(x0, cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(cons2(x0, cons2(z0, z1))) → c17(CONS2(x0, cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, from(active(z0))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, square(active(z0))), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c20(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(from(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(from(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c20(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c20(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c20(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c20(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c20(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c20(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c20(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c20(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c20(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c20(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(cons2(z0, z1))) → c20(FROM(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c20(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c20(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c20(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c25(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c25(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c25(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c25(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c25(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c25(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c25(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c25(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c25(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c25(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c25(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(cons2(z0, z1))) → c25(PI(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c25(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c25(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c25(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c30(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(square(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(square(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c30(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c30(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c30(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c30(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c30(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c30(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c30(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c30(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c30(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(cons2(z0, z1))) → c30(SQUARE(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c30(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c30(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c63(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c63(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c63(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c63(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(cons2(z0, z1))) → c63(S(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(s(rcons(z0, z1))) → c63(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c63(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c63(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c63(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c63(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c63(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c63(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c63(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c63(S(ok(0)))
PROPER(s(nil)) → c63(S(ok(nil)))
PROPER(s(rnil)) → c63(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c64(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c64(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c64(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c64(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(cons2(z0, z1))) → c64(POSRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c64(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c64(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c64(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c64(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c64(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c64(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c64(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c64(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c64(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c64(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c64(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c65(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c65(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c65(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c65(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(cons2(z0, z1))) → c65(NEGRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c65(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c65(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c65(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c65(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c65(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c65(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c65(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c65(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c65(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c65(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c65(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c67(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c67(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c67(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c67(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, cons2(z0, z1))) → c67(CONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c67(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c67(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c67(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c67(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c67(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c67(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c67(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c67(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c67(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c67(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c67(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c67(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(cons2(z0, z1), x1)) → c67(CONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c67(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c67(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c67(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c67(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c67(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c67(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c67(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c67(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c67(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c67(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c67(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c67(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c67(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c67(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(cons2(x0, s(z0))) → c68(CONS2(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons2(x0, posrecip(z0))) → c68(CONS2(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons2(x0, negrecip(z0))) → c68(CONS2(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons2(x0, cons(z0, z1))) → c68(CONS2(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons2(x0, cons2(z0, z1))) → c68(CONS2(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons2(x0, rcons(z0, z1))) → c68(CONS2(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons2(x0, from(z0))) → c68(CONS2(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons2(x0, 2ndspos(z0, z1))) → c68(CONS2(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons2(x0, 2ndsneg(z0, z1))) → c68(CONS2(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons2(x0, pi(z0))) → c68(CONS2(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons2(x0, plus(z0, z1))) → c68(CONS2(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons2(x0, times(z0, z1))) → c68(CONS2(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons2(x0, square(z0))) → c68(CONS2(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons2(s(z0), x1)) → c68(CONS2(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons2(posrecip(z0), x1)) → c68(CONS2(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons2(negrecip(z0), x1)) → c68(CONS2(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons2(cons(z0, z1), x1)) → c68(CONS2(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons2(cons2(z0, z1), x1)) → c68(CONS2(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons2(rcons(z0, z1), x1)) → c68(CONS2(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons2(from(z0), x1)) → c68(CONS2(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons2(2ndspos(z0, z1), x1)) → c68(CONS2(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons2(2ndsneg(z0, z1), x1)) → c68(CONS2(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons2(pi(z0), x1)) → c68(CONS2(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons2(plus(z0, z1), x1)) → c68(CONS2(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons2(times(z0, z1), x1)) → c68(CONS2(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons2(square(z0), x1)) → c68(CONS2(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons2(x0, 0)) → c68(CONS2(proper(x0), ok(0)), PROPER(x0))
PROPER(cons2(x0, nil)) → c68(CONS2(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons2(x0, rnil)) → c68(CONS2(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons2(0, x1)) → c68(CONS2(ok(0), proper(x1)), PROPER(x1))
PROPER(cons2(nil, x1)) → c68(CONS2(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons2(rnil, x1)) → c68(CONS2(ok(rnil), proper(x1)), PROPER(x1))
PROPER(rcons(x0, s(z0))) → c70(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c70(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c70(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, cons(z0, z1))) → c70(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, cons2(z0, z1))) → c70(RCONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(rcons(x0, rcons(z0, z1))) → c70(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c70(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c70(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c70(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c70(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c70(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c70(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c70(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(s(z0), x1)) → c70(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c70(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c70(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c70(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(cons2(z0, z1), x1)) → c70(RCONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c70(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c70(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c70(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c70(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c70(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c70(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c70(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c70(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(rcons(x0, 0)) → c70(RCONS(proper(x0), ok(0)), PROPER(x0))
PROPER(rcons(x0, nil)) → c70(RCONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(rcons(x0, rnil)) → c70(RCONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(rcons(0, x1)) → c70(RCONS(ok(0), proper(x1)), PROPER(x1))
PROPER(rcons(nil, x1)) → c70(RCONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c70(RCONS(ok(rnil), proper(x1)), PROPER(x1))
S tuples:
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
PROPER(from(z0)) → c71(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c72(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c73(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c74(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c75(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c76(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c77(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c78(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c79(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c9(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(2NDSPOS(s(z0), cons2(z1, z2)))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(2NDSNEG(s(z0), cons2(z1, z2)))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c13(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, z2)))) → c13(S(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(s(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, z2)))) → c13(S(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(s(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c13(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c13(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c13(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c13(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c13(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c13(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c13(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c13(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(cons2(z0, z1))) → c13(S(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c13(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c13(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c13(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c14(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c14(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c14(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c14(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c14(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c14(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c14(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c14(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(cons2(z0, z1))) → c14(POSRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c15(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c15(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c15(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c15(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c15(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c15(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c15(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c15(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(cons2(z0, z1))) → c15(NEGRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndspos(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndspos(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndsneg(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndsneg(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c16(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c16(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c16(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c16(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c16(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c16(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c16(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c16(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(cons2(z0, z1), x1)) → c16(CONS(cons2(z0, active(z1)), x1), ACTIVE(cons2(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, 2ndsneg(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(0, z0))) → c17(CONS2(x0, mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(cons2(x0, plus(s(z0), z1))) → c17(CONS2(x0, mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons2(x0, times(0, z0))) → c17(CONS2(x0, mark(0)), ACTIVE(times(0, z0)))
ACTIVE(cons2(x0, times(s(z0), z1))) → c17(CONS2(x0, mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(cons2(x0, s(z0))) → c17(CONS2(x0, s(active(z0))), ACTIVE(s(z0)))
ACTIVE(cons2(x0, posrecip(z0))) → c17(CONS2(x0, posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(cons2(x0, negrecip(z0))) → c17(CONS2(x0, negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(cons2(x0, cons(z0, z1))) → c17(CONS2(x0, cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(cons2(x0, cons2(z0, z1))) → c17(CONS2(x0, cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, from(active(z0))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, square(active(z0))), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c20(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(from(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(from(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c20(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c20(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c20(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c20(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c20(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c20(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c20(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c20(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c20(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c20(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(cons2(z0, z1))) → c20(FROM(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c20(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c20(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c20(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c25(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c25(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c25(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c25(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c25(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c25(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c25(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c25(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c25(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c25(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c25(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(cons2(z0, z1))) → c25(PI(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c25(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c25(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c25(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c30(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(square(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(square(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c30(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c30(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c30(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c30(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c30(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c30(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c30(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c30(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c30(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(cons2(z0, z1))) → c30(SQUARE(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c30(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c30(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c63(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c63(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c63(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c63(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(cons2(z0, z1))) → c63(S(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(s(rcons(z0, z1))) → c63(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c63(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c63(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c63(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c63(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c63(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c63(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c63(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c63(S(ok(0)))
PROPER(s(nil)) → c63(S(ok(nil)))
PROPER(s(rnil)) → c63(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c64(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c64(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c64(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c64(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(cons2(z0, z1))) → c64(POSRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c64(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c64(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c64(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c64(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c64(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c64(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c64(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c64(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c64(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c64(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c64(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c65(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c65(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c65(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c65(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(cons2(z0, z1))) → c65(NEGRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c65(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c65(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c65(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c65(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c65(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c65(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c65(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c65(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c65(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c65(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c65(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c67(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c67(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c67(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c67(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, cons2(z0, z1))) → c67(CONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c67(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c67(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c67(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c67(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c67(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c67(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c67(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c67(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c67(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c67(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c67(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c67(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(cons2(z0, z1), x1)) → c67(CONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c67(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c67(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c67(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c67(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c67(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c67(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c67(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c67(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c67(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c67(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c67(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c67(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c67(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c67(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(cons2(x0, s(z0))) → c68(CONS2(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons2(x0, posrecip(z0))) → c68(CONS2(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons2(x0, negrecip(z0))) → c68(CONS2(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons2(x0, cons(z0, z1))) → c68(CONS2(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons2(x0, cons2(z0, z1))) → c68(CONS2(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons2(x0, rcons(z0, z1))) → c68(CONS2(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons2(x0, from(z0))) → c68(CONS2(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons2(x0, 2ndspos(z0, z1))) → c68(CONS2(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons2(x0, 2ndsneg(z0, z1))) → c68(CONS2(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons2(x0, pi(z0))) → c68(CONS2(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons2(x0, plus(z0, z1))) → c68(CONS2(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons2(x0, times(z0, z1))) → c68(CONS2(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons2(x0, square(z0))) → c68(CONS2(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons2(s(z0), x1)) → c68(CONS2(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons2(posrecip(z0), x1)) → c68(CONS2(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons2(negrecip(z0), x1)) → c68(CONS2(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons2(cons(z0, z1), x1)) → c68(CONS2(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons2(cons2(z0, z1), x1)) → c68(CONS2(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons2(rcons(z0, z1), x1)) → c68(CONS2(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons2(from(z0), x1)) → c68(CONS2(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons2(2ndspos(z0, z1), x1)) → c68(CONS2(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons2(2ndsneg(z0, z1), x1)) → c68(CONS2(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons2(pi(z0), x1)) → c68(CONS2(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons2(plus(z0, z1), x1)) → c68(CONS2(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons2(times(z0, z1), x1)) → c68(CONS2(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons2(square(z0), x1)) → c68(CONS2(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons2(x0, 0)) → c68(CONS2(proper(x0), ok(0)), PROPER(x0))
PROPER(cons2(x0, nil)) → c68(CONS2(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons2(x0, rnil)) → c68(CONS2(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons2(0, x1)) → c68(CONS2(ok(0), proper(x1)), PROPER(x1))
PROPER(cons2(nil, x1)) → c68(CONS2(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons2(rnil, x1)) → c68(CONS2(ok(rnil), proper(x1)), PROPER(x1))
PROPER(rcons(x0, s(z0))) → c70(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c70(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c70(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, cons(z0, z1))) → c70(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, cons2(z0, z1))) → c70(RCONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(rcons(x0, rcons(z0, z1))) → c70(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c70(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c70(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c70(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c70(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c70(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c70(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c70(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(s(z0), x1)) → c70(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c70(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c70(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c70(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(cons2(z0, z1), x1)) → c70(RCONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c70(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c70(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c70(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c70(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c70(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c70(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c70(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c70(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(rcons(x0, 0)) → c70(RCONS(proper(x0), ok(0)), PROPER(x0))
PROPER(rcons(x0, nil)) → c70(RCONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(rcons(x0, rnil)) → c70(RCONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(rcons(0, x1)) → c70(RCONS(ok(0), proper(x1)), PROPER(x1))
PROPER(rcons(nil, x1)) → c70(RCONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c70(RCONS(ok(rnil), proper(x1)), PROPER(x1))
K tuples:none
Defined Rule Symbols:
active, 2ndspos, cons2, rcons, posrecip, 2ndsneg, negrecip, s, cons, from, pi, plus, times, square, proper
Defined Pair Symbols:
ACTIVE, S, POSRECIP, NEGRECIP, CONS, CONS2, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP
Compound Symbols:
c12, c18, c19, c21, c22, c23, c24, c26, c27, c28, c29, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c71, c72, c73, c74, c75, c76, c77, c78, c79, c, c7, c9, c11, c1, c13, c14, c15, c16, c17, c20, c25, c30, c63, c63, c64, c64, c65, c65, c67, c67, c68, c68, c70, c70
(51) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
PROPER(
from(
z0)) →
c71(
FROM(
proper(
z0)),
PROPER(
z0)) by
PROPER(from(0)) → c71(FROM(ok(0)), PROPER(0))
PROPER(from(s(z0))) → c71(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(posrecip(z0))) → c71(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(from(negrecip(z0))) → c71(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(from(nil)) → c71(FROM(ok(nil)), PROPER(nil))
PROPER(from(cons(z0, z1))) → c71(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(cons2(z0, z1))) → c71(FROM(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(from(rnil)) → c71(FROM(ok(rnil)), PROPER(rnil))
PROPER(from(rcons(z0, z1))) → c71(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(from(from(z0))) → c71(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(2ndspos(z0, z1))) → c71(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(from(2ndsneg(z0, z1))) → c71(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(from(pi(z0))) → c71(FROM(pi(proper(z0))), PROPER(pi(z0)))
PROPER(from(plus(z0, z1))) → c71(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(from(times(z0, z1))) → c71(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(from(square(z0))) → c71(FROM(square(proper(z0))), PROPER(square(z0)))
(52) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(2ndspos(0, z0)) → mark(rnil)
active(2ndspos(s(z0), cons(z1, z2))) → mark(2ndspos(s(z0), cons2(z1, z2)))
active(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(z1, z2))) → mark(2ndsneg(s(z0), cons2(z1, z2)))
active(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
active(pi(z0)) → mark(2ndspos(z0, from(0)))
active(plus(0, z0)) → mark(z0)
active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
active(times(0, z0)) → mark(0)
active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
active(square(z0)) → mark(times(z0, z0))
active(s(z0)) → s(active(z0))
active(posrecip(z0)) → posrecip(active(z0))
active(negrecip(z0)) → negrecip(active(z0))
active(cons(z0, z1)) → cons(active(z0), z1)
active(cons2(z0, z1)) → cons2(z0, active(z1))
active(rcons(z0, z1)) → rcons(active(z0), z1)
active(rcons(z0, z1)) → rcons(z0, active(z1))
active(from(z0)) → from(active(z0))
active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
active(pi(z0)) → pi(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(times(z0, z1)) → times(active(z0), z1)
active(times(z0, z1)) → times(z0, active(z1))
active(square(z0)) → square(active(z0))
2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
cons2(z0, mark(z1)) → mark(cons2(z0, z1))
cons2(ok(z0), ok(z1)) → ok(cons2(z0, z1))
rcons(mark(z0), z1) → mark(rcons(z0, z1))
rcons(z0, mark(z1)) → mark(rcons(z0, z1))
rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
posrecip(ok(z0)) → ok(posrecip(z0))
posrecip(mark(z0)) → mark(posrecip(z0))
2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
negrecip(ok(z0)) → ok(negrecip(z0))
negrecip(mark(z0)) → mark(negrecip(z0))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
cons(mark(z0), z1) → mark(cons(z0, z1))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
from(mark(z0)) → mark(from(z0))
from(ok(z0)) → ok(from(z0))
pi(mark(z0)) → mark(pi(z0))
pi(ok(z0)) → ok(pi(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
times(mark(z0), z1) → mark(times(z0, z1))
times(ok(z0), ok(z1)) → ok(times(z0, z1))
times(z0, mark(z1)) → mark(times(z0, z1))
square(mark(z0)) → mark(square(z0))
square(ok(z0)) → ok(square(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(posrecip(z0)) → posrecip(proper(z0))
proper(negrecip(z0)) → negrecip(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(cons2(z0, z1)) → cons2(proper(z0), proper(z1))
proper(rnil) → ok(rnil)
proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
proper(pi(z0)) → pi(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(times(z0, z1)) → times(proper(z0), proper(z1))
proper(square(z0)) → square(proper(z0))
Tuples:
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
PROPER(2ndspos(z0, z1)) → c72(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c73(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c74(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c75(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c76(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c77(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c78(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c79(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c9(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(2NDSPOS(s(z0), cons2(z1, z2)))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(2NDSNEG(s(z0), cons2(z1, z2)))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c13(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, z2)))) → c13(S(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(s(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, z2)))) → c13(S(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(s(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c13(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c13(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c13(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c13(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c13(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c13(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c13(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c13(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(cons2(z0, z1))) → c13(S(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c13(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c13(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c13(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c14(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c14(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c14(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c14(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c14(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c14(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c14(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c14(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(cons2(z0, z1))) → c14(POSRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c15(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c15(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c15(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c15(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c15(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c15(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c15(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c15(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(cons2(z0, z1))) → c15(NEGRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndspos(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndspos(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndsneg(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndsneg(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c16(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c16(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c16(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c16(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c16(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c16(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c16(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c16(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(cons2(z0, z1), x1)) → c16(CONS(cons2(z0, active(z1)), x1), ACTIVE(cons2(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, 2ndsneg(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(0, z0))) → c17(CONS2(x0, mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(cons2(x0, plus(s(z0), z1))) → c17(CONS2(x0, mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons2(x0, times(0, z0))) → c17(CONS2(x0, mark(0)), ACTIVE(times(0, z0)))
ACTIVE(cons2(x0, times(s(z0), z1))) → c17(CONS2(x0, mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(cons2(x0, s(z0))) → c17(CONS2(x0, s(active(z0))), ACTIVE(s(z0)))
ACTIVE(cons2(x0, posrecip(z0))) → c17(CONS2(x0, posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(cons2(x0, negrecip(z0))) → c17(CONS2(x0, negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(cons2(x0, cons(z0, z1))) → c17(CONS2(x0, cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(cons2(x0, cons2(z0, z1))) → c17(CONS2(x0, cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, from(active(z0))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, square(active(z0))), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c20(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(from(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(from(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c20(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c20(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c20(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c20(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c20(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c20(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c20(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c20(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c20(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c20(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(cons2(z0, z1))) → c20(FROM(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c20(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c20(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c20(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c25(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c25(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c25(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c25(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c25(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c25(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c25(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c25(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c25(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c25(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c25(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(cons2(z0, z1))) → c25(PI(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c25(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c25(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c25(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c30(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(square(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(square(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c30(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c30(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c30(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c30(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c30(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c30(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c30(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c30(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c30(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(cons2(z0, z1))) → c30(SQUARE(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c30(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c30(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c63(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c63(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c63(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c63(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(cons2(z0, z1))) → c63(S(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(s(rcons(z0, z1))) → c63(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c63(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c63(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c63(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c63(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c63(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c63(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c63(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c63(S(ok(0)))
PROPER(s(nil)) → c63(S(ok(nil)))
PROPER(s(rnil)) → c63(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c64(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c64(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c64(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c64(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(cons2(z0, z1))) → c64(POSRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c64(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c64(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c64(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c64(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c64(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c64(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c64(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c64(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c64(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c64(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c64(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c65(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c65(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c65(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c65(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(cons2(z0, z1))) → c65(NEGRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c65(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c65(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c65(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c65(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c65(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c65(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c65(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c65(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c65(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c65(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c65(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c67(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c67(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c67(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c67(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, cons2(z0, z1))) → c67(CONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c67(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c67(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c67(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c67(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c67(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c67(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c67(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c67(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c67(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c67(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c67(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c67(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(cons2(z0, z1), x1)) → c67(CONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c67(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c67(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c67(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c67(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c67(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c67(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c67(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c67(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c67(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c67(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c67(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c67(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c67(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c67(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(cons2(x0, s(z0))) → c68(CONS2(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons2(x0, posrecip(z0))) → c68(CONS2(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons2(x0, negrecip(z0))) → c68(CONS2(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons2(x0, cons(z0, z1))) → c68(CONS2(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons2(x0, cons2(z0, z1))) → c68(CONS2(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons2(x0, rcons(z0, z1))) → c68(CONS2(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons2(x0, from(z0))) → c68(CONS2(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons2(x0, 2ndspos(z0, z1))) → c68(CONS2(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons2(x0, 2ndsneg(z0, z1))) → c68(CONS2(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons2(x0, pi(z0))) → c68(CONS2(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons2(x0, plus(z0, z1))) → c68(CONS2(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons2(x0, times(z0, z1))) → c68(CONS2(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons2(x0, square(z0))) → c68(CONS2(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons2(s(z0), x1)) → c68(CONS2(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons2(posrecip(z0), x1)) → c68(CONS2(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons2(negrecip(z0), x1)) → c68(CONS2(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons2(cons(z0, z1), x1)) → c68(CONS2(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons2(cons2(z0, z1), x1)) → c68(CONS2(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons2(rcons(z0, z1), x1)) → c68(CONS2(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons2(from(z0), x1)) → c68(CONS2(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons2(2ndspos(z0, z1), x1)) → c68(CONS2(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons2(2ndsneg(z0, z1), x1)) → c68(CONS2(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons2(pi(z0), x1)) → c68(CONS2(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons2(plus(z0, z1), x1)) → c68(CONS2(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons2(times(z0, z1), x1)) → c68(CONS2(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons2(square(z0), x1)) → c68(CONS2(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons2(x0, 0)) → c68(CONS2(proper(x0), ok(0)), PROPER(x0))
PROPER(cons2(x0, nil)) → c68(CONS2(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons2(x0, rnil)) → c68(CONS2(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons2(0, x1)) → c68(CONS2(ok(0), proper(x1)), PROPER(x1))
PROPER(cons2(nil, x1)) → c68(CONS2(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons2(rnil, x1)) → c68(CONS2(ok(rnil), proper(x1)), PROPER(x1))
PROPER(rcons(x0, s(z0))) → c70(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c70(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c70(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, cons(z0, z1))) → c70(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, cons2(z0, z1))) → c70(RCONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(rcons(x0, rcons(z0, z1))) → c70(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c70(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c70(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c70(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c70(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c70(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c70(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c70(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(s(z0), x1)) → c70(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c70(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c70(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c70(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(cons2(z0, z1), x1)) → c70(RCONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c70(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c70(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c70(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c70(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c70(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c70(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c70(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c70(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(rcons(x0, 0)) → c70(RCONS(proper(x0), ok(0)), PROPER(x0))
PROPER(rcons(x0, nil)) → c70(RCONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(rcons(x0, rnil)) → c70(RCONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(rcons(0, x1)) → c70(RCONS(ok(0), proper(x1)), PROPER(x1))
PROPER(rcons(nil, x1)) → c70(RCONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c70(RCONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(from(0)) → c71(FROM(ok(0)), PROPER(0))
PROPER(from(s(z0))) → c71(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(posrecip(z0))) → c71(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(from(negrecip(z0))) → c71(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(from(nil)) → c71(FROM(ok(nil)), PROPER(nil))
PROPER(from(cons(z0, z1))) → c71(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(cons2(z0, z1))) → c71(FROM(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(from(rnil)) → c71(FROM(ok(rnil)), PROPER(rnil))
PROPER(from(rcons(z0, z1))) → c71(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(from(from(z0))) → c71(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(2ndspos(z0, z1))) → c71(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(from(2ndsneg(z0, z1))) → c71(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(from(pi(z0))) → c71(FROM(pi(proper(z0))), PROPER(pi(z0)))
PROPER(from(plus(z0, z1))) → c71(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(from(times(z0, z1))) → c71(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(from(square(z0))) → c71(FROM(square(proper(z0))), PROPER(square(z0)))
S tuples:
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
PROPER(2ndspos(z0, z1)) → c72(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c73(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c74(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c75(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c76(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c77(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c78(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c79(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c9(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(2NDSPOS(s(z0), cons2(z1, z2)))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(2NDSNEG(s(z0), cons2(z1, z2)))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c13(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, z2)))) → c13(S(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(s(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, z2)))) → c13(S(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(s(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c13(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c13(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c13(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c13(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c13(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c13(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c13(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c13(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(cons2(z0, z1))) → c13(S(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c13(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c13(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c13(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c14(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c14(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c14(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c14(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c14(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c14(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c14(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c14(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(cons2(z0, z1))) → c14(POSRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c15(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c15(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c15(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c15(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c15(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c15(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c15(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c15(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(cons2(z0, z1))) → c15(NEGRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndspos(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndspos(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndsneg(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndsneg(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c16(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c16(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c16(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c16(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c16(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c16(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c16(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c16(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(cons2(z0, z1), x1)) → c16(CONS(cons2(z0, active(z1)), x1), ACTIVE(cons2(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, 2ndsneg(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(0, z0))) → c17(CONS2(x0, mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(cons2(x0, plus(s(z0), z1))) → c17(CONS2(x0, mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons2(x0, times(0, z0))) → c17(CONS2(x0, mark(0)), ACTIVE(times(0, z0)))
ACTIVE(cons2(x0, times(s(z0), z1))) → c17(CONS2(x0, mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(cons2(x0, s(z0))) → c17(CONS2(x0, s(active(z0))), ACTIVE(s(z0)))
ACTIVE(cons2(x0, posrecip(z0))) → c17(CONS2(x0, posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(cons2(x0, negrecip(z0))) → c17(CONS2(x0, negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(cons2(x0, cons(z0, z1))) → c17(CONS2(x0, cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(cons2(x0, cons2(z0, z1))) → c17(CONS2(x0, cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, from(active(z0))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, square(active(z0))), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c20(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(from(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(from(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c20(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c20(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c20(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c20(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c20(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c20(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c20(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c20(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c20(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c20(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(cons2(z0, z1))) → c20(FROM(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c20(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c20(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c20(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c25(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c25(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c25(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c25(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c25(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c25(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c25(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c25(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c25(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c25(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c25(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(cons2(z0, z1))) → c25(PI(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c25(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c25(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c25(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c30(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(square(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(square(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c30(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c30(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c30(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c30(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c30(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c30(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c30(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c30(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c30(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(cons2(z0, z1))) → c30(SQUARE(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c30(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c30(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c63(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c63(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c63(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c63(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(cons2(z0, z1))) → c63(S(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(s(rcons(z0, z1))) → c63(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c63(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c63(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c63(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c63(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c63(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c63(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c63(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c63(S(ok(0)))
PROPER(s(nil)) → c63(S(ok(nil)))
PROPER(s(rnil)) → c63(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c64(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c64(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c64(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c64(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(cons2(z0, z1))) → c64(POSRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c64(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c64(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c64(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c64(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c64(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c64(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c64(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c64(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c64(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c64(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c64(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c65(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c65(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c65(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c65(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(cons2(z0, z1))) → c65(NEGRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c65(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c65(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c65(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c65(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c65(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c65(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c65(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c65(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c65(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c65(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c65(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c67(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c67(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c67(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c67(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, cons2(z0, z1))) → c67(CONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c67(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c67(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c67(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c67(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c67(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c67(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c67(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c67(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c67(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c67(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c67(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c67(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(cons2(z0, z1), x1)) → c67(CONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c67(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c67(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c67(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c67(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c67(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c67(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c67(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c67(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c67(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c67(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c67(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c67(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c67(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c67(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(cons2(x0, s(z0))) → c68(CONS2(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons2(x0, posrecip(z0))) → c68(CONS2(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons2(x0, negrecip(z0))) → c68(CONS2(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons2(x0, cons(z0, z1))) → c68(CONS2(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons2(x0, cons2(z0, z1))) → c68(CONS2(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons2(x0, rcons(z0, z1))) → c68(CONS2(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons2(x0, from(z0))) → c68(CONS2(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons2(x0, 2ndspos(z0, z1))) → c68(CONS2(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons2(x0, 2ndsneg(z0, z1))) → c68(CONS2(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons2(x0, pi(z0))) → c68(CONS2(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons2(x0, plus(z0, z1))) → c68(CONS2(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons2(x0, times(z0, z1))) → c68(CONS2(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons2(x0, square(z0))) → c68(CONS2(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons2(s(z0), x1)) → c68(CONS2(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons2(posrecip(z0), x1)) → c68(CONS2(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons2(negrecip(z0), x1)) → c68(CONS2(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons2(cons(z0, z1), x1)) → c68(CONS2(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons2(cons2(z0, z1), x1)) → c68(CONS2(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons2(rcons(z0, z1), x1)) → c68(CONS2(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons2(from(z0), x1)) → c68(CONS2(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons2(2ndspos(z0, z1), x1)) → c68(CONS2(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons2(2ndsneg(z0, z1), x1)) → c68(CONS2(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons2(pi(z0), x1)) → c68(CONS2(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons2(plus(z0, z1), x1)) → c68(CONS2(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons2(times(z0, z1), x1)) → c68(CONS2(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons2(square(z0), x1)) → c68(CONS2(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons2(x0, 0)) → c68(CONS2(proper(x0), ok(0)), PROPER(x0))
PROPER(cons2(x0, nil)) → c68(CONS2(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons2(x0, rnil)) → c68(CONS2(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons2(0, x1)) → c68(CONS2(ok(0), proper(x1)), PROPER(x1))
PROPER(cons2(nil, x1)) → c68(CONS2(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons2(rnil, x1)) → c68(CONS2(ok(rnil), proper(x1)), PROPER(x1))
PROPER(rcons(x0, s(z0))) → c70(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c70(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c70(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, cons(z0, z1))) → c70(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, cons2(z0, z1))) → c70(RCONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(rcons(x0, rcons(z0, z1))) → c70(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c70(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c70(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c70(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c70(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c70(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c70(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c70(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(s(z0), x1)) → c70(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c70(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c70(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c70(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(cons2(z0, z1), x1)) → c70(RCONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c70(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c70(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c70(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c70(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c70(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c70(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c70(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c70(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(rcons(x0, 0)) → c70(RCONS(proper(x0), ok(0)), PROPER(x0))
PROPER(rcons(x0, nil)) → c70(RCONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(rcons(x0, rnil)) → c70(RCONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(rcons(0, x1)) → c70(RCONS(ok(0), proper(x1)), PROPER(x1))
PROPER(rcons(nil, x1)) → c70(RCONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c70(RCONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(from(0)) → c71(FROM(ok(0)), PROPER(0))
PROPER(from(s(z0))) → c71(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(posrecip(z0))) → c71(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(from(negrecip(z0))) → c71(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(from(nil)) → c71(FROM(ok(nil)), PROPER(nil))
PROPER(from(cons(z0, z1))) → c71(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(cons2(z0, z1))) → c71(FROM(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(from(rnil)) → c71(FROM(ok(rnil)), PROPER(rnil))
PROPER(from(rcons(z0, z1))) → c71(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(from(from(z0))) → c71(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(2ndspos(z0, z1))) → c71(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(from(2ndsneg(z0, z1))) → c71(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(from(pi(z0))) → c71(FROM(pi(proper(z0))), PROPER(pi(z0)))
PROPER(from(plus(z0, z1))) → c71(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(from(times(z0, z1))) → c71(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(from(square(z0))) → c71(FROM(square(proper(z0))), PROPER(square(z0)))
K tuples:none
Defined Rule Symbols:
active, 2ndspos, cons2, rcons, posrecip, 2ndsneg, negrecip, s, cons, from, pi, plus, times, square, proper
Defined Pair Symbols:
ACTIVE, S, POSRECIP, NEGRECIP, CONS, CONS2, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP
Compound Symbols:
c12, c18, c19, c21, c22, c23, c24, c26, c27, c28, c29, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c72, c73, c74, c75, c76, c77, c78, c79, c, c7, c9, c11, c1, c13, c14, c15, c16, c17, c20, c25, c30, c63, c63, c64, c64, c65, c65, c67, c67, c68, c68, c70, c70, c71
(53) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 3 trailing tuple parts
(54) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(2ndspos(0, z0)) → mark(rnil)
active(2ndspos(s(z0), cons(z1, z2))) → mark(2ndspos(s(z0), cons2(z1, z2)))
active(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(z1, z2))) → mark(2ndsneg(s(z0), cons2(z1, z2)))
active(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
active(pi(z0)) → mark(2ndspos(z0, from(0)))
active(plus(0, z0)) → mark(z0)
active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
active(times(0, z0)) → mark(0)
active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
active(square(z0)) → mark(times(z0, z0))
active(s(z0)) → s(active(z0))
active(posrecip(z0)) → posrecip(active(z0))
active(negrecip(z0)) → negrecip(active(z0))
active(cons(z0, z1)) → cons(active(z0), z1)
active(cons2(z0, z1)) → cons2(z0, active(z1))
active(rcons(z0, z1)) → rcons(active(z0), z1)
active(rcons(z0, z1)) → rcons(z0, active(z1))
active(from(z0)) → from(active(z0))
active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
active(pi(z0)) → pi(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(times(z0, z1)) → times(active(z0), z1)
active(times(z0, z1)) → times(z0, active(z1))
active(square(z0)) → square(active(z0))
2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
cons2(z0, mark(z1)) → mark(cons2(z0, z1))
cons2(ok(z0), ok(z1)) → ok(cons2(z0, z1))
rcons(mark(z0), z1) → mark(rcons(z0, z1))
rcons(z0, mark(z1)) → mark(rcons(z0, z1))
rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
posrecip(ok(z0)) → ok(posrecip(z0))
posrecip(mark(z0)) → mark(posrecip(z0))
2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
negrecip(ok(z0)) → ok(negrecip(z0))
negrecip(mark(z0)) → mark(negrecip(z0))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
cons(mark(z0), z1) → mark(cons(z0, z1))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
from(mark(z0)) → mark(from(z0))
from(ok(z0)) → ok(from(z0))
pi(mark(z0)) → mark(pi(z0))
pi(ok(z0)) → ok(pi(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
times(mark(z0), z1) → mark(times(z0, z1))
times(ok(z0), ok(z1)) → ok(times(z0, z1))
times(z0, mark(z1)) → mark(times(z0, z1))
square(mark(z0)) → mark(square(z0))
square(ok(z0)) → ok(square(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(posrecip(z0)) → posrecip(proper(z0))
proper(negrecip(z0)) → negrecip(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(cons2(z0, z1)) → cons2(proper(z0), proper(z1))
proper(rnil) → ok(rnil)
proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
proper(pi(z0)) → pi(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(times(z0, z1)) → times(proper(z0), proper(z1))
proper(square(z0)) → square(proper(z0))
Tuples:
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
PROPER(2ndspos(z0, z1)) → c72(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c73(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c74(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c75(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c76(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c77(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c78(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c79(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c9(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(2NDSPOS(s(z0), cons2(z1, z2)))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(2NDSNEG(s(z0), cons2(z1, z2)))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c13(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, z2)))) → c13(S(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(s(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, z2)))) → c13(S(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(s(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c13(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c13(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c13(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c13(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c13(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c13(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c13(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c13(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(cons2(z0, z1))) → c13(S(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c13(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c13(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c13(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c14(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c14(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c14(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c14(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c14(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c14(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c14(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c14(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(cons2(z0, z1))) → c14(POSRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c15(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c15(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c15(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c15(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c15(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c15(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c15(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c15(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(cons2(z0, z1))) → c15(NEGRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndspos(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndspos(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndsneg(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndsneg(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c16(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c16(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c16(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c16(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c16(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c16(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c16(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c16(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(cons2(z0, z1), x1)) → c16(CONS(cons2(z0, active(z1)), x1), ACTIVE(cons2(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, 2ndsneg(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(0, z0))) → c17(CONS2(x0, mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(cons2(x0, plus(s(z0), z1))) → c17(CONS2(x0, mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons2(x0, times(0, z0))) → c17(CONS2(x0, mark(0)), ACTIVE(times(0, z0)))
ACTIVE(cons2(x0, times(s(z0), z1))) → c17(CONS2(x0, mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(cons2(x0, s(z0))) → c17(CONS2(x0, s(active(z0))), ACTIVE(s(z0)))
ACTIVE(cons2(x0, posrecip(z0))) → c17(CONS2(x0, posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(cons2(x0, negrecip(z0))) → c17(CONS2(x0, negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(cons2(x0, cons(z0, z1))) → c17(CONS2(x0, cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(cons2(x0, cons2(z0, z1))) → c17(CONS2(x0, cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, from(active(z0))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, square(active(z0))), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c20(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(from(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(from(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c20(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c20(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c20(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c20(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c20(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c20(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c20(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c20(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c20(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c20(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(cons2(z0, z1))) → c20(FROM(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c20(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c20(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c20(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c25(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c25(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c25(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c25(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c25(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c25(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c25(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c25(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c25(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c25(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c25(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(cons2(z0, z1))) → c25(PI(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c25(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c25(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c25(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c30(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(square(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(square(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c30(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c30(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c30(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c30(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c30(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c30(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c30(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c30(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c30(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(cons2(z0, z1))) → c30(SQUARE(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c30(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c30(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c63(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c63(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c63(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c63(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(cons2(z0, z1))) → c63(S(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(s(rcons(z0, z1))) → c63(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c63(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c63(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c63(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c63(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c63(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c63(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c63(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c63(S(ok(0)))
PROPER(s(nil)) → c63(S(ok(nil)))
PROPER(s(rnil)) → c63(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c64(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c64(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c64(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c64(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(cons2(z0, z1))) → c64(POSRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c64(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c64(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c64(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c64(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c64(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c64(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c64(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c64(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c64(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c64(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c64(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c65(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c65(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c65(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c65(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(cons2(z0, z1))) → c65(NEGRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c65(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c65(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c65(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c65(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c65(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c65(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c65(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c65(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c65(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c65(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c65(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c67(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c67(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c67(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c67(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, cons2(z0, z1))) → c67(CONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c67(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c67(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c67(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c67(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c67(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c67(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c67(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c67(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c67(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c67(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c67(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c67(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(cons2(z0, z1), x1)) → c67(CONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c67(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c67(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c67(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c67(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c67(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c67(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c67(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c67(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c67(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c67(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c67(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c67(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c67(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c67(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(cons2(x0, s(z0))) → c68(CONS2(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons2(x0, posrecip(z0))) → c68(CONS2(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons2(x0, negrecip(z0))) → c68(CONS2(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons2(x0, cons(z0, z1))) → c68(CONS2(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons2(x0, cons2(z0, z1))) → c68(CONS2(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons2(x0, rcons(z0, z1))) → c68(CONS2(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons2(x0, from(z0))) → c68(CONS2(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons2(x0, 2ndspos(z0, z1))) → c68(CONS2(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons2(x0, 2ndsneg(z0, z1))) → c68(CONS2(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons2(x0, pi(z0))) → c68(CONS2(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons2(x0, plus(z0, z1))) → c68(CONS2(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons2(x0, times(z0, z1))) → c68(CONS2(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons2(x0, square(z0))) → c68(CONS2(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons2(s(z0), x1)) → c68(CONS2(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons2(posrecip(z0), x1)) → c68(CONS2(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons2(negrecip(z0), x1)) → c68(CONS2(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons2(cons(z0, z1), x1)) → c68(CONS2(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons2(cons2(z0, z1), x1)) → c68(CONS2(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons2(rcons(z0, z1), x1)) → c68(CONS2(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons2(from(z0), x1)) → c68(CONS2(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons2(2ndspos(z0, z1), x1)) → c68(CONS2(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons2(2ndsneg(z0, z1), x1)) → c68(CONS2(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons2(pi(z0), x1)) → c68(CONS2(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons2(plus(z0, z1), x1)) → c68(CONS2(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons2(times(z0, z1), x1)) → c68(CONS2(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons2(square(z0), x1)) → c68(CONS2(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons2(x0, 0)) → c68(CONS2(proper(x0), ok(0)), PROPER(x0))
PROPER(cons2(x0, nil)) → c68(CONS2(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons2(x0, rnil)) → c68(CONS2(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons2(0, x1)) → c68(CONS2(ok(0), proper(x1)), PROPER(x1))
PROPER(cons2(nil, x1)) → c68(CONS2(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons2(rnil, x1)) → c68(CONS2(ok(rnil), proper(x1)), PROPER(x1))
PROPER(rcons(x0, s(z0))) → c70(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c70(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c70(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, cons(z0, z1))) → c70(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, cons2(z0, z1))) → c70(RCONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(rcons(x0, rcons(z0, z1))) → c70(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c70(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c70(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c70(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c70(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c70(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c70(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c70(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(s(z0), x1)) → c70(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c70(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c70(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c70(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(cons2(z0, z1), x1)) → c70(RCONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c70(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c70(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c70(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c70(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c70(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c70(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c70(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c70(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(rcons(x0, 0)) → c70(RCONS(proper(x0), ok(0)), PROPER(x0))
PROPER(rcons(x0, nil)) → c70(RCONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(rcons(x0, rnil)) → c70(RCONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(rcons(0, x1)) → c70(RCONS(ok(0), proper(x1)), PROPER(x1))
PROPER(rcons(nil, x1)) → c70(RCONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c70(RCONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(from(s(z0))) → c71(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(posrecip(z0))) → c71(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(from(negrecip(z0))) → c71(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(from(cons(z0, z1))) → c71(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(cons2(z0, z1))) → c71(FROM(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(from(rcons(z0, z1))) → c71(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(from(from(z0))) → c71(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(2ndspos(z0, z1))) → c71(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(from(2ndsneg(z0, z1))) → c71(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(from(pi(z0))) → c71(FROM(pi(proper(z0))), PROPER(pi(z0)))
PROPER(from(plus(z0, z1))) → c71(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(from(times(z0, z1))) → c71(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(from(square(z0))) → c71(FROM(square(proper(z0))), PROPER(square(z0)))
PROPER(from(0)) → c71(FROM(ok(0)))
PROPER(from(nil)) → c71(FROM(ok(nil)))
PROPER(from(rnil)) → c71(FROM(ok(rnil)))
S tuples:
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
PROPER(2ndspos(z0, z1)) → c72(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c73(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c74(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c75(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c76(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c77(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c78(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c79(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c9(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(2NDSPOS(s(z0), cons2(z1, z2)))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(2NDSNEG(s(z0), cons2(z1, z2)))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c13(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, z2)))) → c13(S(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(s(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, z2)))) → c13(S(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(s(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c13(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c13(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c13(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c13(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c13(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c13(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c13(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c13(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(cons2(z0, z1))) → c13(S(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c13(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c13(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c13(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c14(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c14(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c14(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c14(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c14(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c14(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c14(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c14(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(cons2(z0, z1))) → c14(POSRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c15(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c15(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c15(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c15(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c15(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c15(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c15(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c15(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(cons2(z0, z1))) → c15(NEGRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndspos(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndspos(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndsneg(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndsneg(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c16(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c16(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c16(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c16(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c16(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c16(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c16(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c16(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(cons2(z0, z1), x1)) → c16(CONS(cons2(z0, active(z1)), x1), ACTIVE(cons2(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, 2ndsneg(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(0, z0))) → c17(CONS2(x0, mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(cons2(x0, plus(s(z0), z1))) → c17(CONS2(x0, mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons2(x0, times(0, z0))) → c17(CONS2(x0, mark(0)), ACTIVE(times(0, z0)))
ACTIVE(cons2(x0, times(s(z0), z1))) → c17(CONS2(x0, mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(cons2(x0, s(z0))) → c17(CONS2(x0, s(active(z0))), ACTIVE(s(z0)))
ACTIVE(cons2(x0, posrecip(z0))) → c17(CONS2(x0, posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(cons2(x0, negrecip(z0))) → c17(CONS2(x0, negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(cons2(x0, cons(z0, z1))) → c17(CONS2(x0, cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(cons2(x0, cons2(z0, z1))) → c17(CONS2(x0, cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, from(active(z0))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, square(active(z0))), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c20(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(from(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(from(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c20(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c20(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c20(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c20(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c20(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c20(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c20(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c20(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c20(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c20(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(cons2(z0, z1))) → c20(FROM(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c20(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c20(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c20(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c25(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c25(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c25(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c25(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c25(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c25(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c25(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c25(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c25(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c25(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c25(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(cons2(z0, z1))) → c25(PI(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c25(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c25(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c25(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c30(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(square(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(square(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c30(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c30(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c30(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c30(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c30(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c30(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c30(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c30(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c30(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(cons2(z0, z1))) → c30(SQUARE(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c30(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c30(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c63(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c63(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c63(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c63(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(cons2(z0, z1))) → c63(S(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(s(rcons(z0, z1))) → c63(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c63(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c63(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c63(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c63(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c63(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c63(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c63(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c63(S(ok(0)))
PROPER(s(nil)) → c63(S(ok(nil)))
PROPER(s(rnil)) → c63(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c64(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c64(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c64(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c64(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(cons2(z0, z1))) → c64(POSRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c64(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c64(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c64(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c64(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c64(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c64(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c64(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c64(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c64(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c64(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c64(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c65(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c65(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c65(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c65(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(cons2(z0, z1))) → c65(NEGRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c65(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c65(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c65(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c65(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c65(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c65(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c65(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c65(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c65(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c65(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c65(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c67(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c67(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c67(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c67(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, cons2(z0, z1))) → c67(CONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c67(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c67(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c67(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c67(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c67(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c67(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c67(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c67(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c67(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c67(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c67(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c67(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(cons2(z0, z1), x1)) → c67(CONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c67(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c67(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c67(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c67(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c67(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c67(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c67(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c67(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c67(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c67(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c67(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c67(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c67(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c67(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(cons2(x0, s(z0))) → c68(CONS2(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons2(x0, posrecip(z0))) → c68(CONS2(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons2(x0, negrecip(z0))) → c68(CONS2(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons2(x0, cons(z0, z1))) → c68(CONS2(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons2(x0, cons2(z0, z1))) → c68(CONS2(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons2(x0, rcons(z0, z1))) → c68(CONS2(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons2(x0, from(z0))) → c68(CONS2(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons2(x0, 2ndspos(z0, z1))) → c68(CONS2(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons2(x0, 2ndsneg(z0, z1))) → c68(CONS2(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons2(x0, pi(z0))) → c68(CONS2(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons2(x0, plus(z0, z1))) → c68(CONS2(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons2(x0, times(z0, z1))) → c68(CONS2(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons2(x0, square(z0))) → c68(CONS2(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons2(s(z0), x1)) → c68(CONS2(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons2(posrecip(z0), x1)) → c68(CONS2(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons2(negrecip(z0), x1)) → c68(CONS2(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons2(cons(z0, z1), x1)) → c68(CONS2(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons2(cons2(z0, z1), x1)) → c68(CONS2(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons2(rcons(z0, z1), x1)) → c68(CONS2(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons2(from(z0), x1)) → c68(CONS2(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons2(2ndspos(z0, z1), x1)) → c68(CONS2(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons2(2ndsneg(z0, z1), x1)) → c68(CONS2(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons2(pi(z0), x1)) → c68(CONS2(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons2(plus(z0, z1), x1)) → c68(CONS2(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons2(times(z0, z1), x1)) → c68(CONS2(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons2(square(z0), x1)) → c68(CONS2(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons2(x0, 0)) → c68(CONS2(proper(x0), ok(0)), PROPER(x0))
PROPER(cons2(x0, nil)) → c68(CONS2(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons2(x0, rnil)) → c68(CONS2(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons2(0, x1)) → c68(CONS2(ok(0), proper(x1)), PROPER(x1))
PROPER(cons2(nil, x1)) → c68(CONS2(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons2(rnil, x1)) → c68(CONS2(ok(rnil), proper(x1)), PROPER(x1))
PROPER(rcons(x0, s(z0))) → c70(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c70(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c70(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, cons(z0, z1))) → c70(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, cons2(z0, z1))) → c70(RCONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(rcons(x0, rcons(z0, z1))) → c70(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c70(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c70(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c70(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c70(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c70(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c70(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c70(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(s(z0), x1)) → c70(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c70(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c70(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c70(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(cons2(z0, z1), x1)) → c70(RCONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c70(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c70(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c70(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c70(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c70(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c70(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c70(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c70(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(rcons(x0, 0)) → c70(RCONS(proper(x0), ok(0)), PROPER(x0))
PROPER(rcons(x0, nil)) → c70(RCONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(rcons(x0, rnil)) → c70(RCONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(rcons(0, x1)) → c70(RCONS(ok(0), proper(x1)), PROPER(x1))
PROPER(rcons(nil, x1)) → c70(RCONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c70(RCONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(from(s(z0))) → c71(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(posrecip(z0))) → c71(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(from(negrecip(z0))) → c71(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(from(cons(z0, z1))) → c71(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(cons2(z0, z1))) → c71(FROM(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(from(rcons(z0, z1))) → c71(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(from(from(z0))) → c71(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(2ndspos(z0, z1))) → c71(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(from(2ndsneg(z0, z1))) → c71(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(from(pi(z0))) → c71(FROM(pi(proper(z0))), PROPER(pi(z0)))
PROPER(from(plus(z0, z1))) → c71(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(from(times(z0, z1))) → c71(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(from(square(z0))) → c71(FROM(square(proper(z0))), PROPER(square(z0)))
PROPER(from(0)) → c71(FROM(ok(0)))
PROPER(from(nil)) → c71(FROM(ok(nil)))
PROPER(from(rnil)) → c71(FROM(ok(rnil)))
K tuples:none
Defined Rule Symbols:
active, 2ndspos, cons2, rcons, posrecip, 2ndsneg, negrecip, s, cons, from, pi, plus, times, square, proper
Defined Pair Symbols:
ACTIVE, S, POSRECIP, NEGRECIP, CONS, CONS2, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP
Compound Symbols:
c12, c18, c19, c21, c22, c23, c24, c26, c27, c28, c29, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c72, c73, c74, c75, c76, c77, c78, c79, c, c7, c9, c11, c1, c13, c14, c15, c16, c17, c20, c25, c30, c63, c63, c64, c64, c65, c65, c67, c67, c68, c68, c70, c70, c71, c71
(55) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
PROPER(
2ndspos(
z0,
z1)) →
c72(
2NDSPOS(
proper(
z0),
proper(
z1)),
PROPER(
z0),
PROPER(
z1)) by
PROPER(2ndspos(x0, 0)) → c72(2NDSPOS(proper(x0), ok(0)), PROPER(x0), PROPER(0))
PROPER(2ndspos(x0, s(z0))) → c72(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndspos(x0, posrecip(z0))) → c72(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndspos(x0, negrecip(z0))) → c72(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndspos(x0, nil)) → c72(2NDSPOS(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
PROPER(2ndspos(x0, cons(z0, z1))) → c72(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndspos(x0, cons2(z0, z1))) → c72(2NDSPOS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(2ndspos(x0, rnil)) → c72(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0), PROPER(rnil))
PROPER(2ndspos(x0, rcons(z0, z1))) → c72(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndspos(x0, from(z0))) → c72(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c72(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c72(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndspos(x0, pi(z0))) → c72(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndspos(x0, plus(z0, z1))) → c72(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndspos(x0, times(z0, z1))) → c72(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndspos(x0, square(z0))) → c72(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndspos(0, x1)) → c72(2NDSPOS(ok(0), proper(x1)), PROPER(0), PROPER(x1))
PROPER(2ndspos(s(z0), x1)) → c72(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndspos(posrecip(z0), x1)) → c72(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndspos(negrecip(z0), x1)) → c72(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndspos(nil, x1)) → c72(2NDSPOS(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
PROPER(2ndspos(cons(z0, z1), x1)) → c72(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndspos(cons2(z0, z1), x1)) → c72(2NDSPOS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(2ndspos(rnil, x1)) → c72(2NDSPOS(ok(rnil), proper(x1)), PROPER(rnil), PROPER(x1))
PROPER(2ndspos(rcons(z0, z1), x1)) → c72(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndspos(from(z0), x1)) → c72(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c72(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c72(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndspos(pi(z0), x1)) → c72(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndspos(plus(z0, z1), x1)) → c72(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndspos(times(z0, z1), x1)) → c72(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndspos(square(z0), x1)) → c72(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
(56) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(2ndspos(0, z0)) → mark(rnil)
active(2ndspos(s(z0), cons(z1, z2))) → mark(2ndspos(s(z0), cons2(z1, z2)))
active(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(z1, z2))) → mark(2ndsneg(s(z0), cons2(z1, z2)))
active(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
active(pi(z0)) → mark(2ndspos(z0, from(0)))
active(plus(0, z0)) → mark(z0)
active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
active(times(0, z0)) → mark(0)
active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
active(square(z0)) → mark(times(z0, z0))
active(s(z0)) → s(active(z0))
active(posrecip(z0)) → posrecip(active(z0))
active(negrecip(z0)) → negrecip(active(z0))
active(cons(z0, z1)) → cons(active(z0), z1)
active(cons2(z0, z1)) → cons2(z0, active(z1))
active(rcons(z0, z1)) → rcons(active(z0), z1)
active(rcons(z0, z1)) → rcons(z0, active(z1))
active(from(z0)) → from(active(z0))
active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
active(pi(z0)) → pi(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(times(z0, z1)) → times(active(z0), z1)
active(times(z0, z1)) → times(z0, active(z1))
active(square(z0)) → square(active(z0))
2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
cons2(z0, mark(z1)) → mark(cons2(z0, z1))
cons2(ok(z0), ok(z1)) → ok(cons2(z0, z1))
rcons(mark(z0), z1) → mark(rcons(z0, z1))
rcons(z0, mark(z1)) → mark(rcons(z0, z1))
rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
posrecip(ok(z0)) → ok(posrecip(z0))
posrecip(mark(z0)) → mark(posrecip(z0))
2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
negrecip(ok(z0)) → ok(negrecip(z0))
negrecip(mark(z0)) → mark(negrecip(z0))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
cons(mark(z0), z1) → mark(cons(z0, z1))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
from(mark(z0)) → mark(from(z0))
from(ok(z0)) → ok(from(z0))
pi(mark(z0)) → mark(pi(z0))
pi(ok(z0)) → ok(pi(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
times(mark(z0), z1) → mark(times(z0, z1))
times(ok(z0), ok(z1)) → ok(times(z0, z1))
times(z0, mark(z1)) → mark(times(z0, z1))
square(mark(z0)) → mark(square(z0))
square(ok(z0)) → ok(square(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(posrecip(z0)) → posrecip(proper(z0))
proper(negrecip(z0)) → negrecip(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(cons2(z0, z1)) → cons2(proper(z0), proper(z1))
proper(rnil) → ok(rnil)
proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
proper(pi(z0)) → pi(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(times(z0, z1)) → times(proper(z0), proper(z1))
proper(square(z0)) → square(proper(z0))
Tuples:
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
PROPER(2ndsneg(z0, z1)) → c73(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c74(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c75(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c76(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c77(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c78(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c79(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c9(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(2NDSPOS(s(z0), cons2(z1, z2)))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(2NDSNEG(s(z0), cons2(z1, z2)))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c13(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, z2)))) → c13(S(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(s(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, z2)))) → c13(S(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(s(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c13(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c13(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c13(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c13(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c13(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c13(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c13(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c13(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(cons2(z0, z1))) → c13(S(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c13(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c13(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c13(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c14(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c14(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c14(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c14(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c14(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c14(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c14(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c14(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(cons2(z0, z1))) → c14(POSRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c15(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c15(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c15(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c15(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c15(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c15(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c15(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c15(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(cons2(z0, z1))) → c15(NEGRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndspos(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndspos(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndsneg(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndsneg(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c16(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c16(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c16(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c16(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c16(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c16(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c16(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c16(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(cons2(z0, z1), x1)) → c16(CONS(cons2(z0, active(z1)), x1), ACTIVE(cons2(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, 2ndsneg(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(0, z0))) → c17(CONS2(x0, mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(cons2(x0, plus(s(z0), z1))) → c17(CONS2(x0, mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons2(x0, times(0, z0))) → c17(CONS2(x0, mark(0)), ACTIVE(times(0, z0)))
ACTIVE(cons2(x0, times(s(z0), z1))) → c17(CONS2(x0, mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(cons2(x0, s(z0))) → c17(CONS2(x0, s(active(z0))), ACTIVE(s(z0)))
ACTIVE(cons2(x0, posrecip(z0))) → c17(CONS2(x0, posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(cons2(x0, negrecip(z0))) → c17(CONS2(x0, negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(cons2(x0, cons(z0, z1))) → c17(CONS2(x0, cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(cons2(x0, cons2(z0, z1))) → c17(CONS2(x0, cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, from(active(z0))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, square(active(z0))), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c20(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(from(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(from(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c20(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c20(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c20(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c20(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c20(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c20(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c20(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c20(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c20(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c20(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(cons2(z0, z1))) → c20(FROM(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c20(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c20(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c20(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c25(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c25(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c25(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c25(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c25(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c25(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c25(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c25(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c25(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c25(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c25(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(cons2(z0, z1))) → c25(PI(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c25(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c25(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c25(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c30(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(square(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(square(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c30(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c30(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c30(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c30(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c30(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c30(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c30(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c30(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c30(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(cons2(z0, z1))) → c30(SQUARE(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c30(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c30(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c63(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c63(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c63(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c63(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(cons2(z0, z1))) → c63(S(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(s(rcons(z0, z1))) → c63(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c63(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c63(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c63(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c63(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c63(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c63(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c63(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c63(S(ok(0)))
PROPER(s(nil)) → c63(S(ok(nil)))
PROPER(s(rnil)) → c63(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c64(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c64(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c64(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c64(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(cons2(z0, z1))) → c64(POSRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c64(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c64(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c64(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c64(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c64(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c64(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c64(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c64(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c64(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c64(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c64(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c65(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c65(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c65(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c65(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(cons2(z0, z1))) → c65(NEGRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c65(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c65(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c65(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c65(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c65(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c65(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c65(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c65(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c65(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c65(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c65(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c67(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c67(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c67(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c67(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, cons2(z0, z1))) → c67(CONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c67(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c67(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c67(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c67(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c67(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c67(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c67(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c67(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c67(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c67(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c67(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c67(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(cons2(z0, z1), x1)) → c67(CONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c67(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c67(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c67(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c67(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c67(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c67(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c67(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c67(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c67(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c67(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c67(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c67(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c67(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c67(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(cons2(x0, s(z0))) → c68(CONS2(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons2(x0, posrecip(z0))) → c68(CONS2(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons2(x0, negrecip(z0))) → c68(CONS2(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons2(x0, cons(z0, z1))) → c68(CONS2(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons2(x0, cons2(z0, z1))) → c68(CONS2(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons2(x0, rcons(z0, z1))) → c68(CONS2(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons2(x0, from(z0))) → c68(CONS2(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons2(x0, 2ndspos(z0, z1))) → c68(CONS2(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons2(x0, 2ndsneg(z0, z1))) → c68(CONS2(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons2(x0, pi(z0))) → c68(CONS2(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons2(x0, plus(z0, z1))) → c68(CONS2(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons2(x0, times(z0, z1))) → c68(CONS2(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons2(x0, square(z0))) → c68(CONS2(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons2(s(z0), x1)) → c68(CONS2(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons2(posrecip(z0), x1)) → c68(CONS2(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons2(negrecip(z0), x1)) → c68(CONS2(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons2(cons(z0, z1), x1)) → c68(CONS2(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons2(cons2(z0, z1), x1)) → c68(CONS2(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons2(rcons(z0, z1), x1)) → c68(CONS2(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons2(from(z0), x1)) → c68(CONS2(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons2(2ndspos(z0, z1), x1)) → c68(CONS2(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons2(2ndsneg(z0, z1), x1)) → c68(CONS2(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons2(pi(z0), x1)) → c68(CONS2(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons2(plus(z0, z1), x1)) → c68(CONS2(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons2(times(z0, z1), x1)) → c68(CONS2(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons2(square(z0), x1)) → c68(CONS2(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons2(x0, 0)) → c68(CONS2(proper(x0), ok(0)), PROPER(x0))
PROPER(cons2(x0, nil)) → c68(CONS2(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons2(x0, rnil)) → c68(CONS2(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons2(0, x1)) → c68(CONS2(ok(0), proper(x1)), PROPER(x1))
PROPER(cons2(nil, x1)) → c68(CONS2(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons2(rnil, x1)) → c68(CONS2(ok(rnil), proper(x1)), PROPER(x1))
PROPER(rcons(x0, s(z0))) → c70(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c70(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c70(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, cons(z0, z1))) → c70(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, cons2(z0, z1))) → c70(RCONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(rcons(x0, rcons(z0, z1))) → c70(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c70(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c70(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c70(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c70(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c70(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c70(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c70(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(s(z0), x1)) → c70(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c70(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c70(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c70(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(cons2(z0, z1), x1)) → c70(RCONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c70(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c70(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c70(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c70(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c70(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c70(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c70(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c70(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(rcons(x0, 0)) → c70(RCONS(proper(x0), ok(0)), PROPER(x0))
PROPER(rcons(x0, nil)) → c70(RCONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(rcons(x0, rnil)) → c70(RCONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(rcons(0, x1)) → c70(RCONS(ok(0), proper(x1)), PROPER(x1))
PROPER(rcons(nil, x1)) → c70(RCONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c70(RCONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(from(s(z0))) → c71(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(posrecip(z0))) → c71(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(from(negrecip(z0))) → c71(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(from(cons(z0, z1))) → c71(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(cons2(z0, z1))) → c71(FROM(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(from(rcons(z0, z1))) → c71(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(from(from(z0))) → c71(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(2ndspos(z0, z1))) → c71(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(from(2ndsneg(z0, z1))) → c71(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(from(pi(z0))) → c71(FROM(pi(proper(z0))), PROPER(pi(z0)))
PROPER(from(plus(z0, z1))) → c71(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(from(times(z0, z1))) → c71(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(from(square(z0))) → c71(FROM(square(proper(z0))), PROPER(square(z0)))
PROPER(from(0)) → c71(FROM(ok(0)))
PROPER(from(nil)) → c71(FROM(ok(nil)))
PROPER(from(rnil)) → c71(FROM(ok(rnil)))
PROPER(2ndspos(x0, 0)) → c72(2NDSPOS(proper(x0), ok(0)), PROPER(x0), PROPER(0))
PROPER(2ndspos(x0, s(z0))) → c72(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndspos(x0, posrecip(z0))) → c72(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndspos(x0, negrecip(z0))) → c72(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndspos(x0, nil)) → c72(2NDSPOS(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
PROPER(2ndspos(x0, cons(z0, z1))) → c72(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndspos(x0, cons2(z0, z1))) → c72(2NDSPOS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(2ndspos(x0, rnil)) → c72(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0), PROPER(rnil))
PROPER(2ndspos(x0, rcons(z0, z1))) → c72(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndspos(x0, from(z0))) → c72(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c72(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c72(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndspos(x0, pi(z0))) → c72(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndspos(x0, plus(z0, z1))) → c72(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndspos(x0, times(z0, z1))) → c72(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndspos(x0, square(z0))) → c72(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndspos(0, x1)) → c72(2NDSPOS(ok(0), proper(x1)), PROPER(0), PROPER(x1))
PROPER(2ndspos(s(z0), x1)) → c72(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndspos(posrecip(z0), x1)) → c72(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndspos(negrecip(z0), x1)) → c72(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndspos(nil, x1)) → c72(2NDSPOS(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
PROPER(2ndspos(cons(z0, z1), x1)) → c72(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndspos(cons2(z0, z1), x1)) → c72(2NDSPOS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(2ndspos(rnil, x1)) → c72(2NDSPOS(ok(rnil), proper(x1)), PROPER(rnil), PROPER(x1))
PROPER(2ndspos(rcons(z0, z1), x1)) → c72(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndspos(from(z0), x1)) → c72(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c72(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c72(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndspos(pi(z0), x1)) → c72(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndspos(plus(z0, z1), x1)) → c72(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndspos(times(z0, z1), x1)) → c72(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndspos(square(z0), x1)) → c72(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
S tuples:
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
PROPER(2ndsneg(z0, z1)) → c73(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c74(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c75(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c76(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c77(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c78(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c79(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c9(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(2NDSPOS(s(z0), cons2(z1, z2)))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(2NDSNEG(s(z0), cons2(z1, z2)))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c13(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, z2)))) → c13(S(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(s(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, z2)))) → c13(S(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(s(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c13(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c13(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c13(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c13(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c13(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c13(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c13(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c13(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(cons2(z0, z1))) → c13(S(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c13(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c13(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c13(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c14(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c14(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c14(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c14(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c14(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c14(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c14(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c14(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(cons2(z0, z1))) → c14(POSRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c15(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c15(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c15(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c15(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c15(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c15(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c15(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c15(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(cons2(z0, z1))) → c15(NEGRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndspos(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndspos(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndsneg(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndsneg(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c16(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c16(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c16(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c16(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c16(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c16(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c16(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c16(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(cons2(z0, z1), x1)) → c16(CONS(cons2(z0, active(z1)), x1), ACTIVE(cons2(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, 2ndsneg(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(0, z0))) → c17(CONS2(x0, mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(cons2(x0, plus(s(z0), z1))) → c17(CONS2(x0, mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons2(x0, times(0, z0))) → c17(CONS2(x0, mark(0)), ACTIVE(times(0, z0)))
ACTIVE(cons2(x0, times(s(z0), z1))) → c17(CONS2(x0, mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(cons2(x0, s(z0))) → c17(CONS2(x0, s(active(z0))), ACTIVE(s(z0)))
ACTIVE(cons2(x0, posrecip(z0))) → c17(CONS2(x0, posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(cons2(x0, negrecip(z0))) → c17(CONS2(x0, negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(cons2(x0, cons(z0, z1))) → c17(CONS2(x0, cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(cons2(x0, cons2(z0, z1))) → c17(CONS2(x0, cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, from(active(z0))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, square(active(z0))), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c20(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(from(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(from(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c20(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c20(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c20(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c20(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c20(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c20(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c20(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c20(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c20(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c20(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(cons2(z0, z1))) → c20(FROM(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c20(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c20(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c20(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c25(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c25(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c25(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c25(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c25(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c25(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c25(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c25(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c25(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c25(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c25(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(cons2(z0, z1))) → c25(PI(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c25(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c25(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c25(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c30(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(square(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(square(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c30(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c30(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c30(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c30(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c30(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c30(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c30(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c30(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c30(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(cons2(z0, z1))) → c30(SQUARE(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c30(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c30(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c63(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c63(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c63(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c63(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(cons2(z0, z1))) → c63(S(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(s(rcons(z0, z1))) → c63(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c63(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c63(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c63(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c63(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c63(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c63(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c63(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c63(S(ok(0)))
PROPER(s(nil)) → c63(S(ok(nil)))
PROPER(s(rnil)) → c63(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c64(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c64(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c64(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c64(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(cons2(z0, z1))) → c64(POSRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c64(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c64(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c64(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c64(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c64(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c64(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c64(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c64(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c64(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c64(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c64(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c65(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c65(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c65(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c65(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(cons2(z0, z1))) → c65(NEGRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c65(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c65(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c65(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c65(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c65(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c65(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c65(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c65(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c65(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c65(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c65(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c67(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c67(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c67(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c67(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, cons2(z0, z1))) → c67(CONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c67(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c67(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c67(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c67(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c67(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c67(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c67(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c67(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c67(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c67(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c67(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c67(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(cons2(z0, z1), x1)) → c67(CONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c67(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c67(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c67(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c67(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c67(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c67(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c67(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c67(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c67(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c67(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c67(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c67(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c67(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c67(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(cons2(x0, s(z0))) → c68(CONS2(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons2(x0, posrecip(z0))) → c68(CONS2(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons2(x0, negrecip(z0))) → c68(CONS2(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons2(x0, cons(z0, z1))) → c68(CONS2(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons2(x0, cons2(z0, z1))) → c68(CONS2(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons2(x0, rcons(z0, z1))) → c68(CONS2(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons2(x0, from(z0))) → c68(CONS2(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons2(x0, 2ndspos(z0, z1))) → c68(CONS2(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons2(x0, 2ndsneg(z0, z1))) → c68(CONS2(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons2(x0, pi(z0))) → c68(CONS2(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons2(x0, plus(z0, z1))) → c68(CONS2(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons2(x0, times(z0, z1))) → c68(CONS2(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons2(x0, square(z0))) → c68(CONS2(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons2(s(z0), x1)) → c68(CONS2(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons2(posrecip(z0), x1)) → c68(CONS2(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons2(negrecip(z0), x1)) → c68(CONS2(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons2(cons(z0, z1), x1)) → c68(CONS2(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons2(cons2(z0, z1), x1)) → c68(CONS2(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons2(rcons(z0, z1), x1)) → c68(CONS2(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons2(from(z0), x1)) → c68(CONS2(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons2(2ndspos(z0, z1), x1)) → c68(CONS2(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons2(2ndsneg(z0, z1), x1)) → c68(CONS2(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons2(pi(z0), x1)) → c68(CONS2(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons2(plus(z0, z1), x1)) → c68(CONS2(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons2(times(z0, z1), x1)) → c68(CONS2(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons2(square(z0), x1)) → c68(CONS2(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons2(x0, 0)) → c68(CONS2(proper(x0), ok(0)), PROPER(x0))
PROPER(cons2(x0, nil)) → c68(CONS2(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons2(x0, rnil)) → c68(CONS2(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons2(0, x1)) → c68(CONS2(ok(0), proper(x1)), PROPER(x1))
PROPER(cons2(nil, x1)) → c68(CONS2(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons2(rnil, x1)) → c68(CONS2(ok(rnil), proper(x1)), PROPER(x1))
PROPER(rcons(x0, s(z0))) → c70(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c70(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c70(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, cons(z0, z1))) → c70(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, cons2(z0, z1))) → c70(RCONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(rcons(x0, rcons(z0, z1))) → c70(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c70(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c70(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c70(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c70(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c70(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c70(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c70(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(s(z0), x1)) → c70(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c70(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c70(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c70(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(cons2(z0, z1), x1)) → c70(RCONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c70(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c70(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c70(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c70(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c70(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c70(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c70(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c70(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(rcons(x0, 0)) → c70(RCONS(proper(x0), ok(0)), PROPER(x0))
PROPER(rcons(x0, nil)) → c70(RCONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(rcons(x0, rnil)) → c70(RCONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(rcons(0, x1)) → c70(RCONS(ok(0), proper(x1)), PROPER(x1))
PROPER(rcons(nil, x1)) → c70(RCONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c70(RCONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(from(s(z0))) → c71(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(posrecip(z0))) → c71(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(from(negrecip(z0))) → c71(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(from(cons(z0, z1))) → c71(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(cons2(z0, z1))) → c71(FROM(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(from(rcons(z0, z1))) → c71(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(from(from(z0))) → c71(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(2ndspos(z0, z1))) → c71(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(from(2ndsneg(z0, z1))) → c71(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(from(pi(z0))) → c71(FROM(pi(proper(z0))), PROPER(pi(z0)))
PROPER(from(plus(z0, z1))) → c71(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(from(times(z0, z1))) → c71(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(from(square(z0))) → c71(FROM(square(proper(z0))), PROPER(square(z0)))
PROPER(from(0)) → c71(FROM(ok(0)))
PROPER(from(nil)) → c71(FROM(ok(nil)))
PROPER(from(rnil)) → c71(FROM(ok(rnil)))
PROPER(2ndspos(x0, 0)) → c72(2NDSPOS(proper(x0), ok(0)), PROPER(x0), PROPER(0))
PROPER(2ndspos(x0, s(z0))) → c72(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndspos(x0, posrecip(z0))) → c72(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndspos(x0, negrecip(z0))) → c72(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndspos(x0, nil)) → c72(2NDSPOS(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
PROPER(2ndspos(x0, cons(z0, z1))) → c72(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndspos(x0, cons2(z0, z1))) → c72(2NDSPOS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(2ndspos(x0, rnil)) → c72(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0), PROPER(rnil))
PROPER(2ndspos(x0, rcons(z0, z1))) → c72(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndspos(x0, from(z0))) → c72(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c72(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c72(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndspos(x0, pi(z0))) → c72(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndspos(x0, plus(z0, z1))) → c72(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndspos(x0, times(z0, z1))) → c72(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndspos(x0, square(z0))) → c72(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndspos(0, x1)) → c72(2NDSPOS(ok(0), proper(x1)), PROPER(0), PROPER(x1))
PROPER(2ndspos(s(z0), x1)) → c72(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndspos(posrecip(z0), x1)) → c72(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndspos(negrecip(z0), x1)) → c72(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndspos(nil, x1)) → c72(2NDSPOS(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
PROPER(2ndspos(cons(z0, z1), x1)) → c72(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndspos(cons2(z0, z1), x1)) → c72(2NDSPOS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(2ndspos(rnil, x1)) → c72(2NDSPOS(ok(rnil), proper(x1)), PROPER(rnil), PROPER(x1))
PROPER(2ndspos(rcons(z0, z1), x1)) → c72(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndspos(from(z0), x1)) → c72(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c72(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c72(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndspos(pi(z0), x1)) → c72(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndspos(plus(z0, z1), x1)) → c72(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndspos(times(z0, z1), x1)) → c72(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndspos(square(z0), x1)) → c72(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
K tuples:none
Defined Rule Symbols:
active, 2ndspos, cons2, rcons, posrecip, 2ndsneg, negrecip, s, cons, from, pi, plus, times, square, proper
Defined Pair Symbols:
ACTIVE, S, POSRECIP, NEGRECIP, CONS, CONS2, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP
Compound Symbols:
c12, c18, c19, c21, c22, c23, c24, c26, c27, c28, c29, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c73, c74, c75, c76, c77, c78, c79, c, c7, c9, c11, c1, c13, c14, c15, c16, c17, c20, c25, c30, c63, c63, c64, c64, c65, c65, c67, c67, c68, c68, c70, c70, c71, c71, c72
(57) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 6 trailing tuple parts
(58) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(2ndspos(0, z0)) → mark(rnil)
active(2ndspos(s(z0), cons(z1, z2))) → mark(2ndspos(s(z0), cons2(z1, z2)))
active(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(z1, z2))) → mark(2ndsneg(s(z0), cons2(z1, z2)))
active(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
active(pi(z0)) → mark(2ndspos(z0, from(0)))
active(plus(0, z0)) → mark(z0)
active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
active(times(0, z0)) → mark(0)
active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
active(square(z0)) → mark(times(z0, z0))
active(s(z0)) → s(active(z0))
active(posrecip(z0)) → posrecip(active(z0))
active(negrecip(z0)) → negrecip(active(z0))
active(cons(z0, z1)) → cons(active(z0), z1)
active(cons2(z0, z1)) → cons2(z0, active(z1))
active(rcons(z0, z1)) → rcons(active(z0), z1)
active(rcons(z0, z1)) → rcons(z0, active(z1))
active(from(z0)) → from(active(z0))
active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
active(pi(z0)) → pi(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(times(z0, z1)) → times(active(z0), z1)
active(times(z0, z1)) → times(z0, active(z1))
active(square(z0)) → square(active(z0))
2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
cons2(z0, mark(z1)) → mark(cons2(z0, z1))
cons2(ok(z0), ok(z1)) → ok(cons2(z0, z1))
rcons(mark(z0), z1) → mark(rcons(z0, z1))
rcons(z0, mark(z1)) → mark(rcons(z0, z1))
rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
posrecip(ok(z0)) → ok(posrecip(z0))
posrecip(mark(z0)) → mark(posrecip(z0))
2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
negrecip(ok(z0)) → ok(negrecip(z0))
negrecip(mark(z0)) → mark(negrecip(z0))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
cons(mark(z0), z1) → mark(cons(z0, z1))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
from(mark(z0)) → mark(from(z0))
from(ok(z0)) → ok(from(z0))
pi(mark(z0)) → mark(pi(z0))
pi(ok(z0)) → ok(pi(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
times(mark(z0), z1) → mark(times(z0, z1))
times(ok(z0), ok(z1)) → ok(times(z0, z1))
times(z0, mark(z1)) → mark(times(z0, z1))
square(mark(z0)) → mark(square(z0))
square(ok(z0)) → ok(square(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(posrecip(z0)) → posrecip(proper(z0))
proper(negrecip(z0)) → negrecip(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(cons2(z0, z1)) → cons2(proper(z0), proper(z1))
proper(rnil) → ok(rnil)
proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
proper(pi(z0)) → pi(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(times(z0, z1)) → times(proper(z0), proper(z1))
proper(square(z0)) → square(proper(z0))
Tuples:
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
PROPER(2ndsneg(z0, z1)) → c73(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c74(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c75(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c76(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c77(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c78(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c79(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c9(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(2NDSPOS(s(z0), cons2(z1, z2)))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(2NDSNEG(s(z0), cons2(z1, z2)))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c13(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, z2)))) → c13(S(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(s(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, z2)))) → c13(S(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(s(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c13(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c13(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c13(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c13(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c13(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c13(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c13(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c13(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(cons2(z0, z1))) → c13(S(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c13(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c13(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c13(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c14(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c14(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c14(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c14(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c14(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c14(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c14(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c14(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(cons2(z0, z1))) → c14(POSRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c15(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c15(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c15(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c15(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c15(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c15(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c15(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c15(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(cons2(z0, z1))) → c15(NEGRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndspos(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndspos(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndsneg(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndsneg(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c16(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c16(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c16(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c16(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c16(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c16(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c16(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c16(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(cons2(z0, z1), x1)) → c16(CONS(cons2(z0, active(z1)), x1), ACTIVE(cons2(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, 2ndsneg(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(0, z0))) → c17(CONS2(x0, mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(cons2(x0, plus(s(z0), z1))) → c17(CONS2(x0, mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons2(x0, times(0, z0))) → c17(CONS2(x0, mark(0)), ACTIVE(times(0, z0)))
ACTIVE(cons2(x0, times(s(z0), z1))) → c17(CONS2(x0, mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(cons2(x0, s(z0))) → c17(CONS2(x0, s(active(z0))), ACTIVE(s(z0)))
ACTIVE(cons2(x0, posrecip(z0))) → c17(CONS2(x0, posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(cons2(x0, negrecip(z0))) → c17(CONS2(x0, negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(cons2(x0, cons(z0, z1))) → c17(CONS2(x0, cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(cons2(x0, cons2(z0, z1))) → c17(CONS2(x0, cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, from(active(z0))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, square(active(z0))), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c20(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(from(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(from(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c20(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c20(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c20(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c20(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c20(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c20(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c20(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c20(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c20(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c20(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(cons2(z0, z1))) → c20(FROM(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c20(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c20(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c20(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c25(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c25(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c25(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c25(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c25(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c25(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c25(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c25(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c25(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c25(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c25(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(cons2(z0, z1))) → c25(PI(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c25(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c25(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c25(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c30(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(square(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(square(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c30(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c30(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c30(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c30(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c30(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c30(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c30(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c30(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c30(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(cons2(z0, z1))) → c30(SQUARE(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c30(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c30(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c63(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c63(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c63(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c63(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(cons2(z0, z1))) → c63(S(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(s(rcons(z0, z1))) → c63(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c63(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c63(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c63(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c63(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c63(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c63(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c63(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c63(S(ok(0)))
PROPER(s(nil)) → c63(S(ok(nil)))
PROPER(s(rnil)) → c63(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c64(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c64(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c64(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c64(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(cons2(z0, z1))) → c64(POSRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c64(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c64(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c64(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c64(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c64(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c64(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c64(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c64(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c64(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c64(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c64(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c65(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c65(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c65(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c65(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(cons2(z0, z1))) → c65(NEGRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c65(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c65(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c65(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c65(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c65(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c65(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c65(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c65(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c65(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c65(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c65(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c67(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c67(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c67(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c67(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, cons2(z0, z1))) → c67(CONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c67(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c67(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c67(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c67(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c67(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c67(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c67(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c67(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c67(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c67(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c67(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c67(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(cons2(z0, z1), x1)) → c67(CONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c67(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c67(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c67(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c67(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c67(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c67(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c67(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c67(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c67(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c67(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c67(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c67(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c67(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c67(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(cons2(x0, s(z0))) → c68(CONS2(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons2(x0, posrecip(z0))) → c68(CONS2(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons2(x0, negrecip(z0))) → c68(CONS2(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons2(x0, cons(z0, z1))) → c68(CONS2(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons2(x0, cons2(z0, z1))) → c68(CONS2(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons2(x0, rcons(z0, z1))) → c68(CONS2(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons2(x0, from(z0))) → c68(CONS2(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons2(x0, 2ndspos(z0, z1))) → c68(CONS2(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons2(x0, 2ndsneg(z0, z1))) → c68(CONS2(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons2(x0, pi(z0))) → c68(CONS2(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons2(x0, plus(z0, z1))) → c68(CONS2(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons2(x0, times(z0, z1))) → c68(CONS2(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons2(x0, square(z0))) → c68(CONS2(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons2(s(z0), x1)) → c68(CONS2(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons2(posrecip(z0), x1)) → c68(CONS2(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons2(negrecip(z0), x1)) → c68(CONS2(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons2(cons(z0, z1), x1)) → c68(CONS2(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons2(cons2(z0, z1), x1)) → c68(CONS2(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons2(rcons(z0, z1), x1)) → c68(CONS2(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons2(from(z0), x1)) → c68(CONS2(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons2(2ndspos(z0, z1), x1)) → c68(CONS2(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons2(2ndsneg(z0, z1), x1)) → c68(CONS2(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons2(pi(z0), x1)) → c68(CONS2(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons2(plus(z0, z1), x1)) → c68(CONS2(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons2(times(z0, z1), x1)) → c68(CONS2(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons2(square(z0), x1)) → c68(CONS2(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons2(x0, 0)) → c68(CONS2(proper(x0), ok(0)), PROPER(x0))
PROPER(cons2(x0, nil)) → c68(CONS2(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons2(x0, rnil)) → c68(CONS2(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons2(0, x1)) → c68(CONS2(ok(0), proper(x1)), PROPER(x1))
PROPER(cons2(nil, x1)) → c68(CONS2(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons2(rnil, x1)) → c68(CONS2(ok(rnil), proper(x1)), PROPER(x1))
PROPER(rcons(x0, s(z0))) → c70(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c70(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c70(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, cons(z0, z1))) → c70(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, cons2(z0, z1))) → c70(RCONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(rcons(x0, rcons(z0, z1))) → c70(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c70(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c70(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c70(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c70(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c70(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c70(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c70(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(s(z0), x1)) → c70(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c70(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c70(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c70(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(cons2(z0, z1), x1)) → c70(RCONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c70(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c70(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c70(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c70(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c70(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c70(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c70(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c70(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(rcons(x0, 0)) → c70(RCONS(proper(x0), ok(0)), PROPER(x0))
PROPER(rcons(x0, nil)) → c70(RCONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(rcons(x0, rnil)) → c70(RCONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(rcons(0, x1)) → c70(RCONS(ok(0), proper(x1)), PROPER(x1))
PROPER(rcons(nil, x1)) → c70(RCONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c70(RCONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(from(s(z0))) → c71(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(posrecip(z0))) → c71(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(from(negrecip(z0))) → c71(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(from(cons(z0, z1))) → c71(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(cons2(z0, z1))) → c71(FROM(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(from(rcons(z0, z1))) → c71(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(from(from(z0))) → c71(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(2ndspos(z0, z1))) → c71(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(from(2ndsneg(z0, z1))) → c71(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(from(pi(z0))) → c71(FROM(pi(proper(z0))), PROPER(pi(z0)))
PROPER(from(plus(z0, z1))) → c71(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(from(times(z0, z1))) → c71(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(from(square(z0))) → c71(FROM(square(proper(z0))), PROPER(square(z0)))
PROPER(from(0)) → c71(FROM(ok(0)))
PROPER(from(nil)) → c71(FROM(ok(nil)))
PROPER(from(rnil)) → c71(FROM(ok(rnil)))
PROPER(2ndspos(x0, s(z0))) → c72(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndspos(x0, posrecip(z0))) → c72(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndspos(x0, negrecip(z0))) → c72(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndspos(x0, cons(z0, z1))) → c72(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndspos(x0, cons2(z0, z1))) → c72(2NDSPOS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(2ndspos(x0, rcons(z0, z1))) → c72(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndspos(x0, from(z0))) → c72(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c72(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c72(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndspos(x0, pi(z0))) → c72(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndspos(x0, plus(z0, z1))) → c72(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndspos(x0, times(z0, z1))) → c72(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndspos(x0, square(z0))) → c72(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndspos(s(z0), x1)) → c72(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndspos(posrecip(z0), x1)) → c72(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndspos(negrecip(z0), x1)) → c72(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndspos(cons(z0, z1), x1)) → c72(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndspos(cons2(z0, z1), x1)) → c72(2NDSPOS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(2ndspos(rcons(z0, z1), x1)) → c72(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndspos(from(z0), x1)) → c72(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c72(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c72(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndspos(pi(z0), x1)) → c72(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndspos(plus(z0, z1), x1)) → c72(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndspos(times(z0, z1), x1)) → c72(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndspos(square(z0), x1)) → c72(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndspos(x0, 0)) → c72(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndspos(x0, nil)) → c72(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndspos(x0, rnil)) → c72(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndspos(0, x1)) → c72(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndspos(nil, x1)) → c72(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndspos(rnil, x1)) → c72(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
S tuples:
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
PROPER(2ndsneg(z0, z1)) → c73(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c74(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c75(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c76(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c77(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c78(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c79(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c9(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(2NDSPOS(s(z0), cons2(z1, z2)))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(2NDSNEG(s(z0), cons2(z1, z2)))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c13(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, z2)))) → c13(S(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(s(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, z2)))) → c13(S(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(s(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c13(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c13(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c13(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c13(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c13(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c13(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c13(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c13(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(cons2(z0, z1))) → c13(S(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c13(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c13(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c13(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c14(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c14(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c14(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c14(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c14(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c14(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c14(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c14(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(cons2(z0, z1))) → c14(POSRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c15(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c15(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c15(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c15(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c15(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c15(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c15(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c15(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(cons2(z0, z1))) → c15(NEGRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndspos(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndspos(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndsneg(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndsneg(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c16(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c16(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c16(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c16(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c16(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c16(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c16(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c16(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(cons2(z0, z1), x1)) → c16(CONS(cons2(z0, active(z1)), x1), ACTIVE(cons2(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, 2ndsneg(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(0, z0))) → c17(CONS2(x0, mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(cons2(x0, plus(s(z0), z1))) → c17(CONS2(x0, mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons2(x0, times(0, z0))) → c17(CONS2(x0, mark(0)), ACTIVE(times(0, z0)))
ACTIVE(cons2(x0, times(s(z0), z1))) → c17(CONS2(x0, mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(cons2(x0, s(z0))) → c17(CONS2(x0, s(active(z0))), ACTIVE(s(z0)))
ACTIVE(cons2(x0, posrecip(z0))) → c17(CONS2(x0, posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(cons2(x0, negrecip(z0))) → c17(CONS2(x0, negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(cons2(x0, cons(z0, z1))) → c17(CONS2(x0, cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(cons2(x0, cons2(z0, z1))) → c17(CONS2(x0, cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, from(active(z0))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, square(active(z0))), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c20(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(from(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(from(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c20(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c20(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c20(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c20(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c20(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c20(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c20(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c20(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c20(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c20(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(cons2(z0, z1))) → c20(FROM(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c20(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c20(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c20(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c25(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c25(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c25(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c25(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c25(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c25(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c25(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c25(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c25(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c25(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c25(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(cons2(z0, z1))) → c25(PI(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c25(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c25(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c25(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c30(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(square(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(square(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c30(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c30(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c30(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c30(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c30(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c30(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c30(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c30(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c30(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(cons2(z0, z1))) → c30(SQUARE(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c30(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c30(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c63(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c63(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c63(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c63(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(cons2(z0, z1))) → c63(S(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(s(rcons(z0, z1))) → c63(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c63(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c63(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c63(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c63(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c63(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c63(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c63(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c63(S(ok(0)))
PROPER(s(nil)) → c63(S(ok(nil)))
PROPER(s(rnil)) → c63(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c64(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c64(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c64(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c64(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(cons2(z0, z1))) → c64(POSRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c64(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c64(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c64(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c64(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c64(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c64(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c64(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c64(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c64(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c64(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c64(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c65(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c65(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c65(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c65(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(cons2(z0, z1))) → c65(NEGRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c65(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c65(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c65(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c65(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c65(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c65(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c65(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c65(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c65(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c65(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c65(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c67(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c67(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c67(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c67(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, cons2(z0, z1))) → c67(CONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c67(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c67(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c67(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c67(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c67(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c67(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c67(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c67(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c67(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c67(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c67(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c67(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(cons2(z0, z1), x1)) → c67(CONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c67(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c67(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c67(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c67(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c67(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c67(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c67(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c67(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c67(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c67(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c67(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c67(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c67(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c67(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(cons2(x0, s(z0))) → c68(CONS2(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons2(x0, posrecip(z0))) → c68(CONS2(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons2(x0, negrecip(z0))) → c68(CONS2(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons2(x0, cons(z0, z1))) → c68(CONS2(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons2(x0, cons2(z0, z1))) → c68(CONS2(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons2(x0, rcons(z0, z1))) → c68(CONS2(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons2(x0, from(z0))) → c68(CONS2(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons2(x0, 2ndspos(z0, z1))) → c68(CONS2(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons2(x0, 2ndsneg(z0, z1))) → c68(CONS2(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons2(x0, pi(z0))) → c68(CONS2(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons2(x0, plus(z0, z1))) → c68(CONS2(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons2(x0, times(z0, z1))) → c68(CONS2(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons2(x0, square(z0))) → c68(CONS2(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons2(s(z0), x1)) → c68(CONS2(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons2(posrecip(z0), x1)) → c68(CONS2(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons2(negrecip(z0), x1)) → c68(CONS2(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons2(cons(z0, z1), x1)) → c68(CONS2(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons2(cons2(z0, z1), x1)) → c68(CONS2(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons2(rcons(z0, z1), x1)) → c68(CONS2(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons2(from(z0), x1)) → c68(CONS2(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons2(2ndspos(z0, z1), x1)) → c68(CONS2(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons2(2ndsneg(z0, z1), x1)) → c68(CONS2(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons2(pi(z0), x1)) → c68(CONS2(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons2(plus(z0, z1), x1)) → c68(CONS2(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons2(times(z0, z1), x1)) → c68(CONS2(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons2(square(z0), x1)) → c68(CONS2(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons2(x0, 0)) → c68(CONS2(proper(x0), ok(0)), PROPER(x0))
PROPER(cons2(x0, nil)) → c68(CONS2(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons2(x0, rnil)) → c68(CONS2(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons2(0, x1)) → c68(CONS2(ok(0), proper(x1)), PROPER(x1))
PROPER(cons2(nil, x1)) → c68(CONS2(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons2(rnil, x1)) → c68(CONS2(ok(rnil), proper(x1)), PROPER(x1))
PROPER(rcons(x0, s(z0))) → c70(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c70(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c70(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, cons(z0, z1))) → c70(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, cons2(z0, z1))) → c70(RCONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(rcons(x0, rcons(z0, z1))) → c70(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c70(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c70(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c70(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c70(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c70(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c70(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c70(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(s(z0), x1)) → c70(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c70(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c70(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c70(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(cons2(z0, z1), x1)) → c70(RCONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c70(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c70(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c70(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c70(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c70(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c70(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c70(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c70(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(rcons(x0, 0)) → c70(RCONS(proper(x0), ok(0)), PROPER(x0))
PROPER(rcons(x0, nil)) → c70(RCONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(rcons(x0, rnil)) → c70(RCONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(rcons(0, x1)) → c70(RCONS(ok(0), proper(x1)), PROPER(x1))
PROPER(rcons(nil, x1)) → c70(RCONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c70(RCONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(from(s(z0))) → c71(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(posrecip(z0))) → c71(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(from(negrecip(z0))) → c71(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(from(cons(z0, z1))) → c71(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(cons2(z0, z1))) → c71(FROM(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(from(rcons(z0, z1))) → c71(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(from(from(z0))) → c71(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(2ndspos(z0, z1))) → c71(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(from(2ndsneg(z0, z1))) → c71(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(from(pi(z0))) → c71(FROM(pi(proper(z0))), PROPER(pi(z0)))
PROPER(from(plus(z0, z1))) → c71(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(from(times(z0, z1))) → c71(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(from(square(z0))) → c71(FROM(square(proper(z0))), PROPER(square(z0)))
PROPER(from(0)) → c71(FROM(ok(0)))
PROPER(from(nil)) → c71(FROM(ok(nil)))
PROPER(from(rnil)) → c71(FROM(ok(rnil)))
PROPER(2ndspos(x0, s(z0))) → c72(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndspos(x0, posrecip(z0))) → c72(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndspos(x0, negrecip(z0))) → c72(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndspos(x0, cons(z0, z1))) → c72(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndspos(x0, cons2(z0, z1))) → c72(2NDSPOS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(2ndspos(x0, rcons(z0, z1))) → c72(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndspos(x0, from(z0))) → c72(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c72(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c72(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndspos(x0, pi(z0))) → c72(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndspos(x0, plus(z0, z1))) → c72(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndspos(x0, times(z0, z1))) → c72(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndspos(x0, square(z0))) → c72(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndspos(s(z0), x1)) → c72(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndspos(posrecip(z0), x1)) → c72(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndspos(negrecip(z0), x1)) → c72(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndspos(cons(z0, z1), x1)) → c72(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndspos(cons2(z0, z1), x1)) → c72(2NDSPOS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(2ndspos(rcons(z0, z1), x1)) → c72(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndspos(from(z0), x1)) → c72(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c72(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c72(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndspos(pi(z0), x1)) → c72(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndspos(plus(z0, z1), x1)) → c72(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndspos(times(z0, z1), x1)) → c72(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndspos(square(z0), x1)) → c72(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndspos(x0, 0)) → c72(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndspos(x0, nil)) → c72(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndspos(x0, rnil)) → c72(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndspos(0, x1)) → c72(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndspos(nil, x1)) → c72(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndspos(rnil, x1)) → c72(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
K tuples:none
Defined Rule Symbols:
active, 2ndspos, cons2, rcons, posrecip, 2ndsneg, negrecip, s, cons, from, pi, plus, times, square, proper
Defined Pair Symbols:
ACTIVE, S, POSRECIP, NEGRECIP, CONS, CONS2, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP
Compound Symbols:
c12, c18, c19, c21, c22, c23, c24, c26, c27, c28, c29, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c73, c74, c75, c76, c77, c78, c79, c, c7, c9, c11, c1, c13, c14, c15, c16, c17, c20, c25, c30, c63, c63, c64, c64, c65, c65, c67, c67, c68, c68, c70, c70, c71, c71, c72, c72
(59) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
PROPER(
2ndsneg(
z0,
z1)) →
c73(
2NDSNEG(
proper(
z0),
proper(
z1)),
PROPER(
z0),
PROPER(
z1)) by
PROPER(2ndsneg(x0, 0)) → c73(2NDSNEG(proper(x0), ok(0)), PROPER(x0), PROPER(0))
PROPER(2ndsneg(x0, s(z0))) → c73(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndsneg(x0, posrecip(z0))) → c73(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndsneg(x0, negrecip(z0))) → c73(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndsneg(x0, nil)) → c73(2NDSNEG(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
PROPER(2ndsneg(x0, cons(z0, z1))) → c73(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndsneg(x0, cons2(z0, z1))) → c73(2NDSNEG(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(2ndsneg(x0, rnil)) → c73(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0), PROPER(rnil))
PROPER(2ndsneg(x0, rcons(z0, z1))) → c73(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndsneg(x0, from(z0))) → c73(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c73(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c73(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndsneg(x0, pi(z0))) → c73(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndsneg(x0, plus(z0, z1))) → c73(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndsneg(x0, times(z0, z1))) → c73(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndsneg(x0, square(z0))) → c73(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndsneg(0, x1)) → c73(2NDSNEG(ok(0), proper(x1)), PROPER(0), PROPER(x1))
PROPER(2ndsneg(s(z0), x1)) → c73(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndsneg(posrecip(z0), x1)) → c73(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndsneg(negrecip(z0), x1)) → c73(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndsneg(nil, x1)) → c73(2NDSNEG(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
PROPER(2ndsneg(cons(z0, z1), x1)) → c73(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(cons2(z0, z1), x1)) → c73(2NDSNEG(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(2ndsneg(rnil, x1)) → c73(2NDSNEG(ok(rnil), proper(x1)), PROPER(rnil), PROPER(x1))
PROPER(2ndsneg(rcons(z0, z1), x1)) → c73(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(from(z0), x1)) → c73(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c73(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c73(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndsneg(pi(z0), x1)) → c73(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndsneg(plus(z0, z1), x1)) → c73(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndsneg(times(z0, z1), x1)) → c73(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndsneg(square(z0), x1)) → c73(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
(60) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(2ndspos(0, z0)) → mark(rnil)
active(2ndspos(s(z0), cons(z1, z2))) → mark(2ndspos(s(z0), cons2(z1, z2)))
active(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(z1, z2))) → mark(2ndsneg(s(z0), cons2(z1, z2)))
active(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
active(pi(z0)) → mark(2ndspos(z0, from(0)))
active(plus(0, z0)) → mark(z0)
active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
active(times(0, z0)) → mark(0)
active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
active(square(z0)) → mark(times(z0, z0))
active(s(z0)) → s(active(z0))
active(posrecip(z0)) → posrecip(active(z0))
active(negrecip(z0)) → negrecip(active(z0))
active(cons(z0, z1)) → cons(active(z0), z1)
active(cons2(z0, z1)) → cons2(z0, active(z1))
active(rcons(z0, z1)) → rcons(active(z0), z1)
active(rcons(z0, z1)) → rcons(z0, active(z1))
active(from(z0)) → from(active(z0))
active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
active(pi(z0)) → pi(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(times(z0, z1)) → times(active(z0), z1)
active(times(z0, z1)) → times(z0, active(z1))
active(square(z0)) → square(active(z0))
2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
cons2(z0, mark(z1)) → mark(cons2(z0, z1))
cons2(ok(z0), ok(z1)) → ok(cons2(z0, z1))
rcons(mark(z0), z1) → mark(rcons(z0, z1))
rcons(z0, mark(z1)) → mark(rcons(z0, z1))
rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
posrecip(ok(z0)) → ok(posrecip(z0))
posrecip(mark(z0)) → mark(posrecip(z0))
2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
negrecip(ok(z0)) → ok(negrecip(z0))
negrecip(mark(z0)) → mark(negrecip(z0))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
cons(mark(z0), z1) → mark(cons(z0, z1))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
from(mark(z0)) → mark(from(z0))
from(ok(z0)) → ok(from(z0))
pi(mark(z0)) → mark(pi(z0))
pi(ok(z0)) → ok(pi(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
times(mark(z0), z1) → mark(times(z0, z1))
times(ok(z0), ok(z1)) → ok(times(z0, z1))
times(z0, mark(z1)) → mark(times(z0, z1))
square(mark(z0)) → mark(square(z0))
square(ok(z0)) → ok(square(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(posrecip(z0)) → posrecip(proper(z0))
proper(negrecip(z0)) → negrecip(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(cons2(z0, z1)) → cons2(proper(z0), proper(z1))
proper(rnil) → ok(rnil)
proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
proper(pi(z0)) → pi(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(times(z0, z1)) → times(proper(z0), proper(z1))
proper(square(z0)) → square(proper(z0))
Tuples:
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
PROPER(pi(z0)) → c74(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c75(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c76(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c77(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c78(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c79(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c9(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(2NDSPOS(s(z0), cons2(z1, z2)))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(2NDSNEG(s(z0), cons2(z1, z2)))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c13(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, z2)))) → c13(S(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(s(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, z2)))) → c13(S(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(s(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c13(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c13(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c13(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c13(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c13(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c13(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c13(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c13(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(cons2(z0, z1))) → c13(S(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c13(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c13(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c13(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c14(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c14(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c14(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c14(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c14(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c14(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c14(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c14(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(cons2(z0, z1))) → c14(POSRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c15(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c15(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c15(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c15(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c15(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c15(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c15(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c15(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(cons2(z0, z1))) → c15(NEGRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndspos(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndspos(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndsneg(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndsneg(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c16(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c16(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c16(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c16(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c16(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c16(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c16(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c16(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(cons2(z0, z1), x1)) → c16(CONS(cons2(z0, active(z1)), x1), ACTIVE(cons2(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, 2ndsneg(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(0, z0))) → c17(CONS2(x0, mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(cons2(x0, plus(s(z0), z1))) → c17(CONS2(x0, mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons2(x0, times(0, z0))) → c17(CONS2(x0, mark(0)), ACTIVE(times(0, z0)))
ACTIVE(cons2(x0, times(s(z0), z1))) → c17(CONS2(x0, mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(cons2(x0, s(z0))) → c17(CONS2(x0, s(active(z0))), ACTIVE(s(z0)))
ACTIVE(cons2(x0, posrecip(z0))) → c17(CONS2(x0, posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(cons2(x0, negrecip(z0))) → c17(CONS2(x0, negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(cons2(x0, cons(z0, z1))) → c17(CONS2(x0, cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(cons2(x0, cons2(z0, z1))) → c17(CONS2(x0, cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, from(active(z0))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, square(active(z0))), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c20(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(from(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(from(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c20(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c20(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c20(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c20(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c20(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c20(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c20(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c20(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c20(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c20(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(cons2(z0, z1))) → c20(FROM(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c20(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c20(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c20(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c25(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c25(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c25(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c25(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c25(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c25(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c25(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c25(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c25(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c25(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c25(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(cons2(z0, z1))) → c25(PI(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c25(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c25(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c25(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c30(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(square(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(square(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c30(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c30(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c30(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c30(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c30(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c30(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c30(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c30(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c30(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(cons2(z0, z1))) → c30(SQUARE(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c30(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c30(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c63(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c63(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c63(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c63(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(cons2(z0, z1))) → c63(S(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(s(rcons(z0, z1))) → c63(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c63(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c63(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c63(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c63(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c63(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c63(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c63(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c63(S(ok(0)))
PROPER(s(nil)) → c63(S(ok(nil)))
PROPER(s(rnil)) → c63(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c64(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c64(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c64(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c64(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(cons2(z0, z1))) → c64(POSRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c64(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c64(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c64(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c64(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c64(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c64(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c64(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c64(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c64(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c64(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c64(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c65(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c65(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c65(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c65(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(cons2(z0, z1))) → c65(NEGRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c65(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c65(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c65(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c65(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c65(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c65(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c65(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c65(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c65(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c65(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c65(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c67(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c67(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c67(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c67(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, cons2(z0, z1))) → c67(CONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c67(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c67(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c67(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c67(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c67(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c67(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c67(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c67(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c67(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c67(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c67(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c67(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(cons2(z0, z1), x1)) → c67(CONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c67(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c67(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c67(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c67(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c67(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c67(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c67(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c67(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c67(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c67(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c67(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c67(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c67(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c67(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(cons2(x0, s(z0))) → c68(CONS2(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons2(x0, posrecip(z0))) → c68(CONS2(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons2(x0, negrecip(z0))) → c68(CONS2(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons2(x0, cons(z0, z1))) → c68(CONS2(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons2(x0, cons2(z0, z1))) → c68(CONS2(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons2(x0, rcons(z0, z1))) → c68(CONS2(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons2(x0, from(z0))) → c68(CONS2(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons2(x0, 2ndspos(z0, z1))) → c68(CONS2(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons2(x0, 2ndsneg(z0, z1))) → c68(CONS2(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons2(x0, pi(z0))) → c68(CONS2(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons2(x0, plus(z0, z1))) → c68(CONS2(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons2(x0, times(z0, z1))) → c68(CONS2(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons2(x0, square(z0))) → c68(CONS2(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons2(s(z0), x1)) → c68(CONS2(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons2(posrecip(z0), x1)) → c68(CONS2(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons2(negrecip(z0), x1)) → c68(CONS2(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons2(cons(z0, z1), x1)) → c68(CONS2(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons2(cons2(z0, z1), x1)) → c68(CONS2(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons2(rcons(z0, z1), x1)) → c68(CONS2(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons2(from(z0), x1)) → c68(CONS2(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons2(2ndspos(z0, z1), x1)) → c68(CONS2(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons2(2ndsneg(z0, z1), x1)) → c68(CONS2(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons2(pi(z0), x1)) → c68(CONS2(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons2(plus(z0, z1), x1)) → c68(CONS2(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons2(times(z0, z1), x1)) → c68(CONS2(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons2(square(z0), x1)) → c68(CONS2(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons2(x0, 0)) → c68(CONS2(proper(x0), ok(0)), PROPER(x0))
PROPER(cons2(x0, nil)) → c68(CONS2(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons2(x0, rnil)) → c68(CONS2(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons2(0, x1)) → c68(CONS2(ok(0), proper(x1)), PROPER(x1))
PROPER(cons2(nil, x1)) → c68(CONS2(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons2(rnil, x1)) → c68(CONS2(ok(rnil), proper(x1)), PROPER(x1))
PROPER(rcons(x0, s(z0))) → c70(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c70(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c70(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, cons(z0, z1))) → c70(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, cons2(z0, z1))) → c70(RCONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(rcons(x0, rcons(z0, z1))) → c70(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c70(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c70(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c70(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c70(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c70(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c70(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c70(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(s(z0), x1)) → c70(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c70(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c70(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c70(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(cons2(z0, z1), x1)) → c70(RCONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c70(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c70(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c70(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c70(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c70(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c70(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c70(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c70(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(rcons(x0, 0)) → c70(RCONS(proper(x0), ok(0)), PROPER(x0))
PROPER(rcons(x0, nil)) → c70(RCONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(rcons(x0, rnil)) → c70(RCONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(rcons(0, x1)) → c70(RCONS(ok(0), proper(x1)), PROPER(x1))
PROPER(rcons(nil, x1)) → c70(RCONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c70(RCONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(from(s(z0))) → c71(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(posrecip(z0))) → c71(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(from(negrecip(z0))) → c71(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(from(cons(z0, z1))) → c71(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(cons2(z0, z1))) → c71(FROM(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(from(rcons(z0, z1))) → c71(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(from(from(z0))) → c71(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(2ndspos(z0, z1))) → c71(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(from(2ndsneg(z0, z1))) → c71(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(from(pi(z0))) → c71(FROM(pi(proper(z0))), PROPER(pi(z0)))
PROPER(from(plus(z0, z1))) → c71(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(from(times(z0, z1))) → c71(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(from(square(z0))) → c71(FROM(square(proper(z0))), PROPER(square(z0)))
PROPER(from(0)) → c71(FROM(ok(0)))
PROPER(from(nil)) → c71(FROM(ok(nil)))
PROPER(from(rnil)) → c71(FROM(ok(rnil)))
PROPER(2ndspos(x0, s(z0))) → c72(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndspos(x0, posrecip(z0))) → c72(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndspos(x0, negrecip(z0))) → c72(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndspos(x0, cons(z0, z1))) → c72(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndspos(x0, cons2(z0, z1))) → c72(2NDSPOS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(2ndspos(x0, rcons(z0, z1))) → c72(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndspos(x0, from(z0))) → c72(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c72(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c72(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndspos(x0, pi(z0))) → c72(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndspos(x0, plus(z0, z1))) → c72(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndspos(x0, times(z0, z1))) → c72(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndspos(x0, square(z0))) → c72(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndspos(s(z0), x1)) → c72(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndspos(posrecip(z0), x1)) → c72(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndspos(negrecip(z0), x1)) → c72(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndspos(cons(z0, z1), x1)) → c72(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndspos(cons2(z0, z1), x1)) → c72(2NDSPOS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(2ndspos(rcons(z0, z1), x1)) → c72(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndspos(from(z0), x1)) → c72(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c72(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c72(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndspos(pi(z0), x1)) → c72(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndspos(plus(z0, z1), x1)) → c72(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndspos(times(z0, z1), x1)) → c72(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndspos(square(z0), x1)) → c72(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndspos(x0, 0)) → c72(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndspos(x0, nil)) → c72(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndspos(x0, rnil)) → c72(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndspos(0, x1)) → c72(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndspos(nil, x1)) → c72(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndspos(rnil, x1)) → c72(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(x0, 0)) → c73(2NDSNEG(proper(x0), ok(0)), PROPER(x0), PROPER(0))
PROPER(2ndsneg(x0, s(z0))) → c73(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndsneg(x0, posrecip(z0))) → c73(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndsneg(x0, negrecip(z0))) → c73(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndsneg(x0, nil)) → c73(2NDSNEG(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
PROPER(2ndsneg(x0, cons(z0, z1))) → c73(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndsneg(x0, cons2(z0, z1))) → c73(2NDSNEG(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(2ndsneg(x0, rnil)) → c73(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0), PROPER(rnil))
PROPER(2ndsneg(x0, rcons(z0, z1))) → c73(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndsneg(x0, from(z0))) → c73(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c73(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c73(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndsneg(x0, pi(z0))) → c73(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndsneg(x0, plus(z0, z1))) → c73(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndsneg(x0, times(z0, z1))) → c73(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndsneg(x0, square(z0))) → c73(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndsneg(0, x1)) → c73(2NDSNEG(ok(0), proper(x1)), PROPER(0), PROPER(x1))
PROPER(2ndsneg(s(z0), x1)) → c73(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndsneg(posrecip(z0), x1)) → c73(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndsneg(negrecip(z0), x1)) → c73(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndsneg(nil, x1)) → c73(2NDSNEG(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
PROPER(2ndsneg(cons(z0, z1), x1)) → c73(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(cons2(z0, z1), x1)) → c73(2NDSNEG(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(2ndsneg(rnil, x1)) → c73(2NDSNEG(ok(rnil), proper(x1)), PROPER(rnil), PROPER(x1))
PROPER(2ndsneg(rcons(z0, z1), x1)) → c73(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(from(z0), x1)) → c73(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c73(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c73(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndsneg(pi(z0), x1)) → c73(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndsneg(plus(z0, z1), x1)) → c73(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndsneg(times(z0, z1), x1)) → c73(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndsneg(square(z0), x1)) → c73(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
S tuples:
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
PROPER(pi(z0)) → c74(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c75(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c76(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c77(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c78(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c79(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c9(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(2NDSPOS(s(z0), cons2(z1, z2)))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(2NDSNEG(s(z0), cons2(z1, z2)))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c13(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, z2)))) → c13(S(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(s(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, z2)))) → c13(S(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(s(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c13(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c13(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c13(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c13(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c13(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c13(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c13(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c13(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(cons2(z0, z1))) → c13(S(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c13(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c13(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c13(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c14(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c14(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c14(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c14(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c14(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c14(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c14(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c14(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(cons2(z0, z1))) → c14(POSRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c15(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c15(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c15(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c15(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c15(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c15(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c15(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c15(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(cons2(z0, z1))) → c15(NEGRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndspos(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndspos(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndsneg(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndsneg(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c16(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c16(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c16(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c16(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c16(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c16(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c16(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c16(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(cons2(z0, z1), x1)) → c16(CONS(cons2(z0, active(z1)), x1), ACTIVE(cons2(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, 2ndsneg(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(0, z0))) → c17(CONS2(x0, mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(cons2(x0, plus(s(z0), z1))) → c17(CONS2(x0, mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons2(x0, times(0, z0))) → c17(CONS2(x0, mark(0)), ACTIVE(times(0, z0)))
ACTIVE(cons2(x0, times(s(z0), z1))) → c17(CONS2(x0, mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(cons2(x0, s(z0))) → c17(CONS2(x0, s(active(z0))), ACTIVE(s(z0)))
ACTIVE(cons2(x0, posrecip(z0))) → c17(CONS2(x0, posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(cons2(x0, negrecip(z0))) → c17(CONS2(x0, negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(cons2(x0, cons(z0, z1))) → c17(CONS2(x0, cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(cons2(x0, cons2(z0, z1))) → c17(CONS2(x0, cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, from(active(z0))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, square(active(z0))), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c20(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(from(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(from(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c20(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c20(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c20(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c20(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c20(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c20(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c20(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c20(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c20(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c20(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(cons2(z0, z1))) → c20(FROM(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c20(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c20(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c20(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c25(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c25(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c25(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c25(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c25(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c25(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c25(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c25(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c25(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c25(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c25(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(cons2(z0, z1))) → c25(PI(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c25(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c25(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c25(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c30(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(square(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(square(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c30(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c30(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c30(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c30(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c30(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c30(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c30(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c30(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c30(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(cons2(z0, z1))) → c30(SQUARE(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c30(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c30(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c63(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c63(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c63(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c63(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(cons2(z0, z1))) → c63(S(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(s(rcons(z0, z1))) → c63(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c63(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c63(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c63(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c63(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c63(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c63(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c63(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c63(S(ok(0)))
PROPER(s(nil)) → c63(S(ok(nil)))
PROPER(s(rnil)) → c63(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c64(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c64(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c64(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c64(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(cons2(z0, z1))) → c64(POSRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c64(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c64(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c64(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c64(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c64(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c64(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c64(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c64(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c64(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c64(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c64(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c65(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c65(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c65(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c65(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(cons2(z0, z1))) → c65(NEGRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c65(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c65(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c65(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c65(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c65(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c65(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c65(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c65(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c65(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c65(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c65(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c67(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c67(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c67(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c67(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, cons2(z0, z1))) → c67(CONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c67(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c67(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c67(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c67(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c67(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c67(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c67(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c67(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c67(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c67(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c67(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c67(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(cons2(z0, z1), x1)) → c67(CONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c67(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c67(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c67(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c67(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c67(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c67(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c67(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c67(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c67(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c67(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c67(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c67(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c67(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c67(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(cons2(x0, s(z0))) → c68(CONS2(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons2(x0, posrecip(z0))) → c68(CONS2(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons2(x0, negrecip(z0))) → c68(CONS2(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons2(x0, cons(z0, z1))) → c68(CONS2(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons2(x0, cons2(z0, z1))) → c68(CONS2(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons2(x0, rcons(z0, z1))) → c68(CONS2(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons2(x0, from(z0))) → c68(CONS2(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons2(x0, 2ndspos(z0, z1))) → c68(CONS2(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons2(x0, 2ndsneg(z0, z1))) → c68(CONS2(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons2(x0, pi(z0))) → c68(CONS2(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons2(x0, plus(z0, z1))) → c68(CONS2(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons2(x0, times(z0, z1))) → c68(CONS2(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons2(x0, square(z0))) → c68(CONS2(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons2(s(z0), x1)) → c68(CONS2(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons2(posrecip(z0), x1)) → c68(CONS2(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons2(negrecip(z0), x1)) → c68(CONS2(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons2(cons(z0, z1), x1)) → c68(CONS2(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons2(cons2(z0, z1), x1)) → c68(CONS2(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons2(rcons(z0, z1), x1)) → c68(CONS2(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons2(from(z0), x1)) → c68(CONS2(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons2(2ndspos(z0, z1), x1)) → c68(CONS2(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons2(2ndsneg(z0, z1), x1)) → c68(CONS2(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons2(pi(z0), x1)) → c68(CONS2(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons2(plus(z0, z1), x1)) → c68(CONS2(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons2(times(z0, z1), x1)) → c68(CONS2(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons2(square(z0), x1)) → c68(CONS2(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons2(x0, 0)) → c68(CONS2(proper(x0), ok(0)), PROPER(x0))
PROPER(cons2(x0, nil)) → c68(CONS2(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons2(x0, rnil)) → c68(CONS2(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons2(0, x1)) → c68(CONS2(ok(0), proper(x1)), PROPER(x1))
PROPER(cons2(nil, x1)) → c68(CONS2(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons2(rnil, x1)) → c68(CONS2(ok(rnil), proper(x1)), PROPER(x1))
PROPER(rcons(x0, s(z0))) → c70(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c70(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c70(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, cons(z0, z1))) → c70(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, cons2(z0, z1))) → c70(RCONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(rcons(x0, rcons(z0, z1))) → c70(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c70(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c70(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c70(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c70(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c70(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c70(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c70(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(s(z0), x1)) → c70(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c70(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c70(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c70(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(cons2(z0, z1), x1)) → c70(RCONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c70(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c70(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c70(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c70(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c70(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c70(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c70(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c70(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(rcons(x0, 0)) → c70(RCONS(proper(x0), ok(0)), PROPER(x0))
PROPER(rcons(x0, nil)) → c70(RCONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(rcons(x0, rnil)) → c70(RCONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(rcons(0, x1)) → c70(RCONS(ok(0), proper(x1)), PROPER(x1))
PROPER(rcons(nil, x1)) → c70(RCONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c70(RCONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(from(s(z0))) → c71(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(posrecip(z0))) → c71(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(from(negrecip(z0))) → c71(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(from(cons(z0, z1))) → c71(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(cons2(z0, z1))) → c71(FROM(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(from(rcons(z0, z1))) → c71(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(from(from(z0))) → c71(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(2ndspos(z0, z1))) → c71(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(from(2ndsneg(z0, z1))) → c71(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(from(pi(z0))) → c71(FROM(pi(proper(z0))), PROPER(pi(z0)))
PROPER(from(plus(z0, z1))) → c71(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(from(times(z0, z1))) → c71(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(from(square(z0))) → c71(FROM(square(proper(z0))), PROPER(square(z0)))
PROPER(from(0)) → c71(FROM(ok(0)))
PROPER(from(nil)) → c71(FROM(ok(nil)))
PROPER(from(rnil)) → c71(FROM(ok(rnil)))
PROPER(2ndspos(x0, s(z0))) → c72(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndspos(x0, posrecip(z0))) → c72(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndspos(x0, negrecip(z0))) → c72(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndspos(x0, cons(z0, z1))) → c72(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndspos(x0, cons2(z0, z1))) → c72(2NDSPOS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(2ndspos(x0, rcons(z0, z1))) → c72(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndspos(x0, from(z0))) → c72(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c72(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c72(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndspos(x0, pi(z0))) → c72(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndspos(x0, plus(z0, z1))) → c72(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndspos(x0, times(z0, z1))) → c72(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndspos(x0, square(z0))) → c72(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndspos(s(z0), x1)) → c72(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndspos(posrecip(z0), x1)) → c72(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndspos(negrecip(z0), x1)) → c72(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndspos(cons(z0, z1), x1)) → c72(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndspos(cons2(z0, z1), x1)) → c72(2NDSPOS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(2ndspos(rcons(z0, z1), x1)) → c72(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndspos(from(z0), x1)) → c72(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c72(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c72(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndspos(pi(z0), x1)) → c72(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndspos(plus(z0, z1), x1)) → c72(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndspos(times(z0, z1), x1)) → c72(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndspos(square(z0), x1)) → c72(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndspos(x0, 0)) → c72(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndspos(x0, nil)) → c72(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndspos(x0, rnil)) → c72(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndspos(0, x1)) → c72(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndspos(nil, x1)) → c72(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndspos(rnil, x1)) → c72(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(x0, 0)) → c73(2NDSNEG(proper(x0), ok(0)), PROPER(x0), PROPER(0))
PROPER(2ndsneg(x0, s(z0))) → c73(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndsneg(x0, posrecip(z0))) → c73(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndsneg(x0, negrecip(z0))) → c73(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndsneg(x0, nil)) → c73(2NDSNEG(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
PROPER(2ndsneg(x0, cons(z0, z1))) → c73(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndsneg(x0, cons2(z0, z1))) → c73(2NDSNEG(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(2ndsneg(x0, rnil)) → c73(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0), PROPER(rnil))
PROPER(2ndsneg(x0, rcons(z0, z1))) → c73(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndsneg(x0, from(z0))) → c73(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c73(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c73(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndsneg(x0, pi(z0))) → c73(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndsneg(x0, plus(z0, z1))) → c73(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndsneg(x0, times(z0, z1))) → c73(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndsneg(x0, square(z0))) → c73(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndsneg(0, x1)) → c73(2NDSNEG(ok(0), proper(x1)), PROPER(0), PROPER(x1))
PROPER(2ndsneg(s(z0), x1)) → c73(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndsneg(posrecip(z0), x1)) → c73(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndsneg(negrecip(z0), x1)) → c73(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndsneg(nil, x1)) → c73(2NDSNEG(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
PROPER(2ndsneg(cons(z0, z1), x1)) → c73(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(cons2(z0, z1), x1)) → c73(2NDSNEG(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(2ndsneg(rnil, x1)) → c73(2NDSNEG(ok(rnil), proper(x1)), PROPER(rnil), PROPER(x1))
PROPER(2ndsneg(rcons(z0, z1), x1)) → c73(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(from(z0), x1)) → c73(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c73(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c73(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndsneg(pi(z0), x1)) → c73(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndsneg(plus(z0, z1), x1)) → c73(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndsneg(times(z0, z1), x1)) → c73(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndsneg(square(z0), x1)) → c73(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
K tuples:none
Defined Rule Symbols:
active, 2ndspos, cons2, rcons, posrecip, 2ndsneg, negrecip, s, cons, from, pi, plus, times, square, proper
Defined Pair Symbols:
ACTIVE, S, POSRECIP, NEGRECIP, CONS, CONS2, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP
Compound Symbols:
c12, c18, c19, c21, c22, c23, c24, c26, c27, c28, c29, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c74, c75, c76, c77, c78, c79, c, c7, c9, c11, c1, c13, c14, c15, c16, c17, c20, c25, c30, c63, c63, c64, c64, c65, c65, c67, c67, c68, c68, c70, c70, c71, c71, c72, c72, c73
(61) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 6 trailing tuple parts
(62) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(2ndspos(0, z0)) → mark(rnil)
active(2ndspos(s(z0), cons(z1, z2))) → mark(2ndspos(s(z0), cons2(z1, z2)))
active(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(z1, z2))) → mark(2ndsneg(s(z0), cons2(z1, z2)))
active(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
active(pi(z0)) → mark(2ndspos(z0, from(0)))
active(plus(0, z0)) → mark(z0)
active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
active(times(0, z0)) → mark(0)
active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
active(square(z0)) → mark(times(z0, z0))
active(s(z0)) → s(active(z0))
active(posrecip(z0)) → posrecip(active(z0))
active(negrecip(z0)) → negrecip(active(z0))
active(cons(z0, z1)) → cons(active(z0), z1)
active(cons2(z0, z1)) → cons2(z0, active(z1))
active(rcons(z0, z1)) → rcons(active(z0), z1)
active(rcons(z0, z1)) → rcons(z0, active(z1))
active(from(z0)) → from(active(z0))
active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
active(pi(z0)) → pi(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(times(z0, z1)) → times(active(z0), z1)
active(times(z0, z1)) → times(z0, active(z1))
active(square(z0)) → square(active(z0))
2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
cons2(z0, mark(z1)) → mark(cons2(z0, z1))
cons2(ok(z0), ok(z1)) → ok(cons2(z0, z1))
rcons(mark(z0), z1) → mark(rcons(z0, z1))
rcons(z0, mark(z1)) → mark(rcons(z0, z1))
rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
posrecip(ok(z0)) → ok(posrecip(z0))
posrecip(mark(z0)) → mark(posrecip(z0))
2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
negrecip(ok(z0)) → ok(negrecip(z0))
negrecip(mark(z0)) → mark(negrecip(z0))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
cons(mark(z0), z1) → mark(cons(z0, z1))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
from(mark(z0)) → mark(from(z0))
from(ok(z0)) → ok(from(z0))
pi(mark(z0)) → mark(pi(z0))
pi(ok(z0)) → ok(pi(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
times(mark(z0), z1) → mark(times(z0, z1))
times(ok(z0), ok(z1)) → ok(times(z0, z1))
times(z0, mark(z1)) → mark(times(z0, z1))
square(mark(z0)) → mark(square(z0))
square(ok(z0)) → ok(square(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(posrecip(z0)) → posrecip(proper(z0))
proper(negrecip(z0)) → negrecip(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(cons2(z0, z1)) → cons2(proper(z0), proper(z1))
proper(rnil) → ok(rnil)
proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
proper(pi(z0)) → pi(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(times(z0, z1)) → times(proper(z0), proper(z1))
proper(square(z0)) → square(proper(z0))
Tuples:
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
PROPER(pi(z0)) → c74(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c75(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c76(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c77(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c78(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c79(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c9(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(2NDSPOS(s(z0), cons2(z1, z2)))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(2NDSNEG(s(z0), cons2(z1, z2)))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c13(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, z2)))) → c13(S(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(s(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, z2)))) → c13(S(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(s(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c13(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c13(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c13(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c13(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c13(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c13(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c13(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c13(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(cons2(z0, z1))) → c13(S(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c13(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c13(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c13(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c14(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c14(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c14(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c14(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c14(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c14(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c14(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c14(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(cons2(z0, z1))) → c14(POSRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c15(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c15(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c15(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c15(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c15(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c15(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c15(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c15(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(cons2(z0, z1))) → c15(NEGRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndspos(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndspos(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndsneg(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndsneg(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c16(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c16(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c16(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c16(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c16(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c16(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c16(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c16(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(cons2(z0, z1), x1)) → c16(CONS(cons2(z0, active(z1)), x1), ACTIVE(cons2(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, 2ndsneg(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(0, z0))) → c17(CONS2(x0, mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(cons2(x0, plus(s(z0), z1))) → c17(CONS2(x0, mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons2(x0, times(0, z0))) → c17(CONS2(x0, mark(0)), ACTIVE(times(0, z0)))
ACTIVE(cons2(x0, times(s(z0), z1))) → c17(CONS2(x0, mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(cons2(x0, s(z0))) → c17(CONS2(x0, s(active(z0))), ACTIVE(s(z0)))
ACTIVE(cons2(x0, posrecip(z0))) → c17(CONS2(x0, posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(cons2(x0, negrecip(z0))) → c17(CONS2(x0, negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(cons2(x0, cons(z0, z1))) → c17(CONS2(x0, cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(cons2(x0, cons2(z0, z1))) → c17(CONS2(x0, cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, from(active(z0))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, square(active(z0))), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c20(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(from(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(from(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c20(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c20(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c20(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c20(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c20(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c20(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c20(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c20(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c20(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c20(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(cons2(z0, z1))) → c20(FROM(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c20(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c20(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c20(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c25(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c25(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c25(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c25(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c25(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c25(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c25(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c25(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c25(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c25(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c25(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(cons2(z0, z1))) → c25(PI(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c25(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c25(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c25(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c30(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(square(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(square(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c30(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c30(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c30(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c30(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c30(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c30(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c30(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c30(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c30(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(cons2(z0, z1))) → c30(SQUARE(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c30(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c30(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c63(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c63(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c63(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c63(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(cons2(z0, z1))) → c63(S(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(s(rcons(z0, z1))) → c63(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c63(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c63(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c63(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c63(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c63(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c63(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c63(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c63(S(ok(0)))
PROPER(s(nil)) → c63(S(ok(nil)))
PROPER(s(rnil)) → c63(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c64(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c64(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c64(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c64(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(cons2(z0, z1))) → c64(POSRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c64(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c64(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c64(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c64(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c64(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c64(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c64(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c64(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c64(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c64(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c64(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c65(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c65(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c65(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c65(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(cons2(z0, z1))) → c65(NEGRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c65(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c65(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c65(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c65(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c65(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c65(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c65(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c65(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c65(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c65(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c65(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c67(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c67(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c67(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c67(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, cons2(z0, z1))) → c67(CONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c67(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c67(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c67(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c67(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c67(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c67(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c67(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c67(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c67(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c67(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c67(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c67(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(cons2(z0, z1), x1)) → c67(CONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c67(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c67(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c67(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c67(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c67(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c67(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c67(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c67(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c67(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c67(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c67(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c67(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c67(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c67(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(cons2(x0, s(z0))) → c68(CONS2(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons2(x0, posrecip(z0))) → c68(CONS2(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons2(x0, negrecip(z0))) → c68(CONS2(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons2(x0, cons(z0, z1))) → c68(CONS2(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons2(x0, cons2(z0, z1))) → c68(CONS2(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons2(x0, rcons(z0, z1))) → c68(CONS2(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons2(x0, from(z0))) → c68(CONS2(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons2(x0, 2ndspos(z0, z1))) → c68(CONS2(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons2(x0, 2ndsneg(z0, z1))) → c68(CONS2(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons2(x0, pi(z0))) → c68(CONS2(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons2(x0, plus(z0, z1))) → c68(CONS2(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons2(x0, times(z0, z1))) → c68(CONS2(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons2(x0, square(z0))) → c68(CONS2(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons2(s(z0), x1)) → c68(CONS2(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons2(posrecip(z0), x1)) → c68(CONS2(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons2(negrecip(z0), x1)) → c68(CONS2(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons2(cons(z0, z1), x1)) → c68(CONS2(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons2(cons2(z0, z1), x1)) → c68(CONS2(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons2(rcons(z0, z1), x1)) → c68(CONS2(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons2(from(z0), x1)) → c68(CONS2(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons2(2ndspos(z0, z1), x1)) → c68(CONS2(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons2(2ndsneg(z0, z1), x1)) → c68(CONS2(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons2(pi(z0), x1)) → c68(CONS2(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons2(plus(z0, z1), x1)) → c68(CONS2(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons2(times(z0, z1), x1)) → c68(CONS2(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons2(square(z0), x1)) → c68(CONS2(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons2(x0, 0)) → c68(CONS2(proper(x0), ok(0)), PROPER(x0))
PROPER(cons2(x0, nil)) → c68(CONS2(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons2(x0, rnil)) → c68(CONS2(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons2(0, x1)) → c68(CONS2(ok(0), proper(x1)), PROPER(x1))
PROPER(cons2(nil, x1)) → c68(CONS2(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons2(rnil, x1)) → c68(CONS2(ok(rnil), proper(x1)), PROPER(x1))
PROPER(rcons(x0, s(z0))) → c70(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c70(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c70(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, cons(z0, z1))) → c70(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, cons2(z0, z1))) → c70(RCONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(rcons(x0, rcons(z0, z1))) → c70(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c70(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c70(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c70(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c70(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c70(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c70(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c70(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(s(z0), x1)) → c70(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c70(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c70(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c70(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(cons2(z0, z1), x1)) → c70(RCONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c70(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c70(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c70(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c70(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c70(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c70(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c70(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c70(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(rcons(x0, 0)) → c70(RCONS(proper(x0), ok(0)), PROPER(x0))
PROPER(rcons(x0, nil)) → c70(RCONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(rcons(x0, rnil)) → c70(RCONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(rcons(0, x1)) → c70(RCONS(ok(0), proper(x1)), PROPER(x1))
PROPER(rcons(nil, x1)) → c70(RCONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c70(RCONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(from(s(z0))) → c71(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(posrecip(z0))) → c71(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(from(negrecip(z0))) → c71(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(from(cons(z0, z1))) → c71(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(cons2(z0, z1))) → c71(FROM(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(from(rcons(z0, z1))) → c71(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(from(from(z0))) → c71(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(2ndspos(z0, z1))) → c71(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(from(2ndsneg(z0, z1))) → c71(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(from(pi(z0))) → c71(FROM(pi(proper(z0))), PROPER(pi(z0)))
PROPER(from(plus(z0, z1))) → c71(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(from(times(z0, z1))) → c71(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(from(square(z0))) → c71(FROM(square(proper(z0))), PROPER(square(z0)))
PROPER(from(0)) → c71(FROM(ok(0)))
PROPER(from(nil)) → c71(FROM(ok(nil)))
PROPER(from(rnil)) → c71(FROM(ok(rnil)))
PROPER(2ndspos(x0, s(z0))) → c72(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndspos(x0, posrecip(z0))) → c72(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndspos(x0, negrecip(z0))) → c72(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndspos(x0, cons(z0, z1))) → c72(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndspos(x0, cons2(z0, z1))) → c72(2NDSPOS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(2ndspos(x0, rcons(z0, z1))) → c72(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndspos(x0, from(z0))) → c72(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c72(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c72(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndspos(x0, pi(z0))) → c72(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndspos(x0, plus(z0, z1))) → c72(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndspos(x0, times(z0, z1))) → c72(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndspos(x0, square(z0))) → c72(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndspos(s(z0), x1)) → c72(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndspos(posrecip(z0), x1)) → c72(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndspos(negrecip(z0), x1)) → c72(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndspos(cons(z0, z1), x1)) → c72(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndspos(cons2(z0, z1), x1)) → c72(2NDSPOS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(2ndspos(rcons(z0, z1), x1)) → c72(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndspos(from(z0), x1)) → c72(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c72(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c72(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndspos(pi(z0), x1)) → c72(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndspos(plus(z0, z1), x1)) → c72(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndspos(times(z0, z1), x1)) → c72(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndspos(square(z0), x1)) → c72(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndspos(x0, 0)) → c72(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndspos(x0, nil)) → c72(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndspos(x0, rnil)) → c72(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndspos(0, x1)) → c72(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndspos(nil, x1)) → c72(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndspos(rnil, x1)) → c72(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(x0, s(z0))) → c73(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndsneg(x0, posrecip(z0))) → c73(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndsneg(x0, negrecip(z0))) → c73(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndsneg(x0, cons(z0, z1))) → c73(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndsneg(x0, cons2(z0, z1))) → c73(2NDSNEG(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(2ndsneg(x0, rcons(z0, z1))) → c73(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndsneg(x0, from(z0))) → c73(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c73(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c73(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndsneg(x0, pi(z0))) → c73(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndsneg(x0, plus(z0, z1))) → c73(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndsneg(x0, times(z0, z1))) → c73(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndsneg(x0, square(z0))) → c73(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndsneg(s(z0), x1)) → c73(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndsneg(posrecip(z0), x1)) → c73(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndsneg(negrecip(z0), x1)) → c73(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndsneg(cons(z0, z1), x1)) → c73(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(cons2(z0, z1), x1)) → c73(2NDSNEG(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(2ndsneg(rcons(z0, z1), x1)) → c73(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(from(z0), x1)) → c73(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c73(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c73(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndsneg(pi(z0), x1)) → c73(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndsneg(plus(z0, z1), x1)) → c73(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndsneg(times(z0, z1), x1)) → c73(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndsneg(square(z0), x1)) → c73(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndsneg(x0, 0)) → c73(2NDSNEG(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndsneg(x0, nil)) → c73(2NDSNEG(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndsneg(x0, rnil)) → c73(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndsneg(0, x1)) → c73(2NDSNEG(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndsneg(nil, x1)) → c73(2NDSNEG(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(rnil, x1)) → c73(2NDSNEG(ok(rnil), proper(x1)), PROPER(x1))
S tuples:
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
PROPER(pi(z0)) → c74(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c75(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c76(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c77(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c78(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c79(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c9(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(2NDSPOS(s(z0), cons2(z1, z2)))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(2NDSNEG(s(z0), cons2(z1, z2)))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c13(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, z2)))) → c13(S(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(s(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, z2)))) → c13(S(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(s(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c13(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c13(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c13(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c13(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c13(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c13(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c13(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c13(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(cons2(z0, z1))) → c13(S(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c13(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c13(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c13(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c14(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c14(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c14(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c14(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c14(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c14(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c14(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c14(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(cons2(z0, z1))) → c14(POSRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c15(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c15(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c15(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c15(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c15(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c15(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c15(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c15(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(cons2(z0, z1))) → c15(NEGRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndspos(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndspos(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndsneg(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndsneg(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c16(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c16(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c16(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c16(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c16(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c16(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c16(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c16(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(cons2(z0, z1), x1)) → c16(CONS(cons2(z0, active(z1)), x1), ACTIVE(cons2(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, 2ndsneg(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(0, z0))) → c17(CONS2(x0, mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(cons2(x0, plus(s(z0), z1))) → c17(CONS2(x0, mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons2(x0, times(0, z0))) → c17(CONS2(x0, mark(0)), ACTIVE(times(0, z0)))
ACTIVE(cons2(x0, times(s(z0), z1))) → c17(CONS2(x0, mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(cons2(x0, s(z0))) → c17(CONS2(x0, s(active(z0))), ACTIVE(s(z0)))
ACTIVE(cons2(x0, posrecip(z0))) → c17(CONS2(x0, posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(cons2(x0, negrecip(z0))) → c17(CONS2(x0, negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(cons2(x0, cons(z0, z1))) → c17(CONS2(x0, cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(cons2(x0, cons2(z0, z1))) → c17(CONS2(x0, cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, from(active(z0))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, square(active(z0))), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c20(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(from(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(from(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c20(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c20(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c20(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c20(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c20(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c20(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c20(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c20(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c20(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c20(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(cons2(z0, z1))) → c20(FROM(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c20(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c20(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c20(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c25(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c25(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c25(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c25(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c25(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c25(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c25(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c25(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c25(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c25(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c25(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(cons2(z0, z1))) → c25(PI(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c25(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c25(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c25(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c30(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(square(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(square(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c30(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c30(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c30(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c30(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c30(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c30(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c30(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c30(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c30(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(cons2(z0, z1))) → c30(SQUARE(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c30(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c30(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c63(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c63(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c63(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c63(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(cons2(z0, z1))) → c63(S(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(s(rcons(z0, z1))) → c63(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c63(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c63(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c63(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c63(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c63(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c63(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c63(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c63(S(ok(0)))
PROPER(s(nil)) → c63(S(ok(nil)))
PROPER(s(rnil)) → c63(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c64(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c64(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c64(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c64(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(cons2(z0, z1))) → c64(POSRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c64(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c64(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c64(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c64(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c64(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c64(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c64(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c64(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c64(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c64(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c64(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c65(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c65(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c65(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c65(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(cons2(z0, z1))) → c65(NEGRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c65(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c65(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c65(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c65(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c65(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c65(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c65(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c65(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c65(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c65(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c65(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c67(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c67(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c67(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c67(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, cons2(z0, z1))) → c67(CONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c67(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c67(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c67(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c67(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c67(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c67(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c67(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c67(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c67(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c67(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c67(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c67(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(cons2(z0, z1), x1)) → c67(CONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c67(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c67(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c67(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c67(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c67(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c67(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c67(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c67(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c67(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c67(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c67(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c67(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c67(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c67(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(cons2(x0, s(z0))) → c68(CONS2(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons2(x0, posrecip(z0))) → c68(CONS2(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons2(x0, negrecip(z0))) → c68(CONS2(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons2(x0, cons(z0, z1))) → c68(CONS2(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons2(x0, cons2(z0, z1))) → c68(CONS2(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons2(x0, rcons(z0, z1))) → c68(CONS2(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons2(x0, from(z0))) → c68(CONS2(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons2(x0, 2ndspos(z0, z1))) → c68(CONS2(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons2(x0, 2ndsneg(z0, z1))) → c68(CONS2(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons2(x0, pi(z0))) → c68(CONS2(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons2(x0, plus(z0, z1))) → c68(CONS2(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons2(x0, times(z0, z1))) → c68(CONS2(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons2(x0, square(z0))) → c68(CONS2(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons2(s(z0), x1)) → c68(CONS2(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons2(posrecip(z0), x1)) → c68(CONS2(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons2(negrecip(z0), x1)) → c68(CONS2(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons2(cons(z0, z1), x1)) → c68(CONS2(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons2(cons2(z0, z1), x1)) → c68(CONS2(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons2(rcons(z0, z1), x1)) → c68(CONS2(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons2(from(z0), x1)) → c68(CONS2(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons2(2ndspos(z0, z1), x1)) → c68(CONS2(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons2(2ndsneg(z0, z1), x1)) → c68(CONS2(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons2(pi(z0), x1)) → c68(CONS2(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons2(plus(z0, z1), x1)) → c68(CONS2(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons2(times(z0, z1), x1)) → c68(CONS2(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons2(square(z0), x1)) → c68(CONS2(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons2(x0, 0)) → c68(CONS2(proper(x0), ok(0)), PROPER(x0))
PROPER(cons2(x0, nil)) → c68(CONS2(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons2(x0, rnil)) → c68(CONS2(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons2(0, x1)) → c68(CONS2(ok(0), proper(x1)), PROPER(x1))
PROPER(cons2(nil, x1)) → c68(CONS2(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons2(rnil, x1)) → c68(CONS2(ok(rnil), proper(x1)), PROPER(x1))
PROPER(rcons(x0, s(z0))) → c70(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c70(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c70(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, cons(z0, z1))) → c70(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, cons2(z0, z1))) → c70(RCONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(rcons(x0, rcons(z0, z1))) → c70(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c70(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c70(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c70(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c70(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c70(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c70(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c70(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(s(z0), x1)) → c70(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c70(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c70(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c70(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(cons2(z0, z1), x1)) → c70(RCONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c70(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c70(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c70(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c70(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c70(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c70(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c70(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c70(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(rcons(x0, 0)) → c70(RCONS(proper(x0), ok(0)), PROPER(x0))
PROPER(rcons(x0, nil)) → c70(RCONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(rcons(x0, rnil)) → c70(RCONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(rcons(0, x1)) → c70(RCONS(ok(0), proper(x1)), PROPER(x1))
PROPER(rcons(nil, x1)) → c70(RCONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c70(RCONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(from(s(z0))) → c71(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(posrecip(z0))) → c71(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(from(negrecip(z0))) → c71(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(from(cons(z0, z1))) → c71(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(cons2(z0, z1))) → c71(FROM(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(from(rcons(z0, z1))) → c71(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(from(from(z0))) → c71(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(2ndspos(z0, z1))) → c71(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(from(2ndsneg(z0, z1))) → c71(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(from(pi(z0))) → c71(FROM(pi(proper(z0))), PROPER(pi(z0)))
PROPER(from(plus(z0, z1))) → c71(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(from(times(z0, z1))) → c71(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(from(square(z0))) → c71(FROM(square(proper(z0))), PROPER(square(z0)))
PROPER(from(0)) → c71(FROM(ok(0)))
PROPER(from(nil)) → c71(FROM(ok(nil)))
PROPER(from(rnil)) → c71(FROM(ok(rnil)))
PROPER(2ndspos(x0, s(z0))) → c72(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndspos(x0, posrecip(z0))) → c72(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndspos(x0, negrecip(z0))) → c72(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndspos(x0, cons(z0, z1))) → c72(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndspos(x0, cons2(z0, z1))) → c72(2NDSPOS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(2ndspos(x0, rcons(z0, z1))) → c72(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndspos(x0, from(z0))) → c72(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c72(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c72(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndspos(x0, pi(z0))) → c72(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndspos(x0, plus(z0, z1))) → c72(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndspos(x0, times(z0, z1))) → c72(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndspos(x0, square(z0))) → c72(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndspos(s(z0), x1)) → c72(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndspos(posrecip(z0), x1)) → c72(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndspos(negrecip(z0), x1)) → c72(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndspos(cons(z0, z1), x1)) → c72(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndspos(cons2(z0, z1), x1)) → c72(2NDSPOS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(2ndspos(rcons(z0, z1), x1)) → c72(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndspos(from(z0), x1)) → c72(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c72(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c72(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndspos(pi(z0), x1)) → c72(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndspos(plus(z0, z1), x1)) → c72(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndspos(times(z0, z1), x1)) → c72(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndspos(square(z0), x1)) → c72(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndspos(x0, 0)) → c72(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndspos(x0, nil)) → c72(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndspos(x0, rnil)) → c72(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndspos(0, x1)) → c72(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndspos(nil, x1)) → c72(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndspos(rnil, x1)) → c72(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(x0, s(z0))) → c73(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndsneg(x0, posrecip(z0))) → c73(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndsneg(x0, negrecip(z0))) → c73(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndsneg(x0, cons(z0, z1))) → c73(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndsneg(x0, cons2(z0, z1))) → c73(2NDSNEG(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(2ndsneg(x0, rcons(z0, z1))) → c73(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndsneg(x0, from(z0))) → c73(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c73(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c73(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndsneg(x0, pi(z0))) → c73(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndsneg(x0, plus(z0, z1))) → c73(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndsneg(x0, times(z0, z1))) → c73(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndsneg(x0, square(z0))) → c73(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndsneg(s(z0), x1)) → c73(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndsneg(posrecip(z0), x1)) → c73(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndsneg(negrecip(z0), x1)) → c73(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndsneg(cons(z0, z1), x1)) → c73(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(cons2(z0, z1), x1)) → c73(2NDSNEG(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(2ndsneg(rcons(z0, z1), x1)) → c73(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(from(z0), x1)) → c73(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c73(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c73(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndsneg(pi(z0), x1)) → c73(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndsneg(plus(z0, z1), x1)) → c73(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndsneg(times(z0, z1), x1)) → c73(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndsneg(square(z0), x1)) → c73(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndsneg(x0, 0)) → c73(2NDSNEG(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndsneg(x0, nil)) → c73(2NDSNEG(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndsneg(x0, rnil)) → c73(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndsneg(0, x1)) → c73(2NDSNEG(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndsneg(nil, x1)) → c73(2NDSNEG(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(rnil, x1)) → c73(2NDSNEG(ok(rnil), proper(x1)), PROPER(x1))
K tuples:none
Defined Rule Symbols:
active, 2ndspos, cons2, rcons, posrecip, 2ndsneg, negrecip, s, cons, from, pi, plus, times, square, proper
Defined Pair Symbols:
ACTIVE, S, POSRECIP, NEGRECIP, CONS, CONS2, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP
Compound Symbols:
c12, c18, c19, c21, c22, c23, c24, c26, c27, c28, c29, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c74, c75, c76, c77, c78, c79, c, c7, c9, c11, c1, c13, c14, c15, c16, c17, c20, c25, c30, c63, c63, c64, c64, c65, c65, c67, c67, c68, c68, c70, c70, c71, c71, c72, c72, c73, c73
(63) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
PROPER(
pi(
z0)) →
c74(
PI(
proper(
z0)),
PROPER(
z0)) by
PROPER(pi(0)) → c74(PI(ok(0)), PROPER(0))
PROPER(pi(s(z0))) → c74(PI(s(proper(z0))), PROPER(s(z0)))
PROPER(pi(posrecip(z0))) → c74(PI(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(pi(negrecip(z0))) → c74(PI(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(pi(nil)) → c74(PI(ok(nil)), PROPER(nil))
PROPER(pi(cons(z0, z1))) → c74(PI(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(pi(cons2(z0, z1))) → c74(PI(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(pi(rnil)) → c74(PI(ok(rnil)), PROPER(rnil))
PROPER(pi(rcons(z0, z1))) → c74(PI(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(pi(from(z0))) → c74(PI(from(proper(z0))), PROPER(from(z0)))
PROPER(pi(2ndspos(z0, z1))) → c74(PI(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(pi(2ndsneg(z0, z1))) → c74(PI(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(pi(pi(z0))) → c74(PI(pi(proper(z0))), PROPER(pi(z0)))
PROPER(pi(plus(z0, z1))) → c74(PI(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(pi(times(z0, z1))) → c74(PI(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(pi(square(z0))) → c74(PI(square(proper(z0))), PROPER(square(z0)))
(64) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(2ndspos(0, z0)) → mark(rnil)
active(2ndspos(s(z0), cons(z1, z2))) → mark(2ndspos(s(z0), cons2(z1, z2)))
active(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(z1, z2))) → mark(2ndsneg(s(z0), cons2(z1, z2)))
active(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
active(pi(z0)) → mark(2ndspos(z0, from(0)))
active(plus(0, z0)) → mark(z0)
active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
active(times(0, z0)) → mark(0)
active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
active(square(z0)) → mark(times(z0, z0))
active(s(z0)) → s(active(z0))
active(posrecip(z0)) → posrecip(active(z0))
active(negrecip(z0)) → negrecip(active(z0))
active(cons(z0, z1)) → cons(active(z0), z1)
active(cons2(z0, z1)) → cons2(z0, active(z1))
active(rcons(z0, z1)) → rcons(active(z0), z1)
active(rcons(z0, z1)) → rcons(z0, active(z1))
active(from(z0)) → from(active(z0))
active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
active(pi(z0)) → pi(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(times(z0, z1)) → times(active(z0), z1)
active(times(z0, z1)) → times(z0, active(z1))
active(square(z0)) → square(active(z0))
2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
cons2(z0, mark(z1)) → mark(cons2(z0, z1))
cons2(ok(z0), ok(z1)) → ok(cons2(z0, z1))
rcons(mark(z0), z1) → mark(rcons(z0, z1))
rcons(z0, mark(z1)) → mark(rcons(z0, z1))
rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
posrecip(ok(z0)) → ok(posrecip(z0))
posrecip(mark(z0)) → mark(posrecip(z0))
2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
negrecip(ok(z0)) → ok(negrecip(z0))
negrecip(mark(z0)) → mark(negrecip(z0))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
cons(mark(z0), z1) → mark(cons(z0, z1))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
from(mark(z0)) → mark(from(z0))
from(ok(z0)) → ok(from(z0))
pi(mark(z0)) → mark(pi(z0))
pi(ok(z0)) → ok(pi(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
times(mark(z0), z1) → mark(times(z0, z1))
times(ok(z0), ok(z1)) → ok(times(z0, z1))
times(z0, mark(z1)) → mark(times(z0, z1))
square(mark(z0)) → mark(square(z0))
square(ok(z0)) → ok(square(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(posrecip(z0)) → posrecip(proper(z0))
proper(negrecip(z0)) → negrecip(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(cons2(z0, z1)) → cons2(proper(z0), proper(z1))
proper(rnil) → ok(rnil)
proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
proper(pi(z0)) → pi(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(times(z0, z1)) → times(proper(z0), proper(z1))
proper(square(z0)) → square(proper(z0))
Tuples:
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
PROPER(plus(z0, z1)) → c75(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c76(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c77(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c78(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c79(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c9(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(2NDSPOS(s(z0), cons2(z1, z2)))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(2NDSNEG(s(z0), cons2(z1, z2)))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c13(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, z2)))) → c13(S(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(s(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, z2)))) → c13(S(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(s(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c13(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c13(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c13(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c13(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c13(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c13(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c13(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c13(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(cons2(z0, z1))) → c13(S(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c13(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c13(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c13(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c14(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c14(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c14(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c14(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c14(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c14(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c14(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c14(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(cons2(z0, z1))) → c14(POSRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c15(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c15(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c15(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c15(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c15(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c15(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c15(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c15(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(cons2(z0, z1))) → c15(NEGRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndspos(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndspos(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndsneg(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndsneg(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c16(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c16(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c16(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c16(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c16(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c16(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c16(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c16(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(cons2(z0, z1), x1)) → c16(CONS(cons2(z0, active(z1)), x1), ACTIVE(cons2(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, 2ndsneg(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(0, z0))) → c17(CONS2(x0, mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(cons2(x0, plus(s(z0), z1))) → c17(CONS2(x0, mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons2(x0, times(0, z0))) → c17(CONS2(x0, mark(0)), ACTIVE(times(0, z0)))
ACTIVE(cons2(x0, times(s(z0), z1))) → c17(CONS2(x0, mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(cons2(x0, s(z0))) → c17(CONS2(x0, s(active(z0))), ACTIVE(s(z0)))
ACTIVE(cons2(x0, posrecip(z0))) → c17(CONS2(x0, posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(cons2(x0, negrecip(z0))) → c17(CONS2(x0, negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(cons2(x0, cons(z0, z1))) → c17(CONS2(x0, cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(cons2(x0, cons2(z0, z1))) → c17(CONS2(x0, cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, from(active(z0))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, square(active(z0))), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c20(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(from(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(from(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c20(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c20(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c20(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c20(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c20(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c20(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c20(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c20(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c20(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c20(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(cons2(z0, z1))) → c20(FROM(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c20(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c20(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c20(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c25(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c25(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c25(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c25(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c25(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c25(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c25(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c25(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c25(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c25(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c25(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(cons2(z0, z1))) → c25(PI(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c25(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c25(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c25(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c30(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(square(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(square(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c30(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c30(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c30(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c30(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c30(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c30(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c30(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c30(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c30(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(cons2(z0, z1))) → c30(SQUARE(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c30(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c30(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c63(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c63(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c63(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c63(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(cons2(z0, z1))) → c63(S(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(s(rcons(z0, z1))) → c63(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c63(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c63(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c63(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c63(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c63(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c63(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c63(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c63(S(ok(0)))
PROPER(s(nil)) → c63(S(ok(nil)))
PROPER(s(rnil)) → c63(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c64(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c64(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c64(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c64(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(cons2(z0, z1))) → c64(POSRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c64(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c64(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c64(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c64(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c64(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c64(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c64(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c64(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c64(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c64(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c64(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c65(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c65(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c65(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c65(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(cons2(z0, z1))) → c65(NEGRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c65(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c65(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c65(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c65(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c65(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c65(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c65(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c65(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c65(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c65(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c65(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c67(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c67(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c67(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c67(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, cons2(z0, z1))) → c67(CONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c67(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c67(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c67(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c67(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c67(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c67(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c67(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c67(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c67(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c67(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c67(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c67(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(cons2(z0, z1), x1)) → c67(CONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c67(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c67(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c67(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c67(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c67(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c67(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c67(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c67(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c67(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c67(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c67(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c67(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c67(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c67(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(cons2(x0, s(z0))) → c68(CONS2(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons2(x0, posrecip(z0))) → c68(CONS2(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons2(x0, negrecip(z0))) → c68(CONS2(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons2(x0, cons(z0, z1))) → c68(CONS2(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons2(x0, cons2(z0, z1))) → c68(CONS2(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons2(x0, rcons(z0, z1))) → c68(CONS2(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons2(x0, from(z0))) → c68(CONS2(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons2(x0, 2ndspos(z0, z1))) → c68(CONS2(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons2(x0, 2ndsneg(z0, z1))) → c68(CONS2(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons2(x0, pi(z0))) → c68(CONS2(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons2(x0, plus(z0, z1))) → c68(CONS2(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons2(x0, times(z0, z1))) → c68(CONS2(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons2(x0, square(z0))) → c68(CONS2(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons2(s(z0), x1)) → c68(CONS2(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons2(posrecip(z0), x1)) → c68(CONS2(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons2(negrecip(z0), x1)) → c68(CONS2(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons2(cons(z0, z1), x1)) → c68(CONS2(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons2(cons2(z0, z1), x1)) → c68(CONS2(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons2(rcons(z0, z1), x1)) → c68(CONS2(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons2(from(z0), x1)) → c68(CONS2(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons2(2ndspos(z0, z1), x1)) → c68(CONS2(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons2(2ndsneg(z0, z1), x1)) → c68(CONS2(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons2(pi(z0), x1)) → c68(CONS2(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons2(plus(z0, z1), x1)) → c68(CONS2(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons2(times(z0, z1), x1)) → c68(CONS2(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons2(square(z0), x1)) → c68(CONS2(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons2(x0, 0)) → c68(CONS2(proper(x0), ok(0)), PROPER(x0))
PROPER(cons2(x0, nil)) → c68(CONS2(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons2(x0, rnil)) → c68(CONS2(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons2(0, x1)) → c68(CONS2(ok(0), proper(x1)), PROPER(x1))
PROPER(cons2(nil, x1)) → c68(CONS2(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons2(rnil, x1)) → c68(CONS2(ok(rnil), proper(x1)), PROPER(x1))
PROPER(rcons(x0, s(z0))) → c70(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c70(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c70(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, cons(z0, z1))) → c70(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, cons2(z0, z1))) → c70(RCONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(rcons(x0, rcons(z0, z1))) → c70(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c70(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c70(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c70(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c70(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c70(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c70(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c70(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(s(z0), x1)) → c70(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c70(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c70(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c70(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(cons2(z0, z1), x1)) → c70(RCONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c70(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c70(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c70(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c70(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c70(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c70(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c70(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c70(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(rcons(x0, 0)) → c70(RCONS(proper(x0), ok(0)), PROPER(x0))
PROPER(rcons(x0, nil)) → c70(RCONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(rcons(x0, rnil)) → c70(RCONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(rcons(0, x1)) → c70(RCONS(ok(0), proper(x1)), PROPER(x1))
PROPER(rcons(nil, x1)) → c70(RCONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c70(RCONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(from(s(z0))) → c71(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(posrecip(z0))) → c71(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(from(negrecip(z0))) → c71(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(from(cons(z0, z1))) → c71(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(cons2(z0, z1))) → c71(FROM(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(from(rcons(z0, z1))) → c71(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(from(from(z0))) → c71(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(2ndspos(z0, z1))) → c71(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(from(2ndsneg(z0, z1))) → c71(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(from(pi(z0))) → c71(FROM(pi(proper(z0))), PROPER(pi(z0)))
PROPER(from(plus(z0, z1))) → c71(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(from(times(z0, z1))) → c71(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(from(square(z0))) → c71(FROM(square(proper(z0))), PROPER(square(z0)))
PROPER(from(0)) → c71(FROM(ok(0)))
PROPER(from(nil)) → c71(FROM(ok(nil)))
PROPER(from(rnil)) → c71(FROM(ok(rnil)))
PROPER(2ndspos(x0, s(z0))) → c72(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndspos(x0, posrecip(z0))) → c72(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndspos(x0, negrecip(z0))) → c72(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndspos(x0, cons(z0, z1))) → c72(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndspos(x0, cons2(z0, z1))) → c72(2NDSPOS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(2ndspos(x0, rcons(z0, z1))) → c72(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndspos(x0, from(z0))) → c72(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c72(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c72(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndspos(x0, pi(z0))) → c72(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndspos(x0, plus(z0, z1))) → c72(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndspos(x0, times(z0, z1))) → c72(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndspos(x0, square(z0))) → c72(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndspos(s(z0), x1)) → c72(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndspos(posrecip(z0), x1)) → c72(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndspos(negrecip(z0), x1)) → c72(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndspos(cons(z0, z1), x1)) → c72(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndspos(cons2(z0, z1), x1)) → c72(2NDSPOS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(2ndspos(rcons(z0, z1), x1)) → c72(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndspos(from(z0), x1)) → c72(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c72(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c72(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndspos(pi(z0), x1)) → c72(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndspos(plus(z0, z1), x1)) → c72(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndspos(times(z0, z1), x1)) → c72(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndspos(square(z0), x1)) → c72(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndspos(x0, 0)) → c72(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndspos(x0, nil)) → c72(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndspos(x0, rnil)) → c72(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndspos(0, x1)) → c72(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndspos(nil, x1)) → c72(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndspos(rnil, x1)) → c72(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(x0, s(z0))) → c73(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndsneg(x0, posrecip(z0))) → c73(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndsneg(x0, negrecip(z0))) → c73(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndsneg(x0, cons(z0, z1))) → c73(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndsneg(x0, cons2(z0, z1))) → c73(2NDSNEG(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(2ndsneg(x0, rcons(z0, z1))) → c73(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndsneg(x0, from(z0))) → c73(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c73(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c73(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndsneg(x0, pi(z0))) → c73(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndsneg(x0, plus(z0, z1))) → c73(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndsneg(x0, times(z0, z1))) → c73(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndsneg(x0, square(z0))) → c73(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndsneg(s(z0), x1)) → c73(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndsneg(posrecip(z0), x1)) → c73(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndsneg(negrecip(z0), x1)) → c73(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndsneg(cons(z0, z1), x1)) → c73(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(cons2(z0, z1), x1)) → c73(2NDSNEG(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(2ndsneg(rcons(z0, z1), x1)) → c73(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(from(z0), x1)) → c73(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c73(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c73(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndsneg(pi(z0), x1)) → c73(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndsneg(plus(z0, z1), x1)) → c73(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndsneg(times(z0, z1), x1)) → c73(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndsneg(square(z0), x1)) → c73(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndsneg(x0, 0)) → c73(2NDSNEG(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndsneg(x0, nil)) → c73(2NDSNEG(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndsneg(x0, rnil)) → c73(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndsneg(0, x1)) → c73(2NDSNEG(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndsneg(nil, x1)) → c73(2NDSNEG(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(rnil, x1)) → c73(2NDSNEG(ok(rnil), proper(x1)), PROPER(x1))
PROPER(pi(0)) → c74(PI(ok(0)), PROPER(0))
PROPER(pi(s(z0))) → c74(PI(s(proper(z0))), PROPER(s(z0)))
PROPER(pi(posrecip(z0))) → c74(PI(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(pi(negrecip(z0))) → c74(PI(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(pi(nil)) → c74(PI(ok(nil)), PROPER(nil))
PROPER(pi(cons(z0, z1))) → c74(PI(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(pi(cons2(z0, z1))) → c74(PI(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(pi(rnil)) → c74(PI(ok(rnil)), PROPER(rnil))
PROPER(pi(rcons(z0, z1))) → c74(PI(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(pi(from(z0))) → c74(PI(from(proper(z0))), PROPER(from(z0)))
PROPER(pi(2ndspos(z0, z1))) → c74(PI(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(pi(2ndsneg(z0, z1))) → c74(PI(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(pi(pi(z0))) → c74(PI(pi(proper(z0))), PROPER(pi(z0)))
PROPER(pi(plus(z0, z1))) → c74(PI(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(pi(times(z0, z1))) → c74(PI(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(pi(square(z0))) → c74(PI(square(proper(z0))), PROPER(square(z0)))
S tuples:
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
PROPER(plus(z0, z1)) → c75(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c76(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c77(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c78(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c79(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c9(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(2NDSPOS(s(z0), cons2(z1, z2)))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(2NDSNEG(s(z0), cons2(z1, z2)))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c13(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, z2)))) → c13(S(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(s(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, z2)))) → c13(S(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(s(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c13(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c13(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c13(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c13(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c13(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c13(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c13(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c13(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(cons2(z0, z1))) → c13(S(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c13(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c13(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c13(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c14(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c14(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c14(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c14(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c14(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c14(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c14(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c14(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(cons2(z0, z1))) → c14(POSRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c15(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c15(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c15(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c15(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c15(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c15(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c15(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c15(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(cons2(z0, z1))) → c15(NEGRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndspos(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndspos(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndsneg(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndsneg(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c16(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c16(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c16(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c16(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c16(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c16(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c16(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c16(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(cons2(z0, z1), x1)) → c16(CONS(cons2(z0, active(z1)), x1), ACTIVE(cons2(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, 2ndsneg(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(0, z0))) → c17(CONS2(x0, mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(cons2(x0, plus(s(z0), z1))) → c17(CONS2(x0, mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons2(x0, times(0, z0))) → c17(CONS2(x0, mark(0)), ACTIVE(times(0, z0)))
ACTIVE(cons2(x0, times(s(z0), z1))) → c17(CONS2(x0, mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(cons2(x0, s(z0))) → c17(CONS2(x0, s(active(z0))), ACTIVE(s(z0)))
ACTIVE(cons2(x0, posrecip(z0))) → c17(CONS2(x0, posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(cons2(x0, negrecip(z0))) → c17(CONS2(x0, negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(cons2(x0, cons(z0, z1))) → c17(CONS2(x0, cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(cons2(x0, cons2(z0, z1))) → c17(CONS2(x0, cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, from(active(z0))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, square(active(z0))), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c20(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(from(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(from(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c20(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c20(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c20(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c20(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c20(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c20(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c20(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c20(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c20(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c20(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(cons2(z0, z1))) → c20(FROM(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c20(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c20(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c20(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c25(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c25(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c25(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c25(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c25(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c25(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c25(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c25(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c25(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c25(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c25(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(cons2(z0, z1))) → c25(PI(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c25(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c25(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c25(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c30(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(square(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(square(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c30(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c30(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c30(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c30(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c30(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c30(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c30(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c30(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c30(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(cons2(z0, z1))) → c30(SQUARE(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c30(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c30(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c63(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c63(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c63(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c63(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(cons2(z0, z1))) → c63(S(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(s(rcons(z0, z1))) → c63(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c63(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c63(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c63(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c63(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c63(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c63(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c63(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c63(S(ok(0)))
PROPER(s(nil)) → c63(S(ok(nil)))
PROPER(s(rnil)) → c63(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c64(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c64(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c64(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c64(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(cons2(z0, z1))) → c64(POSRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c64(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c64(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c64(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c64(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c64(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c64(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c64(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c64(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c64(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c64(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c64(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c65(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c65(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c65(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c65(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(cons2(z0, z1))) → c65(NEGRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c65(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c65(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c65(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c65(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c65(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c65(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c65(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c65(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c65(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c65(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c65(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c67(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c67(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c67(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c67(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, cons2(z0, z1))) → c67(CONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c67(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c67(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c67(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c67(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c67(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c67(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c67(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c67(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c67(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c67(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c67(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c67(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(cons2(z0, z1), x1)) → c67(CONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c67(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c67(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c67(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c67(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c67(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c67(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c67(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c67(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c67(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c67(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c67(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c67(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c67(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c67(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(cons2(x0, s(z0))) → c68(CONS2(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons2(x0, posrecip(z0))) → c68(CONS2(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons2(x0, negrecip(z0))) → c68(CONS2(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons2(x0, cons(z0, z1))) → c68(CONS2(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons2(x0, cons2(z0, z1))) → c68(CONS2(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons2(x0, rcons(z0, z1))) → c68(CONS2(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons2(x0, from(z0))) → c68(CONS2(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons2(x0, 2ndspos(z0, z1))) → c68(CONS2(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons2(x0, 2ndsneg(z0, z1))) → c68(CONS2(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons2(x0, pi(z0))) → c68(CONS2(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons2(x0, plus(z0, z1))) → c68(CONS2(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons2(x0, times(z0, z1))) → c68(CONS2(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons2(x0, square(z0))) → c68(CONS2(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons2(s(z0), x1)) → c68(CONS2(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons2(posrecip(z0), x1)) → c68(CONS2(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons2(negrecip(z0), x1)) → c68(CONS2(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons2(cons(z0, z1), x1)) → c68(CONS2(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons2(cons2(z0, z1), x1)) → c68(CONS2(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons2(rcons(z0, z1), x1)) → c68(CONS2(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons2(from(z0), x1)) → c68(CONS2(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons2(2ndspos(z0, z1), x1)) → c68(CONS2(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons2(2ndsneg(z0, z1), x1)) → c68(CONS2(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons2(pi(z0), x1)) → c68(CONS2(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons2(plus(z0, z1), x1)) → c68(CONS2(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons2(times(z0, z1), x1)) → c68(CONS2(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons2(square(z0), x1)) → c68(CONS2(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons2(x0, 0)) → c68(CONS2(proper(x0), ok(0)), PROPER(x0))
PROPER(cons2(x0, nil)) → c68(CONS2(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons2(x0, rnil)) → c68(CONS2(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons2(0, x1)) → c68(CONS2(ok(0), proper(x1)), PROPER(x1))
PROPER(cons2(nil, x1)) → c68(CONS2(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons2(rnil, x1)) → c68(CONS2(ok(rnil), proper(x1)), PROPER(x1))
PROPER(rcons(x0, s(z0))) → c70(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c70(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c70(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, cons(z0, z1))) → c70(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, cons2(z0, z1))) → c70(RCONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(rcons(x0, rcons(z0, z1))) → c70(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c70(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c70(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c70(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c70(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c70(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c70(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c70(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(s(z0), x1)) → c70(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c70(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c70(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c70(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(cons2(z0, z1), x1)) → c70(RCONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c70(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c70(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c70(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c70(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c70(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c70(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c70(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c70(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(rcons(x0, 0)) → c70(RCONS(proper(x0), ok(0)), PROPER(x0))
PROPER(rcons(x0, nil)) → c70(RCONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(rcons(x0, rnil)) → c70(RCONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(rcons(0, x1)) → c70(RCONS(ok(0), proper(x1)), PROPER(x1))
PROPER(rcons(nil, x1)) → c70(RCONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c70(RCONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(from(s(z0))) → c71(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(posrecip(z0))) → c71(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(from(negrecip(z0))) → c71(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(from(cons(z0, z1))) → c71(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(cons2(z0, z1))) → c71(FROM(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(from(rcons(z0, z1))) → c71(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(from(from(z0))) → c71(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(2ndspos(z0, z1))) → c71(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(from(2ndsneg(z0, z1))) → c71(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(from(pi(z0))) → c71(FROM(pi(proper(z0))), PROPER(pi(z0)))
PROPER(from(plus(z0, z1))) → c71(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(from(times(z0, z1))) → c71(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(from(square(z0))) → c71(FROM(square(proper(z0))), PROPER(square(z0)))
PROPER(from(0)) → c71(FROM(ok(0)))
PROPER(from(nil)) → c71(FROM(ok(nil)))
PROPER(from(rnil)) → c71(FROM(ok(rnil)))
PROPER(2ndspos(x0, s(z0))) → c72(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndspos(x0, posrecip(z0))) → c72(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndspos(x0, negrecip(z0))) → c72(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndspos(x0, cons(z0, z1))) → c72(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndspos(x0, cons2(z0, z1))) → c72(2NDSPOS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(2ndspos(x0, rcons(z0, z1))) → c72(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndspos(x0, from(z0))) → c72(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c72(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c72(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndspos(x0, pi(z0))) → c72(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndspos(x0, plus(z0, z1))) → c72(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndspos(x0, times(z0, z1))) → c72(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndspos(x0, square(z0))) → c72(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndspos(s(z0), x1)) → c72(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndspos(posrecip(z0), x1)) → c72(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndspos(negrecip(z0), x1)) → c72(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndspos(cons(z0, z1), x1)) → c72(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndspos(cons2(z0, z1), x1)) → c72(2NDSPOS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(2ndspos(rcons(z0, z1), x1)) → c72(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndspos(from(z0), x1)) → c72(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c72(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c72(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndspos(pi(z0), x1)) → c72(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndspos(plus(z0, z1), x1)) → c72(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndspos(times(z0, z1), x1)) → c72(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndspos(square(z0), x1)) → c72(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndspos(x0, 0)) → c72(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndspos(x0, nil)) → c72(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndspos(x0, rnil)) → c72(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndspos(0, x1)) → c72(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndspos(nil, x1)) → c72(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndspos(rnil, x1)) → c72(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(x0, s(z0))) → c73(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndsneg(x0, posrecip(z0))) → c73(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndsneg(x0, negrecip(z0))) → c73(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndsneg(x0, cons(z0, z1))) → c73(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndsneg(x0, cons2(z0, z1))) → c73(2NDSNEG(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(2ndsneg(x0, rcons(z0, z1))) → c73(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndsneg(x0, from(z0))) → c73(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c73(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c73(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndsneg(x0, pi(z0))) → c73(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndsneg(x0, plus(z0, z1))) → c73(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndsneg(x0, times(z0, z1))) → c73(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndsneg(x0, square(z0))) → c73(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndsneg(s(z0), x1)) → c73(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndsneg(posrecip(z0), x1)) → c73(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndsneg(negrecip(z0), x1)) → c73(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndsneg(cons(z0, z1), x1)) → c73(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(cons2(z0, z1), x1)) → c73(2NDSNEG(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(2ndsneg(rcons(z0, z1), x1)) → c73(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(from(z0), x1)) → c73(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c73(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c73(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndsneg(pi(z0), x1)) → c73(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndsneg(plus(z0, z1), x1)) → c73(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndsneg(times(z0, z1), x1)) → c73(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndsneg(square(z0), x1)) → c73(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndsneg(x0, 0)) → c73(2NDSNEG(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndsneg(x0, nil)) → c73(2NDSNEG(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndsneg(x0, rnil)) → c73(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndsneg(0, x1)) → c73(2NDSNEG(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndsneg(nil, x1)) → c73(2NDSNEG(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(rnil, x1)) → c73(2NDSNEG(ok(rnil), proper(x1)), PROPER(x1))
PROPER(pi(0)) → c74(PI(ok(0)), PROPER(0))
PROPER(pi(s(z0))) → c74(PI(s(proper(z0))), PROPER(s(z0)))
PROPER(pi(posrecip(z0))) → c74(PI(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(pi(negrecip(z0))) → c74(PI(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(pi(nil)) → c74(PI(ok(nil)), PROPER(nil))
PROPER(pi(cons(z0, z1))) → c74(PI(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(pi(cons2(z0, z1))) → c74(PI(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(pi(rnil)) → c74(PI(ok(rnil)), PROPER(rnil))
PROPER(pi(rcons(z0, z1))) → c74(PI(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(pi(from(z0))) → c74(PI(from(proper(z0))), PROPER(from(z0)))
PROPER(pi(2ndspos(z0, z1))) → c74(PI(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(pi(2ndsneg(z0, z1))) → c74(PI(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(pi(pi(z0))) → c74(PI(pi(proper(z0))), PROPER(pi(z0)))
PROPER(pi(plus(z0, z1))) → c74(PI(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(pi(times(z0, z1))) → c74(PI(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(pi(square(z0))) → c74(PI(square(proper(z0))), PROPER(square(z0)))
K tuples:none
Defined Rule Symbols:
active, 2ndspos, cons2, rcons, posrecip, 2ndsneg, negrecip, s, cons, from, pi, plus, times, square, proper
Defined Pair Symbols:
ACTIVE, S, POSRECIP, NEGRECIP, CONS, CONS2, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP
Compound Symbols:
c12, c18, c19, c21, c22, c23, c24, c26, c27, c28, c29, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c75, c76, c77, c78, c79, c, c7, c9, c11, c1, c13, c14, c15, c16, c17, c20, c25, c30, c63, c63, c64, c64, c65, c65, c67, c67, c68, c68, c70, c70, c71, c71, c72, c72, c73, c73, c74
(65) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 3 trailing tuple parts
(66) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(2ndspos(0, z0)) → mark(rnil)
active(2ndspos(s(z0), cons(z1, z2))) → mark(2ndspos(s(z0), cons2(z1, z2)))
active(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(z1, z2))) → mark(2ndsneg(s(z0), cons2(z1, z2)))
active(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
active(pi(z0)) → mark(2ndspos(z0, from(0)))
active(plus(0, z0)) → mark(z0)
active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
active(times(0, z0)) → mark(0)
active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
active(square(z0)) → mark(times(z0, z0))
active(s(z0)) → s(active(z0))
active(posrecip(z0)) → posrecip(active(z0))
active(negrecip(z0)) → negrecip(active(z0))
active(cons(z0, z1)) → cons(active(z0), z1)
active(cons2(z0, z1)) → cons2(z0, active(z1))
active(rcons(z0, z1)) → rcons(active(z0), z1)
active(rcons(z0, z1)) → rcons(z0, active(z1))
active(from(z0)) → from(active(z0))
active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
active(pi(z0)) → pi(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(times(z0, z1)) → times(active(z0), z1)
active(times(z0, z1)) → times(z0, active(z1))
active(square(z0)) → square(active(z0))
2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
cons2(z0, mark(z1)) → mark(cons2(z0, z1))
cons2(ok(z0), ok(z1)) → ok(cons2(z0, z1))
rcons(mark(z0), z1) → mark(rcons(z0, z1))
rcons(z0, mark(z1)) → mark(rcons(z0, z1))
rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
posrecip(ok(z0)) → ok(posrecip(z0))
posrecip(mark(z0)) → mark(posrecip(z0))
2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
negrecip(ok(z0)) → ok(negrecip(z0))
negrecip(mark(z0)) → mark(negrecip(z0))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
cons(mark(z0), z1) → mark(cons(z0, z1))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
from(mark(z0)) → mark(from(z0))
from(ok(z0)) → ok(from(z0))
pi(mark(z0)) → mark(pi(z0))
pi(ok(z0)) → ok(pi(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
times(mark(z0), z1) → mark(times(z0, z1))
times(ok(z0), ok(z1)) → ok(times(z0, z1))
times(z0, mark(z1)) → mark(times(z0, z1))
square(mark(z0)) → mark(square(z0))
square(ok(z0)) → ok(square(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(posrecip(z0)) → posrecip(proper(z0))
proper(negrecip(z0)) → negrecip(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(cons2(z0, z1)) → cons2(proper(z0), proper(z1))
proper(rnil) → ok(rnil)
proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
proper(pi(z0)) → pi(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(times(z0, z1)) → times(proper(z0), proper(z1))
proper(square(z0)) → square(proper(z0))
Tuples:
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
PROPER(plus(z0, z1)) → c75(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c76(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c77(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c78(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c79(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c9(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(2NDSPOS(s(z0), cons2(z1, z2)))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(2NDSNEG(s(z0), cons2(z1, z2)))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c13(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, z2)))) → c13(S(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(s(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, z2)))) → c13(S(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(s(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c13(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c13(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c13(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c13(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c13(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c13(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c13(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c13(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(cons2(z0, z1))) → c13(S(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c13(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c13(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c13(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c14(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c14(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c14(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c14(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c14(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c14(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c14(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c14(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(cons2(z0, z1))) → c14(POSRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c15(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c15(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c15(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c15(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c15(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c15(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c15(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c15(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(cons2(z0, z1))) → c15(NEGRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndspos(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndspos(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndsneg(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndsneg(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c16(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c16(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c16(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c16(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c16(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c16(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c16(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c16(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(cons2(z0, z1), x1)) → c16(CONS(cons2(z0, active(z1)), x1), ACTIVE(cons2(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, 2ndsneg(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(0, z0))) → c17(CONS2(x0, mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(cons2(x0, plus(s(z0), z1))) → c17(CONS2(x0, mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons2(x0, times(0, z0))) → c17(CONS2(x0, mark(0)), ACTIVE(times(0, z0)))
ACTIVE(cons2(x0, times(s(z0), z1))) → c17(CONS2(x0, mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(cons2(x0, s(z0))) → c17(CONS2(x0, s(active(z0))), ACTIVE(s(z0)))
ACTIVE(cons2(x0, posrecip(z0))) → c17(CONS2(x0, posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(cons2(x0, negrecip(z0))) → c17(CONS2(x0, negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(cons2(x0, cons(z0, z1))) → c17(CONS2(x0, cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(cons2(x0, cons2(z0, z1))) → c17(CONS2(x0, cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, from(active(z0))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, square(active(z0))), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c20(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(from(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(from(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c20(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c20(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c20(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c20(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c20(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c20(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c20(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c20(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c20(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c20(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(cons2(z0, z1))) → c20(FROM(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c20(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c20(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c20(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c25(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c25(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c25(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c25(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c25(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c25(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c25(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c25(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c25(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c25(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c25(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(cons2(z0, z1))) → c25(PI(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c25(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c25(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c25(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c30(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(square(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(square(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c30(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c30(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c30(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c30(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c30(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c30(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c30(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c30(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c30(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(cons2(z0, z1))) → c30(SQUARE(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c30(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c30(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c63(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c63(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c63(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c63(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(cons2(z0, z1))) → c63(S(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(s(rcons(z0, z1))) → c63(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c63(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c63(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c63(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c63(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c63(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c63(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c63(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c63(S(ok(0)))
PROPER(s(nil)) → c63(S(ok(nil)))
PROPER(s(rnil)) → c63(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c64(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c64(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c64(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c64(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(cons2(z0, z1))) → c64(POSRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c64(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c64(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c64(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c64(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c64(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c64(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c64(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c64(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c64(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c64(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c64(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c65(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c65(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c65(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c65(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(cons2(z0, z1))) → c65(NEGRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c65(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c65(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c65(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c65(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c65(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c65(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c65(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c65(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c65(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c65(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c65(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c67(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c67(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c67(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c67(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, cons2(z0, z1))) → c67(CONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c67(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c67(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c67(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c67(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c67(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c67(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c67(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c67(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c67(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c67(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c67(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c67(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(cons2(z0, z1), x1)) → c67(CONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c67(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c67(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c67(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c67(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c67(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c67(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c67(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c67(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c67(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c67(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c67(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c67(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c67(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c67(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(cons2(x0, s(z0))) → c68(CONS2(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons2(x0, posrecip(z0))) → c68(CONS2(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons2(x0, negrecip(z0))) → c68(CONS2(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons2(x0, cons(z0, z1))) → c68(CONS2(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons2(x0, cons2(z0, z1))) → c68(CONS2(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons2(x0, rcons(z0, z1))) → c68(CONS2(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons2(x0, from(z0))) → c68(CONS2(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons2(x0, 2ndspos(z0, z1))) → c68(CONS2(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons2(x0, 2ndsneg(z0, z1))) → c68(CONS2(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons2(x0, pi(z0))) → c68(CONS2(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons2(x0, plus(z0, z1))) → c68(CONS2(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons2(x0, times(z0, z1))) → c68(CONS2(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons2(x0, square(z0))) → c68(CONS2(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons2(s(z0), x1)) → c68(CONS2(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons2(posrecip(z0), x1)) → c68(CONS2(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons2(negrecip(z0), x1)) → c68(CONS2(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons2(cons(z0, z1), x1)) → c68(CONS2(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons2(cons2(z0, z1), x1)) → c68(CONS2(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons2(rcons(z0, z1), x1)) → c68(CONS2(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons2(from(z0), x1)) → c68(CONS2(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons2(2ndspos(z0, z1), x1)) → c68(CONS2(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons2(2ndsneg(z0, z1), x1)) → c68(CONS2(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons2(pi(z0), x1)) → c68(CONS2(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons2(plus(z0, z1), x1)) → c68(CONS2(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons2(times(z0, z1), x1)) → c68(CONS2(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons2(square(z0), x1)) → c68(CONS2(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons2(x0, 0)) → c68(CONS2(proper(x0), ok(0)), PROPER(x0))
PROPER(cons2(x0, nil)) → c68(CONS2(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons2(x0, rnil)) → c68(CONS2(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons2(0, x1)) → c68(CONS2(ok(0), proper(x1)), PROPER(x1))
PROPER(cons2(nil, x1)) → c68(CONS2(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons2(rnil, x1)) → c68(CONS2(ok(rnil), proper(x1)), PROPER(x1))
PROPER(rcons(x0, s(z0))) → c70(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c70(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c70(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, cons(z0, z1))) → c70(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, cons2(z0, z1))) → c70(RCONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(rcons(x0, rcons(z0, z1))) → c70(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c70(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c70(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c70(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c70(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c70(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c70(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c70(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(s(z0), x1)) → c70(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c70(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c70(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c70(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(cons2(z0, z1), x1)) → c70(RCONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c70(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c70(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c70(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c70(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c70(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c70(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c70(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c70(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(rcons(x0, 0)) → c70(RCONS(proper(x0), ok(0)), PROPER(x0))
PROPER(rcons(x0, nil)) → c70(RCONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(rcons(x0, rnil)) → c70(RCONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(rcons(0, x1)) → c70(RCONS(ok(0), proper(x1)), PROPER(x1))
PROPER(rcons(nil, x1)) → c70(RCONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c70(RCONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(from(s(z0))) → c71(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(posrecip(z0))) → c71(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(from(negrecip(z0))) → c71(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(from(cons(z0, z1))) → c71(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(cons2(z0, z1))) → c71(FROM(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(from(rcons(z0, z1))) → c71(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(from(from(z0))) → c71(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(2ndspos(z0, z1))) → c71(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(from(2ndsneg(z0, z1))) → c71(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(from(pi(z0))) → c71(FROM(pi(proper(z0))), PROPER(pi(z0)))
PROPER(from(plus(z0, z1))) → c71(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(from(times(z0, z1))) → c71(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(from(square(z0))) → c71(FROM(square(proper(z0))), PROPER(square(z0)))
PROPER(from(0)) → c71(FROM(ok(0)))
PROPER(from(nil)) → c71(FROM(ok(nil)))
PROPER(from(rnil)) → c71(FROM(ok(rnil)))
PROPER(2ndspos(x0, s(z0))) → c72(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndspos(x0, posrecip(z0))) → c72(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndspos(x0, negrecip(z0))) → c72(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndspos(x0, cons(z0, z1))) → c72(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndspos(x0, cons2(z0, z1))) → c72(2NDSPOS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(2ndspos(x0, rcons(z0, z1))) → c72(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndspos(x0, from(z0))) → c72(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c72(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c72(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndspos(x0, pi(z0))) → c72(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndspos(x0, plus(z0, z1))) → c72(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndspos(x0, times(z0, z1))) → c72(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndspos(x0, square(z0))) → c72(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndspos(s(z0), x1)) → c72(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndspos(posrecip(z0), x1)) → c72(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndspos(negrecip(z0), x1)) → c72(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndspos(cons(z0, z1), x1)) → c72(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndspos(cons2(z0, z1), x1)) → c72(2NDSPOS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(2ndspos(rcons(z0, z1), x1)) → c72(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndspos(from(z0), x1)) → c72(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c72(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c72(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndspos(pi(z0), x1)) → c72(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndspos(plus(z0, z1), x1)) → c72(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndspos(times(z0, z1), x1)) → c72(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndspos(square(z0), x1)) → c72(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndspos(x0, 0)) → c72(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndspos(x0, nil)) → c72(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndspos(x0, rnil)) → c72(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndspos(0, x1)) → c72(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndspos(nil, x1)) → c72(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndspos(rnil, x1)) → c72(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(x0, s(z0))) → c73(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndsneg(x0, posrecip(z0))) → c73(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndsneg(x0, negrecip(z0))) → c73(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndsneg(x0, cons(z0, z1))) → c73(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndsneg(x0, cons2(z0, z1))) → c73(2NDSNEG(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(2ndsneg(x0, rcons(z0, z1))) → c73(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndsneg(x0, from(z0))) → c73(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c73(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c73(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndsneg(x0, pi(z0))) → c73(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndsneg(x0, plus(z0, z1))) → c73(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndsneg(x0, times(z0, z1))) → c73(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndsneg(x0, square(z0))) → c73(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndsneg(s(z0), x1)) → c73(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndsneg(posrecip(z0), x1)) → c73(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndsneg(negrecip(z0), x1)) → c73(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndsneg(cons(z0, z1), x1)) → c73(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(cons2(z0, z1), x1)) → c73(2NDSNEG(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(2ndsneg(rcons(z0, z1), x1)) → c73(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(from(z0), x1)) → c73(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c73(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c73(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndsneg(pi(z0), x1)) → c73(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndsneg(plus(z0, z1), x1)) → c73(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndsneg(times(z0, z1), x1)) → c73(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndsneg(square(z0), x1)) → c73(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndsneg(x0, 0)) → c73(2NDSNEG(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndsneg(x0, nil)) → c73(2NDSNEG(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndsneg(x0, rnil)) → c73(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndsneg(0, x1)) → c73(2NDSNEG(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndsneg(nil, x1)) → c73(2NDSNEG(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(rnil, x1)) → c73(2NDSNEG(ok(rnil), proper(x1)), PROPER(x1))
PROPER(pi(s(z0))) → c74(PI(s(proper(z0))), PROPER(s(z0)))
PROPER(pi(posrecip(z0))) → c74(PI(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(pi(negrecip(z0))) → c74(PI(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(pi(cons(z0, z1))) → c74(PI(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(pi(cons2(z0, z1))) → c74(PI(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(pi(rcons(z0, z1))) → c74(PI(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(pi(from(z0))) → c74(PI(from(proper(z0))), PROPER(from(z0)))
PROPER(pi(2ndspos(z0, z1))) → c74(PI(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(pi(2ndsneg(z0, z1))) → c74(PI(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(pi(pi(z0))) → c74(PI(pi(proper(z0))), PROPER(pi(z0)))
PROPER(pi(plus(z0, z1))) → c74(PI(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(pi(times(z0, z1))) → c74(PI(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(pi(square(z0))) → c74(PI(square(proper(z0))), PROPER(square(z0)))
PROPER(pi(0)) → c74(PI(ok(0)))
PROPER(pi(nil)) → c74(PI(ok(nil)))
PROPER(pi(rnil)) → c74(PI(ok(rnil)))
S tuples:
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
PROPER(plus(z0, z1)) → c75(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c76(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c77(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c78(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c79(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c9(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(2NDSPOS(s(z0), cons2(z1, z2)))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(2NDSNEG(s(z0), cons2(z1, z2)))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c13(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, z2)))) → c13(S(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(s(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, z2)))) → c13(S(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(s(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c13(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c13(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c13(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c13(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c13(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c13(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c13(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c13(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(cons2(z0, z1))) → c13(S(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c13(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c13(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c13(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c14(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c14(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c14(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c14(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c14(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c14(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c14(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c14(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(cons2(z0, z1))) → c14(POSRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c15(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c15(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c15(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c15(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c15(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c15(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c15(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c15(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(cons2(z0, z1))) → c15(NEGRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndspos(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndspos(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndsneg(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndsneg(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c16(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c16(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c16(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c16(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c16(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c16(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c16(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c16(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(cons2(z0, z1), x1)) → c16(CONS(cons2(z0, active(z1)), x1), ACTIVE(cons2(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, 2ndsneg(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(0, z0))) → c17(CONS2(x0, mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(cons2(x0, plus(s(z0), z1))) → c17(CONS2(x0, mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons2(x0, times(0, z0))) → c17(CONS2(x0, mark(0)), ACTIVE(times(0, z0)))
ACTIVE(cons2(x0, times(s(z0), z1))) → c17(CONS2(x0, mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(cons2(x0, s(z0))) → c17(CONS2(x0, s(active(z0))), ACTIVE(s(z0)))
ACTIVE(cons2(x0, posrecip(z0))) → c17(CONS2(x0, posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(cons2(x0, negrecip(z0))) → c17(CONS2(x0, negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(cons2(x0, cons(z0, z1))) → c17(CONS2(x0, cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(cons2(x0, cons2(z0, z1))) → c17(CONS2(x0, cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, from(active(z0))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, square(active(z0))), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c20(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(from(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(from(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c20(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c20(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c20(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c20(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c20(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c20(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c20(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c20(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c20(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c20(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(cons2(z0, z1))) → c20(FROM(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c20(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c20(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c20(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c25(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c25(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c25(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c25(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c25(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c25(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c25(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c25(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c25(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c25(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c25(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(cons2(z0, z1))) → c25(PI(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c25(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c25(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c25(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c30(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(square(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(square(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c30(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c30(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c30(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c30(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c30(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c30(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c30(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c30(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c30(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(cons2(z0, z1))) → c30(SQUARE(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c30(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c30(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c63(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c63(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c63(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c63(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(cons2(z0, z1))) → c63(S(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(s(rcons(z0, z1))) → c63(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c63(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c63(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c63(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c63(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c63(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c63(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c63(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c63(S(ok(0)))
PROPER(s(nil)) → c63(S(ok(nil)))
PROPER(s(rnil)) → c63(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c64(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c64(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c64(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c64(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(cons2(z0, z1))) → c64(POSRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c64(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c64(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c64(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c64(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c64(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c64(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c64(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c64(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c64(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c64(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c64(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c65(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c65(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c65(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c65(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(cons2(z0, z1))) → c65(NEGRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c65(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c65(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c65(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c65(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c65(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c65(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c65(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c65(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c65(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c65(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c65(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c67(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c67(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c67(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c67(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, cons2(z0, z1))) → c67(CONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c67(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c67(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c67(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c67(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c67(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c67(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c67(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c67(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c67(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c67(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c67(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c67(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(cons2(z0, z1), x1)) → c67(CONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c67(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c67(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c67(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c67(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c67(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c67(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c67(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c67(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c67(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c67(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c67(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c67(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c67(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c67(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(cons2(x0, s(z0))) → c68(CONS2(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons2(x0, posrecip(z0))) → c68(CONS2(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons2(x0, negrecip(z0))) → c68(CONS2(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons2(x0, cons(z0, z1))) → c68(CONS2(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons2(x0, cons2(z0, z1))) → c68(CONS2(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons2(x0, rcons(z0, z1))) → c68(CONS2(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons2(x0, from(z0))) → c68(CONS2(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons2(x0, 2ndspos(z0, z1))) → c68(CONS2(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons2(x0, 2ndsneg(z0, z1))) → c68(CONS2(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons2(x0, pi(z0))) → c68(CONS2(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons2(x0, plus(z0, z1))) → c68(CONS2(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons2(x0, times(z0, z1))) → c68(CONS2(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons2(x0, square(z0))) → c68(CONS2(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons2(s(z0), x1)) → c68(CONS2(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons2(posrecip(z0), x1)) → c68(CONS2(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons2(negrecip(z0), x1)) → c68(CONS2(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons2(cons(z0, z1), x1)) → c68(CONS2(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons2(cons2(z0, z1), x1)) → c68(CONS2(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons2(rcons(z0, z1), x1)) → c68(CONS2(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons2(from(z0), x1)) → c68(CONS2(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons2(2ndspos(z0, z1), x1)) → c68(CONS2(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons2(2ndsneg(z0, z1), x1)) → c68(CONS2(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons2(pi(z0), x1)) → c68(CONS2(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons2(plus(z0, z1), x1)) → c68(CONS2(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons2(times(z0, z1), x1)) → c68(CONS2(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons2(square(z0), x1)) → c68(CONS2(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons2(x0, 0)) → c68(CONS2(proper(x0), ok(0)), PROPER(x0))
PROPER(cons2(x0, nil)) → c68(CONS2(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons2(x0, rnil)) → c68(CONS2(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons2(0, x1)) → c68(CONS2(ok(0), proper(x1)), PROPER(x1))
PROPER(cons2(nil, x1)) → c68(CONS2(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons2(rnil, x1)) → c68(CONS2(ok(rnil), proper(x1)), PROPER(x1))
PROPER(rcons(x0, s(z0))) → c70(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c70(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c70(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, cons(z0, z1))) → c70(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, cons2(z0, z1))) → c70(RCONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(rcons(x0, rcons(z0, z1))) → c70(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c70(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c70(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c70(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c70(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c70(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c70(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c70(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(s(z0), x1)) → c70(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c70(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c70(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c70(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(cons2(z0, z1), x1)) → c70(RCONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c70(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c70(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c70(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c70(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c70(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c70(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c70(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c70(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(rcons(x0, 0)) → c70(RCONS(proper(x0), ok(0)), PROPER(x0))
PROPER(rcons(x0, nil)) → c70(RCONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(rcons(x0, rnil)) → c70(RCONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(rcons(0, x1)) → c70(RCONS(ok(0), proper(x1)), PROPER(x1))
PROPER(rcons(nil, x1)) → c70(RCONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c70(RCONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(from(s(z0))) → c71(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(posrecip(z0))) → c71(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(from(negrecip(z0))) → c71(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(from(cons(z0, z1))) → c71(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(cons2(z0, z1))) → c71(FROM(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(from(rcons(z0, z1))) → c71(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(from(from(z0))) → c71(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(2ndspos(z0, z1))) → c71(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(from(2ndsneg(z0, z1))) → c71(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(from(pi(z0))) → c71(FROM(pi(proper(z0))), PROPER(pi(z0)))
PROPER(from(plus(z0, z1))) → c71(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(from(times(z0, z1))) → c71(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(from(square(z0))) → c71(FROM(square(proper(z0))), PROPER(square(z0)))
PROPER(from(0)) → c71(FROM(ok(0)))
PROPER(from(nil)) → c71(FROM(ok(nil)))
PROPER(from(rnil)) → c71(FROM(ok(rnil)))
PROPER(2ndspos(x0, s(z0))) → c72(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndspos(x0, posrecip(z0))) → c72(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndspos(x0, negrecip(z0))) → c72(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndspos(x0, cons(z0, z1))) → c72(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndspos(x0, cons2(z0, z1))) → c72(2NDSPOS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(2ndspos(x0, rcons(z0, z1))) → c72(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndspos(x0, from(z0))) → c72(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c72(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c72(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndspos(x0, pi(z0))) → c72(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndspos(x0, plus(z0, z1))) → c72(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndspos(x0, times(z0, z1))) → c72(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndspos(x0, square(z0))) → c72(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndspos(s(z0), x1)) → c72(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndspos(posrecip(z0), x1)) → c72(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndspos(negrecip(z0), x1)) → c72(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndspos(cons(z0, z1), x1)) → c72(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndspos(cons2(z0, z1), x1)) → c72(2NDSPOS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(2ndspos(rcons(z0, z1), x1)) → c72(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndspos(from(z0), x1)) → c72(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c72(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c72(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndspos(pi(z0), x1)) → c72(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndspos(plus(z0, z1), x1)) → c72(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndspos(times(z0, z1), x1)) → c72(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndspos(square(z0), x1)) → c72(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndspos(x0, 0)) → c72(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndspos(x0, nil)) → c72(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndspos(x0, rnil)) → c72(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndspos(0, x1)) → c72(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndspos(nil, x1)) → c72(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndspos(rnil, x1)) → c72(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(x0, s(z0))) → c73(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndsneg(x0, posrecip(z0))) → c73(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndsneg(x0, negrecip(z0))) → c73(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndsneg(x0, cons(z0, z1))) → c73(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndsneg(x0, cons2(z0, z1))) → c73(2NDSNEG(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(2ndsneg(x0, rcons(z0, z1))) → c73(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndsneg(x0, from(z0))) → c73(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c73(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c73(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndsneg(x0, pi(z0))) → c73(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndsneg(x0, plus(z0, z1))) → c73(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndsneg(x0, times(z0, z1))) → c73(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndsneg(x0, square(z0))) → c73(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndsneg(s(z0), x1)) → c73(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndsneg(posrecip(z0), x1)) → c73(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndsneg(negrecip(z0), x1)) → c73(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndsneg(cons(z0, z1), x1)) → c73(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(cons2(z0, z1), x1)) → c73(2NDSNEG(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(2ndsneg(rcons(z0, z1), x1)) → c73(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(from(z0), x1)) → c73(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c73(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c73(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndsneg(pi(z0), x1)) → c73(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndsneg(plus(z0, z1), x1)) → c73(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndsneg(times(z0, z1), x1)) → c73(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndsneg(square(z0), x1)) → c73(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndsneg(x0, 0)) → c73(2NDSNEG(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndsneg(x0, nil)) → c73(2NDSNEG(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndsneg(x0, rnil)) → c73(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndsneg(0, x1)) → c73(2NDSNEG(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndsneg(nil, x1)) → c73(2NDSNEG(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(rnil, x1)) → c73(2NDSNEG(ok(rnil), proper(x1)), PROPER(x1))
PROPER(pi(s(z0))) → c74(PI(s(proper(z0))), PROPER(s(z0)))
PROPER(pi(posrecip(z0))) → c74(PI(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(pi(negrecip(z0))) → c74(PI(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(pi(cons(z0, z1))) → c74(PI(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(pi(cons2(z0, z1))) → c74(PI(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(pi(rcons(z0, z1))) → c74(PI(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(pi(from(z0))) → c74(PI(from(proper(z0))), PROPER(from(z0)))
PROPER(pi(2ndspos(z0, z1))) → c74(PI(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(pi(2ndsneg(z0, z1))) → c74(PI(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(pi(pi(z0))) → c74(PI(pi(proper(z0))), PROPER(pi(z0)))
PROPER(pi(plus(z0, z1))) → c74(PI(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(pi(times(z0, z1))) → c74(PI(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(pi(square(z0))) → c74(PI(square(proper(z0))), PROPER(square(z0)))
PROPER(pi(0)) → c74(PI(ok(0)))
PROPER(pi(nil)) → c74(PI(ok(nil)))
PROPER(pi(rnil)) → c74(PI(ok(rnil)))
K tuples:none
Defined Rule Symbols:
active, 2ndspos, cons2, rcons, posrecip, 2ndsneg, negrecip, s, cons, from, pi, plus, times, square, proper
Defined Pair Symbols:
ACTIVE, S, POSRECIP, NEGRECIP, CONS, CONS2, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP
Compound Symbols:
c12, c18, c19, c21, c22, c23, c24, c26, c27, c28, c29, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c75, c76, c77, c78, c79, c, c7, c9, c11, c1, c13, c14, c15, c16, c17, c20, c25, c30, c63, c63, c64, c64, c65, c65, c67, c67, c68, c68, c70, c70, c71, c71, c72, c72, c73, c73, c74, c74
(67) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
PROPER(
plus(
z0,
z1)) →
c75(
PLUS(
proper(
z0),
proper(
z1)),
PROPER(
z0),
PROPER(
z1)) by
PROPER(plus(x0, 0)) → c75(PLUS(proper(x0), ok(0)), PROPER(x0), PROPER(0))
PROPER(plus(x0, s(z0))) → c75(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(plus(x0, posrecip(z0))) → c75(PLUS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(plus(x0, negrecip(z0))) → c75(PLUS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(plus(x0, nil)) → c75(PLUS(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
PROPER(plus(x0, cons(z0, z1))) → c75(PLUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(plus(x0, cons2(z0, z1))) → c75(PLUS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(plus(x0, rnil)) → c75(PLUS(proper(x0), ok(rnil)), PROPER(x0), PROPER(rnil))
PROPER(plus(x0, rcons(z0, z1))) → c75(PLUS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(plus(x0, from(z0))) → c75(PLUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(plus(x0, 2ndspos(z0, z1))) → c75(PLUS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(plus(x0, 2ndsneg(z0, z1))) → c75(PLUS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(plus(x0, pi(z0))) → c75(PLUS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(plus(x0, plus(z0, z1))) → c75(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(plus(x0, times(z0, z1))) → c75(PLUS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(plus(x0, square(z0))) → c75(PLUS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(plus(0, x1)) → c75(PLUS(ok(0), proper(x1)), PROPER(0), PROPER(x1))
PROPER(plus(s(z0), x1)) → c75(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(plus(posrecip(z0), x1)) → c75(PLUS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(plus(negrecip(z0), x1)) → c75(PLUS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(plus(nil, x1)) → c75(PLUS(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
PROPER(plus(cons(z0, z1), x1)) → c75(PLUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(plus(cons2(z0, z1), x1)) → c75(PLUS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(plus(rnil, x1)) → c75(PLUS(ok(rnil), proper(x1)), PROPER(rnil), PROPER(x1))
PROPER(plus(rcons(z0, z1), x1)) → c75(PLUS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(plus(from(z0), x1)) → c75(PLUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(plus(2ndspos(z0, z1), x1)) → c75(PLUS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(plus(2ndsneg(z0, z1), x1)) → c75(PLUS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(plus(pi(z0), x1)) → c75(PLUS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(plus(plus(z0, z1), x1)) → c75(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(plus(times(z0, z1), x1)) → c75(PLUS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(plus(square(z0), x1)) → c75(PLUS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
(68) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(2ndspos(0, z0)) → mark(rnil)
active(2ndspos(s(z0), cons(z1, z2))) → mark(2ndspos(s(z0), cons2(z1, z2)))
active(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(z1, z2))) → mark(2ndsneg(s(z0), cons2(z1, z2)))
active(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
active(pi(z0)) → mark(2ndspos(z0, from(0)))
active(plus(0, z0)) → mark(z0)
active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
active(times(0, z0)) → mark(0)
active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
active(square(z0)) → mark(times(z0, z0))
active(s(z0)) → s(active(z0))
active(posrecip(z0)) → posrecip(active(z0))
active(negrecip(z0)) → negrecip(active(z0))
active(cons(z0, z1)) → cons(active(z0), z1)
active(cons2(z0, z1)) → cons2(z0, active(z1))
active(rcons(z0, z1)) → rcons(active(z0), z1)
active(rcons(z0, z1)) → rcons(z0, active(z1))
active(from(z0)) → from(active(z0))
active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
active(pi(z0)) → pi(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(times(z0, z1)) → times(active(z0), z1)
active(times(z0, z1)) → times(z0, active(z1))
active(square(z0)) → square(active(z0))
2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
cons2(z0, mark(z1)) → mark(cons2(z0, z1))
cons2(ok(z0), ok(z1)) → ok(cons2(z0, z1))
rcons(mark(z0), z1) → mark(rcons(z0, z1))
rcons(z0, mark(z1)) → mark(rcons(z0, z1))
rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
posrecip(ok(z0)) → ok(posrecip(z0))
posrecip(mark(z0)) → mark(posrecip(z0))
2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
negrecip(ok(z0)) → ok(negrecip(z0))
negrecip(mark(z0)) → mark(negrecip(z0))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
cons(mark(z0), z1) → mark(cons(z0, z1))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
from(mark(z0)) → mark(from(z0))
from(ok(z0)) → ok(from(z0))
pi(mark(z0)) → mark(pi(z0))
pi(ok(z0)) → ok(pi(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
times(mark(z0), z1) → mark(times(z0, z1))
times(ok(z0), ok(z1)) → ok(times(z0, z1))
times(z0, mark(z1)) → mark(times(z0, z1))
square(mark(z0)) → mark(square(z0))
square(ok(z0)) → ok(square(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(posrecip(z0)) → posrecip(proper(z0))
proper(negrecip(z0)) → negrecip(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(cons2(z0, z1)) → cons2(proper(z0), proper(z1))
proper(rnil) → ok(rnil)
proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
proper(pi(z0)) → pi(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(times(z0, z1)) → times(proper(z0), proper(z1))
proper(square(z0)) → square(proper(z0))
Tuples:
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
PROPER(times(z0, z1)) → c76(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c77(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c78(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c79(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c9(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(2NDSPOS(s(z0), cons2(z1, z2)))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(2NDSNEG(s(z0), cons2(z1, z2)))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c13(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, z2)))) → c13(S(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(s(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, z2)))) → c13(S(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(s(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c13(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c13(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c13(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c13(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c13(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c13(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c13(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c13(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(cons2(z0, z1))) → c13(S(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c13(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c13(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c13(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c14(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c14(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c14(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c14(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c14(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c14(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c14(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c14(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(cons2(z0, z1))) → c14(POSRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c15(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c15(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c15(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c15(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c15(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c15(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c15(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c15(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(cons2(z0, z1))) → c15(NEGRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndspos(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndspos(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndsneg(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndsneg(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c16(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c16(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c16(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c16(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c16(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c16(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c16(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c16(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(cons2(z0, z1), x1)) → c16(CONS(cons2(z0, active(z1)), x1), ACTIVE(cons2(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, 2ndsneg(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(0, z0))) → c17(CONS2(x0, mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(cons2(x0, plus(s(z0), z1))) → c17(CONS2(x0, mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons2(x0, times(0, z0))) → c17(CONS2(x0, mark(0)), ACTIVE(times(0, z0)))
ACTIVE(cons2(x0, times(s(z0), z1))) → c17(CONS2(x0, mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(cons2(x0, s(z0))) → c17(CONS2(x0, s(active(z0))), ACTIVE(s(z0)))
ACTIVE(cons2(x0, posrecip(z0))) → c17(CONS2(x0, posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(cons2(x0, negrecip(z0))) → c17(CONS2(x0, negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(cons2(x0, cons(z0, z1))) → c17(CONS2(x0, cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(cons2(x0, cons2(z0, z1))) → c17(CONS2(x0, cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, from(active(z0))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, square(active(z0))), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c20(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(from(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(from(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c20(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c20(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c20(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c20(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c20(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c20(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c20(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c20(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c20(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c20(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(cons2(z0, z1))) → c20(FROM(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c20(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c20(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c20(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c25(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c25(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c25(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c25(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c25(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c25(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c25(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c25(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c25(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c25(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c25(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(cons2(z0, z1))) → c25(PI(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c25(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c25(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c25(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c30(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(square(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(square(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c30(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c30(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c30(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c30(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c30(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c30(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c30(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c30(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c30(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(cons2(z0, z1))) → c30(SQUARE(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c30(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c30(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c63(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c63(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c63(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c63(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(cons2(z0, z1))) → c63(S(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(s(rcons(z0, z1))) → c63(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c63(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c63(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c63(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c63(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c63(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c63(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c63(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c63(S(ok(0)))
PROPER(s(nil)) → c63(S(ok(nil)))
PROPER(s(rnil)) → c63(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c64(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c64(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c64(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c64(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(cons2(z0, z1))) → c64(POSRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c64(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c64(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c64(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c64(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c64(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c64(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c64(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c64(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c64(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c64(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c64(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c65(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c65(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c65(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c65(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(cons2(z0, z1))) → c65(NEGRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c65(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c65(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c65(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c65(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c65(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c65(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c65(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c65(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c65(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c65(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c65(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c67(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c67(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c67(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c67(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, cons2(z0, z1))) → c67(CONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c67(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c67(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c67(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c67(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c67(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c67(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c67(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c67(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c67(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c67(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c67(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c67(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(cons2(z0, z1), x1)) → c67(CONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c67(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c67(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c67(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c67(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c67(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c67(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c67(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c67(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c67(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c67(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c67(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c67(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c67(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c67(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(cons2(x0, s(z0))) → c68(CONS2(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons2(x0, posrecip(z0))) → c68(CONS2(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons2(x0, negrecip(z0))) → c68(CONS2(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons2(x0, cons(z0, z1))) → c68(CONS2(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons2(x0, cons2(z0, z1))) → c68(CONS2(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons2(x0, rcons(z0, z1))) → c68(CONS2(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons2(x0, from(z0))) → c68(CONS2(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons2(x0, 2ndspos(z0, z1))) → c68(CONS2(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons2(x0, 2ndsneg(z0, z1))) → c68(CONS2(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons2(x0, pi(z0))) → c68(CONS2(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons2(x0, plus(z0, z1))) → c68(CONS2(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons2(x0, times(z0, z1))) → c68(CONS2(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons2(x0, square(z0))) → c68(CONS2(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons2(s(z0), x1)) → c68(CONS2(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons2(posrecip(z0), x1)) → c68(CONS2(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons2(negrecip(z0), x1)) → c68(CONS2(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons2(cons(z0, z1), x1)) → c68(CONS2(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons2(cons2(z0, z1), x1)) → c68(CONS2(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons2(rcons(z0, z1), x1)) → c68(CONS2(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons2(from(z0), x1)) → c68(CONS2(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons2(2ndspos(z0, z1), x1)) → c68(CONS2(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons2(2ndsneg(z0, z1), x1)) → c68(CONS2(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons2(pi(z0), x1)) → c68(CONS2(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons2(plus(z0, z1), x1)) → c68(CONS2(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons2(times(z0, z1), x1)) → c68(CONS2(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons2(square(z0), x1)) → c68(CONS2(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons2(x0, 0)) → c68(CONS2(proper(x0), ok(0)), PROPER(x0))
PROPER(cons2(x0, nil)) → c68(CONS2(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons2(x0, rnil)) → c68(CONS2(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons2(0, x1)) → c68(CONS2(ok(0), proper(x1)), PROPER(x1))
PROPER(cons2(nil, x1)) → c68(CONS2(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons2(rnil, x1)) → c68(CONS2(ok(rnil), proper(x1)), PROPER(x1))
PROPER(rcons(x0, s(z0))) → c70(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c70(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c70(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, cons(z0, z1))) → c70(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, cons2(z0, z1))) → c70(RCONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(rcons(x0, rcons(z0, z1))) → c70(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c70(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c70(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c70(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c70(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c70(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c70(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c70(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(s(z0), x1)) → c70(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c70(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c70(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c70(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(cons2(z0, z1), x1)) → c70(RCONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c70(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c70(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c70(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c70(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c70(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c70(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c70(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c70(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(rcons(x0, 0)) → c70(RCONS(proper(x0), ok(0)), PROPER(x0))
PROPER(rcons(x0, nil)) → c70(RCONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(rcons(x0, rnil)) → c70(RCONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(rcons(0, x1)) → c70(RCONS(ok(0), proper(x1)), PROPER(x1))
PROPER(rcons(nil, x1)) → c70(RCONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c70(RCONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(from(s(z0))) → c71(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(posrecip(z0))) → c71(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(from(negrecip(z0))) → c71(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(from(cons(z0, z1))) → c71(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(cons2(z0, z1))) → c71(FROM(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(from(rcons(z0, z1))) → c71(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(from(from(z0))) → c71(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(2ndspos(z0, z1))) → c71(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(from(2ndsneg(z0, z1))) → c71(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(from(pi(z0))) → c71(FROM(pi(proper(z0))), PROPER(pi(z0)))
PROPER(from(plus(z0, z1))) → c71(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(from(times(z0, z1))) → c71(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(from(square(z0))) → c71(FROM(square(proper(z0))), PROPER(square(z0)))
PROPER(from(0)) → c71(FROM(ok(0)))
PROPER(from(nil)) → c71(FROM(ok(nil)))
PROPER(from(rnil)) → c71(FROM(ok(rnil)))
PROPER(2ndspos(x0, s(z0))) → c72(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndspos(x0, posrecip(z0))) → c72(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndspos(x0, negrecip(z0))) → c72(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndspos(x0, cons(z0, z1))) → c72(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndspos(x0, cons2(z0, z1))) → c72(2NDSPOS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(2ndspos(x0, rcons(z0, z1))) → c72(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndspos(x0, from(z0))) → c72(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c72(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c72(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndspos(x0, pi(z0))) → c72(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndspos(x0, plus(z0, z1))) → c72(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndspos(x0, times(z0, z1))) → c72(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndspos(x0, square(z0))) → c72(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndspos(s(z0), x1)) → c72(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndspos(posrecip(z0), x1)) → c72(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndspos(negrecip(z0), x1)) → c72(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndspos(cons(z0, z1), x1)) → c72(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndspos(cons2(z0, z1), x1)) → c72(2NDSPOS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(2ndspos(rcons(z0, z1), x1)) → c72(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndspos(from(z0), x1)) → c72(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c72(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c72(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndspos(pi(z0), x1)) → c72(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndspos(plus(z0, z1), x1)) → c72(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndspos(times(z0, z1), x1)) → c72(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndspos(square(z0), x1)) → c72(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndspos(x0, 0)) → c72(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndspos(x0, nil)) → c72(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndspos(x0, rnil)) → c72(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndspos(0, x1)) → c72(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndspos(nil, x1)) → c72(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndspos(rnil, x1)) → c72(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(x0, s(z0))) → c73(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndsneg(x0, posrecip(z0))) → c73(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndsneg(x0, negrecip(z0))) → c73(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndsneg(x0, cons(z0, z1))) → c73(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndsneg(x0, cons2(z0, z1))) → c73(2NDSNEG(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(2ndsneg(x0, rcons(z0, z1))) → c73(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndsneg(x0, from(z0))) → c73(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c73(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c73(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndsneg(x0, pi(z0))) → c73(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndsneg(x0, plus(z0, z1))) → c73(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndsneg(x0, times(z0, z1))) → c73(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndsneg(x0, square(z0))) → c73(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndsneg(s(z0), x1)) → c73(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndsneg(posrecip(z0), x1)) → c73(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndsneg(negrecip(z0), x1)) → c73(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndsneg(cons(z0, z1), x1)) → c73(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(cons2(z0, z1), x1)) → c73(2NDSNEG(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(2ndsneg(rcons(z0, z1), x1)) → c73(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(from(z0), x1)) → c73(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c73(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c73(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndsneg(pi(z0), x1)) → c73(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndsneg(plus(z0, z1), x1)) → c73(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndsneg(times(z0, z1), x1)) → c73(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndsneg(square(z0), x1)) → c73(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndsneg(x0, 0)) → c73(2NDSNEG(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndsneg(x0, nil)) → c73(2NDSNEG(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndsneg(x0, rnil)) → c73(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndsneg(0, x1)) → c73(2NDSNEG(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndsneg(nil, x1)) → c73(2NDSNEG(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(rnil, x1)) → c73(2NDSNEG(ok(rnil), proper(x1)), PROPER(x1))
PROPER(pi(s(z0))) → c74(PI(s(proper(z0))), PROPER(s(z0)))
PROPER(pi(posrecip(z0))) → c74(PI(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(pi(negrecip(z0))) → c74(PI(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(pi(cons(z0, z1))) → c74(PI(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(pi(cons2(z0, z1))) → c74(PI(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(pi(rcons(z0, z1))) → c74(PI(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(pi(from(z0))) → c74(PI(from(proper(z0))), PROPER(from(z0)))
PROPER(pi(2ndspos(z0, z1))) → c74(PI(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(pi(2ndsneg(z0, z1))) → c74(PI(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(pi(pi(z0))) → c74(PI(pi(proper(z0))), PROPER(pi(z0)))
PROPER(pi(plus(z0, z1))) → c74(PI(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(pi(times(z0, z1))) → c74(PI(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(pi(square(z0))) → c74(PI(square(proper(z0))), PROPER(square(z0)))
PROPER(pi(0)) → c74(PI(ok(0)))
PROPER(pi(nil)) → c74(PI(ok(nil)))
PROPER(pi(rnil)) → c74(PI(ok(rnil)))
PROPER(plus(x0, 0)) → c75(PLUS(proper(x0), ok(0)), PROPER(x0), PROPER(0))
PROPER(plus(x0, s(z0))) → c75(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(plus(x0, posrecip(z0))) → c75(PLUS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(plus(x0, negrecip(z0))) → c75(PLUS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(plus(x0, nil)) → c75(PLUS(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
PROPER(plus(x0, cons(z0, z1))) → c75(PLUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(plus(x0, cons2(z0, z1))) → c75(PLUS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(plus(x0, rnil)) → c75(PLUS(proper(x0), ok(rnil)), PROPER(x0), PROPER(rnil))
PROPER(plus(x0, rcons(z0, z1))) → c75(PLUS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(plus(x0, from(z0))) → c75(PLUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(plus(x0, 2ndspos(z0, z1))) → c75(PLUS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(plus(x0, 2ndsneg(z0, z1))) → c75(PLUS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(plus(x0, pi(z0))) → c75(PLUS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(plus(x0, plus(z0, z1))) → c75(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(plus(x0, times(z0, z1))) → c75(PLUS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(plus(x0, square(z0))) → c75(PLUS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(plus(0, x1)) → c75(PLUS(ok(0), proper(x1)), PROPER(0), PROPER(x1))
PROPER(plus(s(z0), x1)) → c75(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(plus(posrecip(z0), x1)) → c75(PLUS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(plus(negrecip(z0), x1)) → c75(PLUS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(plus(nil, x1)) → c75(PLUS(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
PROPER(plus(cons(z0, z1), x1)) → c75(PLUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(plus(cons2(z0, z1), x1)) → c75(PLUS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(plus(rnil, x1)) → c75(PLUS(ok(rnil), proper(x1)), PROPER(rnil), PROPER(x1))
PROPER(plus(rcons(z0, z1), x1)) → c75(PLUS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(plus(from(z0), x1)) → c75(PLUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(plus(2ndspos(z0, z1), x1)) → c75(PLUS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(plus(2ndsneg(z0, z1), x1)) → c75(PLUS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(plus(pi(z0), x1)) → c75(PLUS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(plus(plus(z0, z1), x1)) → c75(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(plus(times(z0, z1), x1)) → c75(PLUS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(plus(square(z0), x1)) → c75(PLUS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
S tuples:
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
PROPER(times(z0, z1)) → c76(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c77(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c78(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c79(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c9(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(2NDSPOS(s(z0), cons2(z1, z2)))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(2NDSNEG(s(z0), cons2(z1, z2)))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c13(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, z2)))) → c13(S(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(s(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, z2)))) → c13(S(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(s(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c13(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c13(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c13(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c13(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c13(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c13(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c13(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c13(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(cons2(z0, z1))) → c13(S(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c13(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c13(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c13(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c14(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c14(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c14(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c14(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c14(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c14(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c14(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c14(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(cons2(z0, z1))) → c14(POSRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c15(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c15(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c15(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c15(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c15(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c15(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c15(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c15(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(cons2(z0, z1))) → c15(NEGRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndspos(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndspos(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndsneg(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndsneg(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c16(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c16(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c16(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c16(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c16(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c16(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c16(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c16(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(cons2(z0, z1), x1)) → c16(CONS(cons2(z0, active(z1)), x1), ACTIVE(cons2(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, 2ndsneg(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(0, z0))) → c17(CONS2(x0, mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(cons2(x0, plus(s(z0), z1))) → c17(CONS2(x0, mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons2(x0, times(0, z0))) → c17(CONS2(x0, mark(0)), ACTIVE(times(0, z0)))
ACTIVE(cons2(x0, times(s(z0), z1))) → c17(CONS2(x0, mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(cons2(x0, s(z0))) → c17(CONS2(x0, s(active(z0))), ACTIVE(s(z0)))
ACTIVE(cons2(x0, posrecip(z0))) → c17(CONS2(x0, posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(cons2(x0, negrecip(z0))) → c17(CONS2(x0, negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(cons2(x0, cons(z0, z1))) → c17(CONS2(x0, cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(cons2(x0, cons2(z0, z1))) → c17(CONS2(x0, cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, from(active(z0))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, square(active(z0))), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c20(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(from(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(from(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c20(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c20(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c20(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c20(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c20(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c20(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c20(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c20(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c20(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c20(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(cons2(z0, z1))) → c20(FROM(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c20(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c20(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c20(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c25(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c25(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c25(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c25(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c25(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c25(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c25(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c25(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c25(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c25(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c25(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(cons2(z0, z1))) → c25(PI(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c25(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c25(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c25(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c30(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(square(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(square(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c30(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c30(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c30(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c30(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c30(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c30(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c30(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c30(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c30(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(cons2(z0, z1))) → c30(SQUARE(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c30(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c30(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c63(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c63(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c63(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c63(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(cons2(z0, z1))) → c63(S(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(s(rcons(z0, z1))) → c63(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c63(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c63(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c63(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c63(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c63(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c63(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c63(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c63(S(ok(0)))
PROPER(s(nil)) → c63(S(ok(nil)))
PROPER(s(rnil)) → c63(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c64(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c64(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c64(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c64(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(cons2(z0, z1))) → c64(POSRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c64(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c64(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c64(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c64(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c64(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c64(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c64(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c64(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c64(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c64(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c64(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c65(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c65(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c65(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c65(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(cons2(z0, z1))) → c65(NEGRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c65(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c65(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c65(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c65(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c65(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c65(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c65(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c65(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c65(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c65(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c65(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c67(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c67(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c67(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c67(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, cons2(z0, z1))) → c67(CONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c67(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c67(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c67(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c67(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c67(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c67(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c67(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c67(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c67(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c67(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c67(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c67(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(cons2(z0, z1), x1)) → c67(CONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c67(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c67(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c67(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c67(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c67(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c67(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c67(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c67(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c67(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c67(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c67(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c67(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c67(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c67(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(cons2(x0, s(z0))) → c68(CONS2(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons2(x0, posrecip(z0))) → c68(CONS2(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons2(x0, negrecip(z0))) → c68(CONS2(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons2(x0, cons(z0, z1))) → c68(CONS2(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons2(x0, cons2(z0, z1))) → c68(CONS2(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons2(x0, rcons(z0, z1))) → c68(CONS2(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons2(x0, from(z0))) → c68(CONS2(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons2(x0, 2ndspos(z0, z1))) → c68(CONS2(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons2(x0, 2ndsneg(z0, z1))) → c68(CONS2(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons2(x0, pi(z0))) → c68(CONS2(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons2(x0, plus(z0, z1))) → c68(CONS2(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons2(x0, times(z0, z1))) → c68(CONS2(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons2(x0, square(z0))) → c68(CONS2(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons2(s(z0), x1)) → c68(CONS2(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons2(posrecip(z0), x1)) → c68(CONS2(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons2(negrecip(z0), x1)) → c68(CONS2(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons2(cons(z0, z1), x1)) → c68(CONS2(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons2(cons2(z0, z1), x1)) → c68(CONS2(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons2(rcons(z0, z1), x1)) → c68(CONS2(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons2(from(z0), x1)) → c68(CONS2(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons2(2ndspos(z0, z1), x1)) → c68(CONS2(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons2(2ndsneg(z0, z1), x1)) → c68(CONS2(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons2(pi(z0), x1)) → c68(CONS2(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons2(plus(z0, z1), x1)) → c68(CONS2(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons2(times(z0, z1), x1)) → c68(CONS2(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons2(square(z0), x1)) → c68(CONS2(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons2(x0, 0)) → c68(CONS2(proper(x0), ok(0)), PROPER(x0))
PROPER(cons2(x0, nil)) → c68(CONS2(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons2(x0, rnil)) → c68(CONS2(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons2(0, x1)) → c68(CONS2(ok(0), proper(x1)), PROPER(x1))
PROPER(cons2(nil, x1)) → c68(CONS2(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons2(rnil, x1)) → c68(CONS2(ok(rnil), proper(x1)), PROPER(x1))
PROPER(rcons(x0, s(z0))) → c70(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c70(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c70(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, cons(z0, z1))) → c70(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, cons2(z0, z1))) → c70(RCONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(rcons(x0, rcons(z0, z1))) → c70(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c70(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c70(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c70(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c70(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c70(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c70(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c70(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(s(z0), x1)) → c70(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c70(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c70(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c70(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(cons2(z0, z1), x1)) → c70(RCONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c70(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c70(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c70(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c70(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c70(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c70(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c70(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c70(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(rcons(x0, 0)) → c70(RCONS(proper(x0), ok(0)), PROPER(x0))
PROPER(rcons(x0, nil)) → c70(RCONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(rcons(x0, rnil)) → c70(RCONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(rcons(0, x1)) → c70(RCONS(ok(0), proper(x1)), PROPER(x1))
PROPER(rcons(nil, x1)) → c70(RCONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c70(RCONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(from(s(z0))) → c71(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(posrecip(z0))) → c71(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(from(negrecip(z0))) → c71(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(from(cons(z0, z1))) → c71(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(cons2(z0, z1))) → c71(FROM(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(from(rcons(z0, z1))) → c71(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(from(from(z0))) → c71(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(2ndspos(z0, z1))) → c71(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(from(2ndsneg(z0, z1))) → c71(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(from(pi(z0))) → c71(FROM(pi(proper(z0))), PROPER(pi(z0)))
PROPER(from(plus(z0, z1))) → c71(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(from(times(z0, z1))) → c71(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(from(square(z0))) → c71(FROM(square(proper(z0))), PROPER(square(z0)))
PROPER(from(0)) → c71(FROM(ok(0)))
PROPER(from(nil)) → c71(FROM(ok(nil)))
PROPER(from(rnil)) → c71(FROM(ok(rnil)))
PROPER(2ndspos(x0, s(z0))) → c72(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndspos(x0, posrecip(z0))) → c72(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndspos(x0, negrecip(z0))) → c72(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndspos(x0, cons(z0, z1))) → c72(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndspos(x0, cons2(z0, z1))) → c72(2NDSPOS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(2ndspos(x0, rcons(z0, z1))) → c72(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndspos(x0, from(z0))) → c72(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c72(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c72(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndspos(x0, pi(z0))) → c72(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndspos(x0, plus(z0, z1))) → c72(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndspos(x0, times(z0, z1))) → c72(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndspos(x0, square(z0))) → c72(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndspos(s(z0), x1)) → c72(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndspos(posrecip(z0), x1)) → c72(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndspos(negrecip(z0), x1)) → c72(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndspos(cons(z0, z1), x1)) → c72(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndspos(cons2(z0, z1), x1)) → c72(2NDSPOS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(2ndspos(rcons(z0, z1), x1)) → c72(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndspos(from(z0), x1)) → c72(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c72(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c72(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndspos(pi(z0), x1)) → c72(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndspos(plus(z0, z1), x1)) → c72(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndspos(times(z0, z1), x1)) → c72(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndspos(square(z0), x1)) → c72(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndspos(x0, 0)) → c72(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndspos(x0, nil)) → c72(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndspos(x0, rnil)) → c72(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndspos(0, x1)) → c72(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndspos(nil, x1)) → c72(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndspos(rnil, x1)) → c72(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(x0, s(z0))) → c73(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndsneg(x0, posrecip(z0))) → c73(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndsneg(x0, negrecip(z0))) → c73(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndsneg(x0, cons(z0, z1))) → c73(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndsneg(x0, cons2(z0, z1))) → c73(2NDSNEG(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(2ndsneg(x0, rcons(z0, z1))) → c73(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndsneg(x0, from(z0))) → c73(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c73(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c73(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndsneg(x0, pi(z0))) → c73(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndsneg(x0, plus(z0, z1))) → c73(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndsneg(x0, times(z0, z1))) → c73(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndsneg(x0, square(z0))) → c73(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndsneg(s(z0), x1)) → c73(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndsneg(posrecip(z0), x1)) → c73(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndsneg(negrecip(z0), x1)) → c73(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndsneg(cons(z0, z1), x1)) → c73(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(cons2(z0, z1), x1)) → c73(2NDSNEG(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(2ndsneg(rcons(z0, z1), x1)) → c73(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(from(z0), x1)) → c73(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c73(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c73(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndsneg(pi(z0), x1)) → c73(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndsneg(plus(z0, z1), x1)) → c73(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndsneg(times(z0, z1), x1)) → c73(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndsneg(square(z0), x1)) → c73(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndsneg(x0, 0)) → c73(2NDSNEG(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndsneg(x0, nil)) → c73(2NDSNEG(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndsneg(x0, rnil)) → c73(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndsneg(0, x1)) → c73(2NDSNEG(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndsneg(nil, x1)) → c73(2NDSNEG(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(rnil, x1)) → c73(2NDSNEG(ok(rnil), proper(x1)), PROPER(x1))
PROPER(pi(s(z0))) → c74(PI(s(proper(z0))), PROPER(s(z0)))
PROPER(pi(posrecip(z0))) → c74(PI(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(pi(negrecip(z0))) → c74(PI(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(pi(cons(z0, z1))) → c74(PI(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(pi(cons2(z0, z1))) → c74(PI(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(pi(rcons(z0, z1))) → c74(PI(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(pi(from(z0))) → c74(PI(from(proper(z0))), PROPER(from(z0)))
PROPER(pi(2ndspos(z0, z1))) → c74(PI(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(pi(2ndsneg(z0, z1))) → c74(PI(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(pi(pi(z0))) → c74(PI(pi(proper(z0))), PROPER(pi(z0)))
PROPER(pi(plus(z0, z1))) → c74(PI(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(pi(times(z0, z1))) → c74(PI(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(pi(square(z0))) → c74(PI(square(proper(z0))), PROPER(square(z0)))
PROPER(pi(0)) → c74(PI(ok(0)))
PROPER(pi(nil)) → c74(PI(ok(nil)))
PROPER(pi(rnil)) → c74(PI(ok(rnil)))
PROPER(plus(x0, 0)) → c75(PLUS(proper(x0), ok(0)), PROPER(x0), PROPER(0))
PROPER(plus(x0, s(z0))) → c75(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(plus(x0, posrecip(z0))) → c75(PLUS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(plus(x0, negrecip(z0))) → c75(PLUS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(plus(x0, nil)) → c75(PLUS(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
PROPER(plus(x0, cons(z0, z1))) → c75(PLUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(plus(x0, cons2(z0, z1))) → c75(PLUS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(plus(x0, rnil)) → c75(PLUS(proper(x0), ok(rnil)), PROPER(x0), PROPER(rnil))
PROPER(plus(x0, rcons(z0, z1))) → c75(PLUS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(plus(x0, from(z0))) → c75(PLUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(plus(x0, 2ndspos(z0, z1))) → c75(PLUS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(plus(x0, 2ndsneg(z0, z1))) → c75(PLUS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(plus(x0, pi(z0))) → c75(PLUS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(plus(x0, plus(z0, z1))) → c75(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(plus(x0, times(z0, z1))) → c75(PLUS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(plus(x0, square(z0))) → c75(PLUS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(plus(0, x1)) → c75(PLUS(ok(0), proper(x1)), PROPER(0), PROPER(x1))
PROPER(plus(s(z0), x1)) → c75(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(plus(posrecip(z0), x1)) → c75(PLUS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(plus(negrecip(z0), x1)) → c75(PLUS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(plus(nil, x1)) → c75(PLUS(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
PROPER(plus(cons(z0, z1), x1)) → c75(PLUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(plus(cons2(z0, z1), x1)) → c75(PLUS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(plus(rnil, x1)) → c75(PLUS(ok(rnil), proper(x1)), PROPER(rnil), PROPER(x1))
PROPER(plus(rcons(z0, z1), x1)) → c75(PLUS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(plus(from(z0), x1)) → c75(PLUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(plus(2ndspos(z0, z1), x1)) → c75(PLUS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(plus(2ndsneg(z0, z1), x1)) → c75(PLUS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(plus(pi(z0), x1)) → c75(PLUS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(plus(plus(z0, z1), x1)) → c75(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(plus(times(z0, z1), x1)) → c75(PLUS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(plus(square(z0), x1)) → c75(PLUS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
K tuples:none
Defined Rule Symbols:
active, 2ndspos, cons2, rcons, posrecip, 2ndsneg, negrecip, s, cons, from, pi, plus, times, square, proper
Defined Pair Symbols:
ACTIVE, S, POSRECIP, NEGRECIP, CONS, CONS2, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP
Compound Symbols:
c12, c18, c19, c21, c22, c23, c24, c26, c27, c28, c29, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c76, c77, c78, c79, c, c7, c9, c11, c1, c13, c14, c15, c16, c17, c20, c25, c30, c63, c63, c64, c64, c65, c65, c67, c67, c68, c68, c70, c70, c71, c71, c72, c72, c73, c73, c74, c74, c75
(69) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 6 trailing tuple parts
(70) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(2ndspos(0, z0)) → mark(rnil)
active(2ndspos(s(z0), cons(z1, z2))) → mark(2ndspos(s(z0), cons2(z1, z2)))
active(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(z1, z2))) → mark(2ndsneg(s(z0), cons2(z1, z2)))
active(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
active(pi(z0)) → mark(2ndspos(z0, from(0)))
active(plus(0, z0)) → mark(z0)
active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
active(times(0, z0)) → mark(0)
active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
active(square(z0)) → mark(times(z0, z0))
active(s(z0)) → s(active(z0))
active(posrecip(z0)) → posrecip(active(z0))
active(negrecip(z0)) → negrecip(active(z0))
active(cons(z0, z1)) → cons(active(z0), z1)
active(cons2(z0, z1)) → cons2(z0, active(z1))
active(rcons(z0, z1)) → rcons(active(z0), z1)
active(rcons(z0, z1)) → rcons(z0, active(z1))
active(from(z0)) → from(active(z0))
active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
active(pi(z0)) → pi(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(times(z0, z1)) → times(active(z0), z1)
active(times(z0, z1)) → times(z0, active(z1))
active(square(z0)) → square(active(z0))
2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
cons2(z0, mark(z1)) → mark(cons2(z0, z1))
cons2(ok(z0), ok(z1)) → ok(cons2(z0, z1))
rcons(mark(z0), z1) → mark(rcons(z0, z1))
rcons(z0, mark(z1)) → mark(rcons(z0, z1))
rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
posrecip(ok(z0)) → ok(posrecip(z0))
posrecip(mark(z0)) → mark(posrecip(z0))
2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
negrecip(ok(z0)) → ok(negrecip(z0))
negrecip(mark(z0)) → mark(negrecip(z0))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
cons(mark(z0), z1) → mark(cons(z0, z1))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
from(mark(z0)) → mark(from(z0))
from(ok(z0)) → ok(from(z0))
pi(mark(z0)) → mark(pi(z0))
pi(ok(z0)) → ok(pi(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
times(mark(z0), z1) → mark(times(z0, z1))
times(ok(z0), ok(z1)) → ok(times(z0, z1))
times(z0, mark(z1)) → mark(times(z0, z1))
square(mark(z0)) → mark(square(z0))
square(ok(z0)) → ok(square(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(posrecip(z0)) → posrecip(proper(z0))
proper(negrecip(z0)) → negrecip(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(cons2(z0, z1)) → cons2(proper(z0), proper(z1))
proper(rnil) → ok(rnil)
proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
proper(pi(z0)) → pi(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(times(z0, z1)) → times(proper(z0), proper(z1))
proper(square(z0)) → square(proper(z0))
Tuples:
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
PROPER(times(z0, z1)) → c76(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c77(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c78(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c79(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c9(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(2NDSPOS(s(z0), cons2(z1, z2)))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(2NDSNEG(s(z0), cons2(z1, z2)))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c13(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, z2)))) → c13(S(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(s(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, z2)))) → c13(S(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(s(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c13(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c13(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c13(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c13(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c13(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c13(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c13(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c13(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(cons2(z0, z1))) → c13(S(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c13(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c13(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c13(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c14(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c14(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c14(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c14(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c14(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c14(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c14(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c14(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(cons2(z0, z1))) → c14(POSRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c15(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c15(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c15(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c15(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c15(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c15(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c15(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c15(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(cons2(z0, z1))) → c15(NEGRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndspos(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndspos(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndsneg(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndsneg(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c16(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c16(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c16(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c16(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c16(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c16(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c16(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c16(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(cons2(z0, z1), x1)) → c16(CONS(cons2(z0, active(z1)), x1), ACTIVE(cons2(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, 2ndsneg(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(0, z0))) → c17(CONS2(x0, mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(cons2(x0, plus(s(z0), z1))) → c17(CONS2(x0, mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons2(x0, times(0, z0))) → c17(CONS2(x0, mark(0)), ACTIVE(times(0, z0)))
ACTIVE(cons2(x0, times(s(z0), z1))) → c17(CONS2(x0, mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(cons2(x0, s(z0))) → c17(CONS2(x0, s(active(z0))), ACTIVE(s(z0)))
ACTIVE(cons2(x0, posrecip(z0))) → c17(CONS2(x0, posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(cons2(x0, negrecip(z0))) → c17(CONS2(x0, negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(cons2(x0, cons(z0, z1))) → c17(CONS2(x0, cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(cons2(x0, cons2(z0, z1))) → c17(CONS2(x0, cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, from(active(z0))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, square(active(z0))), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c20(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(from(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(from(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c20(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c20(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c20(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c20(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c20(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c20(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c20(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c20(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c20(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c20(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(cons2(z0, z1))) → c20(FROM(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c20(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c20(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c20(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c25(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c25(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c25(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c25(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c25(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c25(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c25(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c25(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c25(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c25(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c25(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(cons2(z0, z1))) → c25(PI(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c25(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c25(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c25(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c30(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(square(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(square(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c30(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c30(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c30(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c30(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c30(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c30(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c30(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c30(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c30(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(cons2(z0, z1))) → c30(SQUARE(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c30(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c30(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c63(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c63(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c63(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c63(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(cons2(z0, z1))) → c63(S(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(s(rcons(z0, z1))) → c63(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c63(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c63(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c63(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c63(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c63(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c63(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c63(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c63(S(ok(0)))
PROPER(s(nil)) → c63(S(ok(nil)))
PROPER(s(rnil)) → c63(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c64(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c64(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c64(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c64(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(cons2(z0, z1))) → c64(POSRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c64(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c64(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c64(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c64(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c64(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c64(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c64(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c64(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c64(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c64(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c64(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c65(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c65(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c65(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c65(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(cons2(z0, z1))) → c65(NEGRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c65(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c65(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c65(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c65(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c65(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c65(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c65(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c65(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c65(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c65(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c65(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c67(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c67(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c67(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c67(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, cons2(z0, z1))) → c67(CONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c67(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c67(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c67(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c67(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c67(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c67(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c67(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c67(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c67(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c67(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c67(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c67(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(cons2(z0, z1), x1)) → c67(CONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c67(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c67(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c67(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c67(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c67(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c67(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c67(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c67(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c67(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c67(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c67(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c67(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c67(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c67(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(cons2(x0, s(z0))) → c68(CONS2(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons2(x0, posrecip(z0))) → c68(CONS2(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons2(x0, negrecip(z0))) → c68(CONS2(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons2(x0, cons(z0, z1))) → c68(CONS2(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons2(x0, cons2(z0, z1))) → c68(CONS2(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons2(x0, rcons(z0, z1))) → c68(CONS2(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons2(x0, from(z0))) → c68(CONS2(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons2(x0, 2ndspos(z0, z1))) → c68(CONS2(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons2(x0, 2ndsneg(z0, z1))) → c68(CONS2(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons2(x0, pi(z0))) → c68(CONS2(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons2(x0, plus(z0, z1))) → c68(CONS2(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons2(x0, times(z0, z1))) → c68(CONS2(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons2(x0, square(z0))) → c68(CONS2(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons2(s(z0), x1)) → c68(CONS2(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons2(posrecip(z0), x1)) → c68(CONS2(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons2(negrecip(z0), x1)) → c68(CONS2(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons2(cons(z0, z1), x1)) → c68(CONS2(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons2(cons2(z0, z1), x1)) → c68(CONS2(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons2(rcons(z0, z1), x1)) → c68(CONS2(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons2(from(z0), x1)) → c68(CONS2(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons2(2ndspos(z0, z1), x1)) → c68(CONS2(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons2(2ndsneg(z0, z1), x1)) → c68(CONS2(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons2(pi(z0), x1)) → c68(CONS2(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons2(plus(z0, z1), x1)) → c68(CONS2(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons2(times(z0, z1), x1)) → c68(CONS2(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons2(square(z0), x1)) → c68(CONS2(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons2(x0, 0)) → c68(CONS2(proper(x0), ok(0)), PROPER(x0))
PROPER(cons2(x0, nil)) → c68(CONS2(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons2(x0, rnil)) → c68(CONS2(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons2(0, x1)) → c68(CONS2(ok(0), proper(x1)), PROPER(x1))
PROPER(cons2(nil, x1)) → c68(CONS2(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons2(rnil, x1)) → c68(CONS2(ok(rnil), proper(x1)), PROPER(x1))
PROPER(rcons(x0, s(z0))) → c70(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c70(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c70(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, cons(z0, z1))) → c70(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, cons2(z0, z1))) → c70(RCONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(rcons(x0, rcons(z0, z1))) → c70(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c70(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c70(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c70(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c70(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c70(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c70(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c70(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(s(z0), x1)) → c70(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c70(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c70(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c70(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(cons2(z0, z1), x1)) → c70(RCONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c70(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c70(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c70(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c70(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c70(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c70(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c70(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c70(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(rcons(x0, 0)) → c70(RCONS(proper(x0), ok(0)), PROPER(x0))
PROPER(rcons(x0, nil)) → c70(RCONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(rcons(x0, rnil)) → c70(RCONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(rcons(0, x1)) → c70(RCONS(ok(0), proper(x1)), PROPER(x1))
PROPER(rcons(nil, x1)) → c70(RCONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c70(RCONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(from(s(z0))) → c71(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(posrecip(z0))) → c71(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(from(negrecip(z0))) → c71(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(from(cons(z0, z1))) → c71(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(cons2(z0, z1))) → c71(FROM(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(from(rcons(z0, z1))) → c71(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(from(from(z0))) → c71(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(2ndspos(z0, z1))) → c71(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(from(2ndsneg(z0, z1))) → c71(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(from(pi(z0))) → c71(FROM(pi(proper(z0))), PROPER(pi(z0)))
PROPER(from(plus(z0, z1))) → c71(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(from(times(z0, z1))) → c71(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(from(square(z0))) → c71(FROM(square(proper(z0))), PROPER(square(z0)))
PROPER(from(0)) → c71(FROM(ok(0)))
PROPER(from(nil)) → c71(FROM(ok(nil)))
PROPER(from(rnil)) → c71(FROM(ok(rnil)))
PROPER(2ndspos(x0, s(z0))) → c72(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndspos(x0, posrecip(z0))) → c72(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndspos(x0, negrecip(z0))) → c72(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndspos(x0, cons(z0, z1))) → c72(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndspos(x0, cons2(z0, z1))) → c72(2NDSPOS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(2ndspos(x0, rcons(z0, z1))) → c72(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndspos(x0, from(z0))) → c72(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c72(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c72(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndspos(x0, pi(z0))) → c72(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndspos(x0, plus(z0, z1))) → c72(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndspos(x0, times(z0, z1))) → c72(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndspos(x0, square(z0))) → c72(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndspos(s(z0), x1)) → c72(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndspos(posrecip(z0), x1)) → c72(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndspos(negrecip(z0), x1)) → c72(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndspos(cons(z0, z1), x1)) → c72(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndspos(cons2(z0, z1), x1)) → c72(2NDSPOS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(2ndspos(rcons(z0, z1), x1)) → c72(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndspos(from(z0), x1)) → c72(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c72(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c72(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndspos(pi(z0), x1)) → c72(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndspos(plus(z0, z1), x1)) → c72(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndspos(times(z0, z1), x1)) → c72(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndspos(square(z0), x1)) → c72(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndspos(x0, 0)) → c72(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndspos(x0, nil)) → c72(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndspos(x0, rnil)) → c72(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndspos(0, x1)) → c72(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndspos(nil, x1)) → c72(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndspos(rnil, x1)) → c72(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(x0, s(z0))) → c73(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndsneg(x0, posrecip(z0))) → c73(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndsneg(x0, negrecip(z0))) → c73(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndsneg(x0, cons(z0, z1))) → c73(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndsneg(x0, cons2(z0, z1))) → c73(2NDSNEG(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(2ndsneg(x0, rcons(z0, z1))) → c73(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndsneg(x0, from(z0))) → c73(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c73(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c73(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndsneg(x0, pi(z0))) → c73(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndsneg(x0, plus(z0, z1))) → c73(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndsneg(x0, times(z0, z1))) → c73(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndsneg(x0, square(z0))) → c73(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndsneg(s(z0), x1)) → c73(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndsneg(posrecip(z0), x1)) → c73(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndsneg(negrecip(z0), x1)) → c73(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndsneg(cons(z0, z1), x1)) → c73(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(cons2(z0, z1), x1)) → c73(2NDSNEG(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(2ndsneg(rcons(z0, z1), x1)) → c73(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(from(z0), x1)) → c73(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c73(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c73(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndsneg(pi(z0), x1)) → c73(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndsneg(plus(z0, z1), x1)) → c73(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndsneg(times(z0, z1), x1)) → c73(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndsneg(square(z0), x1)) → c73(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndsneg(x0, 0)) → c73(2NDSNEG(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndsneg(x0, nil)) → c73(2NDSNEG(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndsneg(x0, rnil)) → c73(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndsneg(0, x1)) → c73(2NDSNEG(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndsneg(nil, x1)) → c73(2NDSNEG(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(rnil, x1)) → c73(2NDSNEG(ok(rnil), proper(x1)), PROPER(x1))
PROPER(pi(s(z0))) → c74(PI(s(proper(z0))), PROPER(s(z0)))
PROPER(pi(posrecip(z0))) → c74(PI(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(pi(negrecip(z0))) → c74(PI(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(pi(cons(z0, z1))) → c74(PI(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(pi(cons2(z0, z1))) → c74(PI(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(pi(rcons(z0, z1))) → c74(PI(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(pi(from(z0))) → c74(PI(from(proper(z0))), PROPER(from(z0)))
PROPER(pi(2ndspos(z0, z1))) → c74(PI(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(pi(2ndsneg(z0, z1))) → c74(PI(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(pi(pi(z0))) → c74(PI(pi(proper(z0))), PROPER(pi(z0)))
PROPER(pi(plus(z0, z1))) → c74(PI(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(pi(times(z0, z1))) → c74(PI(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(pi(square(z0))) → c74(PI(square(proper(z0))), PROPER(square(z0)))
PROPER(pi(0)) → c74(PI(ok(0)))
PROPER(pi(nil)) → c74(PI(ok(nil)))
PROPER(pi(rnil)) → c74(PI(ok(rnil)))
PROPER(plus(x0, s(z0))) → c75(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(plus(x0, posrecip(z0))) → c75(PLUS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(plus(x0, negrecip(z0))) → c75(PLUS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(plus(x0, cons(z0, z1))) → c75(PLUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(plus(x0, cons2(z0, z1))) → c75(PLUS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(plus(x0, rcons(z0, z1))) → c75(PLUS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(plus(x0, from(z0))) → c75(PLUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(plus(x0, 2ndspos(z0, z1))) → c75(PLUS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(plus(x0, 2ndsneg(z0, z1))) → c75(PLUS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(plus(x0, pi(z0))) → c75(PLUS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(plus(x0, plus(z0, z1))) → c75(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(plus(x0, times(z0, z1))) → c75(PLUS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(plus(x0, square(z0))) → c75(PLUS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(plus(s(z0), x1)) → c75(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(plus(posrecip(z0), x1)) → c75(PLUS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(plus(negrecip(z0), x1)) → c75(PLUS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(plus(cons(z0, z1), x1)) → c75(PLUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(plus(cons2(z0, z1), x1)) → c75(PLUS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(plus(rcons(z0, z1), x1)) → c75(PLUS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(plus(from(z0), x1)) → c75(PLUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(plus(2ndspos(z0, z1), x1)) → c75(PLUS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(plus(2ndsneg(z0, z1), x1)) → c75(PLUS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(plus(pi(z0), x1)) → c75(PLUS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(plus(plus(z0, z1), x1)) → c75(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(plus(times(z0, z1), x1)) → c75(PLUS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(plus(square(z0), x1)) → c75(PLUS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(plus(x0, 0)) → c75(PLUS(proper(x0), ok(0)), PROPER(x0))
PROPER(plus(x0, nil)) → c75(PLUS(proper(x0), ok(nil)), PROPER(x0))
PROPER(plus(x0, rnil)) → c75(PLUS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(plus(0, x1)) → c75(PLUS(ok(0), proper(x1)), PROPER(x1))
PROPER(plus(nil, x1)) → c75(PLUS(ok(nil), proper(x1)), PROPER(x1))
PROPER(plus(rnil, x1)) → c75(PLUS(ok(rnil), proper(x1)), PROPER(x1))
S tuples:
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
PROPER(times(z0, z1)) → c76(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c77(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c78(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c79(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c9(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(2NDSPOS(s(z0), cons2(z1, z2)))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(2NDSNEG(s(z0), cons2(z1, z2)))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c13(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, z2)))) → c13(S(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(s(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, z2)))) → c13(S(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(s(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c13(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c13(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c13(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c13(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c13(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c13(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c13(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c13(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(cons2(z0, z1))) → c13(S(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c13(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c13(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c13(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c14(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c14(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c14(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c14(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c14(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c14(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c14(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c14(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(cons2(z0, z1))) → c14(POSRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c15(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c15(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c15(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c15(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c15(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c15(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c15(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c15(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(cons2(z0, z1))) → c15(NEGRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndspos(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndspos(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndsneg(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndsneg(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c16(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c16(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c16(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c16(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c16(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c16(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c16(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c16(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(cons2(z0, z1), x1)) → c16(CONS(cons2(z0, active(z1)), x1), ACTIVE(cons2(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, 2ndsneg(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(0, z0))) → c17(CONS2(x0, mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(cons2(x0, plus(s(z0), z1))) → c17(CONS2(x0, mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons2(x0, times(0, z0))) → c17(CONS2(x0, mark(0)), ACTIVE(times(0, z0)))
ACTIVE(cons2(x0, times(s(z0), z1))) → c17(CONS2(x0, mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(cons2(x0, s(z0))) → c17(CONS2(x0, s(active(z0))), ACTIVE(s(z0)))
ACTIVE(cons2(x0, posrecip(z0))) → c17(CONS2(x0, posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(cons2(x0, negrecip(z0))) → c17(CONS2(x0, negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(cons2(x0, cons(z0, z1))) → c17(CONS2(x0, cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(cons2(x0, cons2(z0, z1))) → c17(CONS2(x0, cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, from(active(z0))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, square(active(z0))), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c20(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(from(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(from(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c20(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c20(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c20(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c20(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c20(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c20(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c20(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c20(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c20(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c20(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(cons2(z0, z1))) → c20(FROM(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c20(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c20(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c20(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c25(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c25(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c25(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c25(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c25(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c25(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c25(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c25(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c25(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c25(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c25(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(cons2(z0, z1))) → c25(PI(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c25(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c25(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c25(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c30(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(square(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(square(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c30(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c30(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c30(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c30(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c30(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c30(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c30(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c30(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c30(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(cons2(z0, z1))) → c30(SQUARE(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c30(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c30(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c63(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c63(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c63(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c63(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(cons2(z0, z1))) → c63(S(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(s(rcons(z0, z1))) → c63(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c63(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c63(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c63(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c63(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c63(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c63(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c63(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c63(S(ok(0)))
PROPER(s(nil)) → c63(S(ok(nil)))
PROPER(s(rnil)) → c63(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c64(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c64(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c64(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c64(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(cons2(z0, z1))) → c64(POSRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c64(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c64(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c64(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c64(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c64(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c64(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c64(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c64(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c64(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c64(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c64(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c65(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c65(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c65(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c65(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(cons2(z0, z1))) → c65(NEGRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c65(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c65(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c65(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c65(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c65(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c65(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c65(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c65(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c65(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c65(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c65(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c67(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c67(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c67(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c67(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, cons2(z0, z1))) → c67(CONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c67(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c67(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c67(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c67(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c67(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c67(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c67(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c67(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c67(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c67(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c67(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c67(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(cons2(z0, z1), x1)) → c67(CONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c67(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c67(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c67(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c67(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c67(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c67(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c67(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c67(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c67(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c67(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c67(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c67(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c67(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c67(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(cons2(x0, s(z0))) → c68(CONS2(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons2(x0, posrecip(z0))) → c68(CONS2(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons2(x0, negrecip(z0))) → c68(CONS2(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons2(x0, cons(z0, z1))) → c68(CONS2(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons2(x0, cons2(z0, z1))) → c68(CONS2(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons2(x0, rcons(z0, z1))) → c68(CONS2(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons2(x0, from(z0))) → c68(CONS2(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons2(x0, 2ndspos(z0, z1))) → c68(CONS2(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons2(x0, 2ndsneg(z0, z1))) → c68(CONS2(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons2(x0, pi(z0))) → c68(CONS2(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons2(x0, plus(z0, z1))) → c68(CONS2(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons2(x0, times(z0, z1))) → c68(CONS2(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons2(x0, square(z0))) → c68(CONS2(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons2(s(z0), x1)) → c68(CONS2(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons2(posrecip(z0), x1)) → c68(CONS2(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons2(negrecip(z0), x1)) → c68(CONS2(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons2(cons(z0, z1), x1)) → c68(CONS2(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons2(cons2(z0, z1), x1)) → c68(CONS2(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons2(rcons(z0, z1), x1)) → c68(CONS2(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons2(from(z0), x1)) → c68(CONS2(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons2(2ndspos(z0, z1), x1)) → c68(CONS2(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons2(2ndsneg(z0, z1), x1)) → c68(CONS2(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons2(pi(z0), x1)) → c68(CONS2(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons2(plus(z0, z1), x1)) → c68(CONS2(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons2(times(z0, z1), x1)) → c68(CONS2(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons2(square(z0), x1)) → c68(CONS2(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons2(x0, 0)) → c68(CONS2(proper(x0), ok(0)), PROPER(x0))
PROPER(cons2(x0, nil)) → c68(CONS2(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons2(x0, rnil)) → c68(CONS2(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons2(0, x1)) → c68(CONS2(ok(0), proper(x1)), PROPER(x1))
PROPER(cons2(nil, x1)) → c68(CONS2(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons2(rnil, x1)) → c68(CONS2(ok(rnil), proper(x1)), PROPER(x1))
PROPER(rcons(x0, s(z0))) → c70(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c70(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c70(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, cons(z0, z1))) → c70(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, cons2(z0, z1))) → c70(RCONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(rcons(x0, rcons(z0, z1))) → c70(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c70(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c70(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c70(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c70(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c70(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c70(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c70(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(s(z0), x1)) → c70(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c70(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c70(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c70(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(cons2(z0, z1), x1)) → c70(RCONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c70(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c70(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c70(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c70(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c70(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c70(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c70(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c70(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(rcons(x0, 0)) → c70(RCONS(proper(x0), ok(0)), PROPER(x0))
PROPER(rcons(x0, nil)) → c70(RCONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(rcons(x0, rnil)) → c70(RCONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(rcons(0, x1)) → c70(RCONS(ok(0), proper(x1)), PROPER(x1))
PROPER(rcons(nil, x1)) → c70(RCONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c70(RCONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(from(s(z0))) → c71(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(posrecip(z0))) → c71(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(from(negrecip(z0))) → c71(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(from(cons(z0, z1))) → c71(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(cons2(z0, z1))) → c71(FROM(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(from(rcons(z0, z1))) → c71(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(from(from(z0))) → c71(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(2ndspos(z0, z1))) → c71(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(from(2ndsneg(z0, z1))) → c71(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(from(pi(z0))) → c71(FROM(pi(proper(z0))), PROPER(pi(z0)))
PROPER(from(plus(z0, z1))) → c71(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(from(times(z0, z1))) → c71(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(from(square(z0))) → c71(FROM(square(proper(z0))), PROPER(square(z0)))
PROPER(from(0)) → c71(FROM(ok(0)))
PROPER(from(nil)) → c71(FROM(ok(nil)))
PROPER(from(rnil)) → c71(FROM(ok(rnil)))
PROPER(2ndspos(x0, s(z0))) → c72(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndspos(x0, posrecip(z0))) → c72(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndspos(x0, negrecip(z0))) → c72(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndspos(x0, cons(z0, z1))) → c72(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndspos(x0, cons2(z0, z1))) → c72(2NDSPOS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(2ndspos(x0, rcons(z0, z1))) → c72(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndspos(x0, from(z0))) → c72(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c72(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c72(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndspos(x0, pi(z0))) → c72(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndspos(x0, plus(z0, z1))) → c72(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndspos(x0, times(z0, z1))) → c72(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndspos(x0, square(z0))) → c72(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndspos(s(z0), x1)) → c72(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndspos(posrecip(z0), x1)) → c72(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndspos(negrecip(z0), x1)) → c72(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndspos(cons(z0, z1), x1)) → c72(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndspos(cons2(z0, z1), x1)) → c72(2NDSPOS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(2ndspos(rcons(z0, z1), x1)) → c72(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndspos(from(z0), x1)) → c72(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c72(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c72(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndspos(pi(z0), x1)) → c72(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndspos(plus(z0, z1), x1)) → c72(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndspos(times(z0, z1), x1)) → c72(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndspos(square(z0), x1)) → c72(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndspos(x0, 0)) → c72(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndspos(x0, nil)) → c72(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndspos(x0, rnil)) → c72(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndspos(0, x1)) → c72(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndspos(nil, x1)) → c72(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndspos(rnil, x1)) → c72(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(x0, s(z0))) → c73(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndsneg(x0, posrecip(z0))) → c73(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndsneg(x0, negrecip(z0))) → c73(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndsneg(x0, cons(z0, z1))) → c73(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndsneg(x0, cons2(z0, z1))) → c73(2NDSNEG(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(2ndsneg(x0, rcons(z0, z1))) → c73(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndsneg(x0, from(z0))) → c73(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c73(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c73(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndsneg(x0, pi(z0))) → c73(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndsneg(x0, plus(z0, z1))) → c73(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndsneg(x0, times(z0, z1))) → c73(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndsneg(x0, square(z0))) → c73(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndsneg(s(z0), x1)) → c73(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndsneg(posrecip(z0), x1)) → c73(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndsneg(negrecip(z0), x1)) → c73(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndsneg(cons(z0, z1), x1)) → c73(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(cons2(z0, z1), x1)) → c73(2NDSNEG(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(2ndsneg(rcons(z0, z1), x1)) → c73(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(from(z0), x1)) → c73(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c73(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c73(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndsneg(pi(z0), x1)) → c73(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndsneg(plus(z0, z1), x1)) → c73(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndsneg(times(z0, z1), x1)) → c73(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndsneg(square(z0), x1)) → c73(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndsneg(x0, 0)) → c73(2NDSNEG(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndsneg(x0, nil)) → c73(2NDSNEG(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndsneg(x0, rnil)) → c73(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndsneg(0, x1)) → c73(2NDSNEG(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndsneg(nil, x1)) → c73(2NDSNEG(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(rnil, x1)) → c73(2NDSNEG(ok(rnil), proper(x1)), PROPER(x1))
PROPER(pi(s(z0))) → c74(PI(s(proper(z0))), PROPER(s(z0)))
PROPER(pi(posrecip(z0))) → c74(PI(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(pi(negrecip(z0))) → c74(PI(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(pi(cons(z0, z1))) → c74(PI(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(pi(cons2(z0, z1))) → c74(PI(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(pi(rcons(z0, z1))) → c74(PI(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(pi(from(z0))) → c74(PI(from(proper(z0))), PROPER(from(z0)))
PROPER(pi(2ndspos(z0, z1))) → c74(PI(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(pi(2ndsneg(z0, z1))) → c74(PI(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(pi(pi(z0))) → c74(PI(pi(proper(z0))), PROPER(pi(z0)))
PROPER(pi(plus(z0, z1))) → c74(PI(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(pi(times(z0, z1))) → c74(PI(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(pi(square(z0))) → c74(PI(square(proper(z0))), PROPER(square(z0)))
PROPER(pi(0)) → c74(PI(ok(0)))
PROPER(pi(nil)) → c74(PI(ok(nil)))
PROPER(pi(rnil)) → c74(PI(ok(rnil)))
PROPER(plus(x0, s(z0))) → c75(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(plus(x0, posrecip(z0))) → c75(PLUS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(plus(x0, negrecip(z0))) → c75(PLUS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(plus(x0, cons(z0, z1))) → c75(PLUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(plus(x0, cons2(z0, z1))) → c75(PLUS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(plus(x0, rcons(z0, z1))) → c75(PLUS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(plus(x0, from(z0))) → c75(PLUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(plus(x0, 2ndspos(z0, z1))) → c75(PLUS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(plus(x0, 2ndsneg(z0, z1))) → c75(PLUS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(plus(x0, pi(z0))) → c75(PLUS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(plus(x0, plus(z0, z1))) → c75(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(plus(x0, times(z0, z1))) → c75(PLUS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(plus(x0, square(z0))) → c75(PLUS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(plus(s(z0), x1)) → c75(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(plus(posrecip(z0), x1)) → c75(PLUS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(plus(negrecip(z0), x1)) → c75(PLUS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(plus(cons(z0, z1), x1)) → c75(PLUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(plus(cons2(z0, z1), x1)) → c75(PLUS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(plus(rcons(z0, z1), x1)) → c75(PLUS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(plus(from(z0), x1)) → c75(PLUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(plus(2ndspos(z0, z1), x1)) → c75(PLUS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(plus(2ndsneg(z0, z1), x1)) → c75(PLUS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(plus(pi(z0), x1)) → c75(PLUS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(plus(plus(z0, z1), x1)) → c75(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(plus(times(z0, z1), x1)) → c75(PLUS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(plus(square(z0), x1)) → c75(PLUS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(plus(x0, 0)) → c75(PLUS(proper(x0), ok(0)), PROPER(x0))
PROPER(plus(x0, nil)) → c75(PLUS(proper(x0), ok(nil)), PROPER(x0))
PROPER(plus(x0, rnil)) → c75(PLUS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(plus(0, x1)) → c75(PLUS(ok(0), proper(x1)), PROPER(x1))
PROPER(plus(nil, x1)) → c75(PLUS(ok(nil), proper(x1)), PROPER(x1))
PROPER(plus(rnil, x1)) → c75(PLUS(ok(rnil), proper(x1)), PROPER(x1))
K tuples:none
Defined Rule Symbols:
active, 2ndspos, cons2, rcons, posrecip, 2ndsneg, negrecip, s, cons, from, pi, plus, times, square, proper
Defined Pair Symbols:
ACTIVE, S, POSRECIP, NEGRECIP, CONS, CONS2, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP
Compound Symbols:
c12, c18, c19, c21, c22, c23, c24, c26, c27, c28, c29, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c76, c77, c78, c79, c, c7, c9, c11, c1, c13, c14, c15, c16, c17, c20, c25, c30, c63, c63, c64, c64, c65, c65, c67, c67, c68, c68, c70, c70, c71, c71, c72, c72, c73, c73, c74, c74, c75, c75
(71) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
PROPER(
times(
z0,
z1)) →
c76(
TIMES(
proper(
z0),
proper(
z1)),
PROPER(
z0),
PROPER(
z1)) by
PROPER(times(x0, 0)) → c76(TIMES(proper(x0), ok(0)), PROPER(x0), PROPER(0))
PROPER(times(x0, s(z0))) → c76(TIMES(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(times(x0, posrecip(z0))) → c76(TIMES(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(times(x0, negrecip(z0))) → c76(TIMES(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(times(x0, nil)) → c76(TIMES(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
PROPER(times(x0, cons(z0, z1))) → c76(TIMES(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(times(x0, cons2(z0, z1))) → c76(TIMES(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(times(x0, rnil)) → c76(TIMES(proper(x0), ok(rnil)), PROPER(x0), PROPER(rnil))
PROPER(times(x0, rcons(z0, z1))) → c76(TIMES(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(times(x0, from(z0))) → c76(TIMES(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(times(x0, 2ndspos(z0, z1))) → c76(TIMES(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(times(x0, 2ndsneg(z0, z1))) → c76(TIMES(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(times(x0, pi(z0))) → c76(TIMES(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(times(x0, plus(z0, z1))) → c76(TIMES(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(times(x0, times(z0, z1))) → c76(TIMES(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(times(x0, square(z0))) → c76(TIMES(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(times(0, x1)) → c76(TIMES(ok(0), proper(x1)), PROPER(0), PROPER(x1))
PROPER(times(s(z0), x1)) → c76(TIMES(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(times(posrecip(z0), x1)) → c76(TIMES(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(times(negrecip(z0), x1)) → c76(TIMES(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(times(nil, x1)) → c76(TIMES(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
PROPER(times(cons(z0, z1), x1)) → c76(TIMES(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(times(cons2(z0, z1), x1)) → c76(TIMES(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(times(rnil, x1)) → c76(TIMES(ok(rnil), proper(x1)), PROPER(rnil), PROPER(x1))
PROPER(times(rcons(z0, z1), x1)) → c76(TIMES(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(times(from(z0), x1)) → c76(TIMES(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(times(2ndspos(z0, z1), x1)) → c76(TIMES(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(times(2ndsneg(z0, z1), x1)) → c76(TIMES(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(times(pi(z0), x1)) → c76(TIMES(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(times(plus(z0, z1), x1)) → c76(TIMES(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(times(times(z0, z1), x1)) → c76(TIMES(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(times(square(z0), x1)) → c76(TIMES(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
(72) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(2ndspos(0, z0)) → mark(rnil)
active(2ndspos(s(z0), cons(z1, z2))) → mark(2ndspos(s(z0), cons2(z1, z2)))
active(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(z1, z2))) → mark(2ndsneg(s(z0), cons2(z1, z2)))
active(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
active(pi(z0)) → mark(2ndspos(z0, from(0)))
active(plus(0, z0)) → mark(z0)
active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
active(times(0, z0)) → mark(0)
active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
active(square(z0)) → mark(times(z0, z0))
active(s(z0)) → s(active(z0))
active(posrecip(z0)) → posrecip(active(z0))
active(negrecip(z0)) → negrecip(active(z0))
active(cons(z0, z1)) → cons(active(z0), z1)
active(cons2(z0, z1)) → cons2(z0, active(z1))
active(rcons(z0, z1)) → rcons(active(z0), z1)
active(rcons(z0, z1)) → rcons(z0, active(z1))
active(from(z0)) → from(active(z0))
active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
active(pi(z0)) → pi(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(times(z0, z1)) → times(active(z0), z1)
active(times(z0, z1)) → times(z0, active(z1))
active(square(z0)) → square(active(z0))
2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
cons2(z0, mark(z1)) → mark(cons2(z0, z1))
cons2(ok(z0), ok(z1)) → ok(cons2(z0, z1))
rcons(mark(z0), z1) → mark(rcons(z0, z1))
rcons(z0, mark(z1)) → mark(rcons(z0, z1))
rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
posrecip(ok(z0)) → ok(posrecip(z0))
posrecip(mark(z0)) → mark(posrecip(z0))
2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
negrecip(ok(z0)) → ok(negrecip(z0))
negrecip(mark(z0)) → mark(negrecip(z0))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
cons(mark(z0), z1) → mark(cons(z0, z1))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
from(mark(z0)) → mark(from(z0))
from(ok(z0)) → ok(from(z0))
pi(mark(z0)) → mark(pi(z0))
pi(ok(z0)) → ok(pi(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
times(mark(z0), z1) → mark(times(z0, z1))
times(ok(z0), ok(z1)) → ok(times(z0, z1))
times(z0, mark(z1)) → mark(times(z0, z1))
square(mark(z0)) → mark(square(z0))
square(ok(z0)) → ok(square(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(posrecip(z0)) → posrecip(proper(z0))
proper(negrecip(z0)) → negrecip(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(cons2(z0, z1)) → cons2(proper(z0), proper(z1))
proper(rnil) → ok(rnil)
proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
proper(pi(z0)) → pi(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(times(z0, z1)) → times(proper(z0), proper(z1))
proper(square(z0)) → square(proper(z0))
Tuples:
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
PROPER(square(z0)) → c77(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c78(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c79(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c9(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(2NDSPOS(s(z0), cons2(z1, z2)))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(2NDSNEG(s(z0), cons2(z1, z2)))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c13(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, z2)))) → c13(S(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(s(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, z2)))) → c13(S(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(s(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c13(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c13(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c13(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c13(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c13(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c13(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c13(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c13(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(cons2(z0, z1))) → c13(S(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c13(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c13(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c13(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c14(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c14(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c14(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c14(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c14(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c14(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c14(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c14(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(cons2(z0, z1))) → c14(POSRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c15(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c15(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c15(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c15(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c15(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c15(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c15(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c15(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(cons2(z0, z1))) → c15(NEGRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndspos(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndspos(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndsneg(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndsneg(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c16(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c16(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c16(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c16(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c16(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c16(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c16(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c16(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(cons2(z0, z1), x1)) → c16(CONS(cons2(z0, active(z1)), x1), ACTIVE(cons2(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, 2ndsneg(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(0, z0))) → c17(CONS2(x0, mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(cons2(x0, plus(s(z0), z1))) → c17(CONS2(x0, mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons2(x0, times(0, z0))) → c17(CONS2(x0, mark(0)), ACTIVE(times(0, z0)))
ACTIVE(cons2(x0, times(s(z0), z1))) → c17(CONS2(x0, mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(cons2(x0, s(z0))) → c17(CONS2(x0, s(active(z0))), ACTIVE(s(z0)))
ACTIVE(cons2(x0, posrecip(z0))) → c17(CONS2(x0, posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(cons2(x0, negrecip(z0))) → c17(CONS2(x0, negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(cons2(x0, cons(z0, z1))) → c17(CONS2(x0, cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(cons2(x0, cons2(z0, z1))) → c17(CONS2(x0, cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, from(active(z0))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, square(active(z0))), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c20(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(from(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(from(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c20(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c20(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c20(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c20(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c20(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c20(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c20(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c20(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c20(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c20(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(cons2(z0, z1))) → c20(FROM(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c20(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c20(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c20(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c25(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c25(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c25(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c25(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c25(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c25(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c25(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c25(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c25(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c25(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c25(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(cons2(z0, z1))) → c25(PI(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c25(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c25(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c25(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c30(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(square(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(square(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c30(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c30(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c30(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c30(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c30(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c30(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c30(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c30(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c30(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(cons2(z0, z1))) → c30(SQUARE(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c30(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c30(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c63(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c63(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c63(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c63(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(cons2(z0, z1))) → c63(S(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(s(rcons(z0, z1))) → c63(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c63(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c63(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c63(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c63(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c63(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c63(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c63(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c63(S(ok(0)))
PROPER(s(nil)) → c63(S(ok(nil)))
PROPER(s(rnil)) → c63(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c64(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c64(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c64(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c64(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(cons2(z0, z1))) → c64(POSRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c64(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c64(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c64(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c64(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c64(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c64(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c64(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c64(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c64(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c64(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c64(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c65(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c65(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c65(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c65(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(cons2(z0, z1))) → c65(NEGRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c65(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c65(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c65(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c65(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c65(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c65(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c65(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c65(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c65(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c65(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c65(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c67(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c67(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c67(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c67(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, cons2(z0, z1))) → c67(CONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c67(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c67(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c67(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c67(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c67(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c67(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c67(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c67(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c67(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c67(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c67(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c67(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(cons2(z0, z1), x1)) → c67(CONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c67(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c67(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c67(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c67(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c67(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c67(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c67(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c67(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c67(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c67(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c67(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c67(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c67(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c67(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(cons2(x0, s(z0))) → c68(CONS2(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons2(x0, posrecip(z0))) → c68(CONS2(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons2(x0, negrecip(z0))) → c68(CONS2(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons2(x0, cons(z0, z1))) → c68(CONS2(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons2(x0, cons2(z0, z1))) → c68(CONS2(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons2(x0, rcons(z0, z1))) → c68(CONS2(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons2(x0, from(z0))) → c68(CONS2(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons2(x0, 2ndspos(z0, z1))) → c68(CONS2(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons2(x0, 2ndsneg(z0, z1))) → c68(CONS2(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons2(x0, pi(z0))) → c68(CONS2(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons2(x0, plus(z0, z1))) → c68(CONS2(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons2(x0, times(z0, z1))) → c68(CONS2(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons2(x0, square(z0))) → c68(CONS2(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons2(s(z0), x1)) → c68(CONS2(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons2(posrecip(z0), x1)) → c68(CONS2(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons2(negrecip(z0), x1)) → c68(CONS2(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons2(cons(z0, z1), x1)) → c68(CONS2(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons2(cons2(z0, z1), x1)) → c68(CONS2(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons2(rcons(z0, z1), x1)) → c68(CONS2(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons2(from(z0), x1)) → c68(CONS2(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons2(2ndspos(z0, z1), x1)) → c68(CONS2(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons2(2ndsneg(z0, z1), x1)) → c68(CONS2(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons2(pi(z0), x1)) → c68(CONS2(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons2(plus(z0, z1), x1)) → c68(CONS2(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons2(times(z0, z1), x1)) → c68(CONS2(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons2(square(z0), x1)) → c68(CONS2(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons2(x0, 0)) → c68(CONS2(proper(x0), ok(0)), PROPER(x0))
PROPER(cons2(x0, nil)) → c68(CONS2(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons2(x0, rnil)) → c68(CONS2(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons2(0, x1)) → c68(CONS2(ok(0), proper(x1)), PROPER(x1))
PROPER(cons2(nil, x1)) → c68(CONS2(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons2(rnil, x1)) → c68(CONS2(ok(rnil), proper(x1)), PROPER(x1))
PROPER(rcons(x0, s(z0))) → c70(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c70(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c70(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, cons(z0, z1))) → c70(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, cons2(z0, z1))) → c70(RCONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(rcons(x0, rcons(z0, z1))) → c70(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c70(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c70(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c70(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c70(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c70(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c70(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c70(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(s(z0), x1)) → c70(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c70(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c70(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c70(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(cons2(z0, z1), x1)) → c70(RCONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c70(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c70(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c70(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c70(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c70(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c70(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c70(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c70(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(rcons(x0, 0)) → c70(RCONS(proper(x0), ok(0)), PROPER(x0))
PROPER(rcons(x0, nil)) → c70(RCONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(rcons(x0, rnil)) → c70(RCONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(rcons(0, x1)) → c70(RCONS(ok(0), proper(x1)), PROPER(x1))
PROPER(rcons(nil, x1)) → c70(RCONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c70(RCONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(from(s(z0))) → c71(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(posrecip(z0))) → c71(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(from(negrecip(z0))) → c71(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(from(cons(z0, z1))) → c71(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(cons2(z0, z1))) → c71(FROM(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(from(rcons(z0, z1))) → c71(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(from(from(z0))) → c71(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(2ndspos(z0, z1))) → c71(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(from(2ndsneg(z0, z1))) → c71(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(from(pi(z0))) → c71(FROM(pi(proper(z0))), PROPER(pi(z0)))
PROPER(from(plus(z0, z1))) → c71(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(from(times(z0, z1))) → c71(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(from(square(z0))) → c71(FROM(square(proper(z0))), PROPER(square(z0)))
PROPER(from(0)) → c71(FROM(ok(0)))
PROPER(from(nil)) → c71(FROM(ok(nil)))
PROPER(from(rnil)) → c71(FROM(ok(rnil)))
PROPER(2ndspos(x0, s(z0))) → c72(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndspos(x0, posrecip(z0))) → c72(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndspos(x0, negrecip(z0))) → c72(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndspos(x0, cons(z0, z1))) → c72(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndspos(x0, cons2(z0, z1))) → c72(2NDSPOS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(2ndspos(x0, rcons(z0, z1))) → c72(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndspos(x0, from(z0))) → c72(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c72(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c72(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndspos(x0, pi(z0))) → c72(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndspos(x0, plus(z0, z1))) → c72(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndspos(x0, times(z0, z1))) → c72(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndspos(x0, square(z0))) → c72(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndspos(s(z0), x1)) → c72(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndspos(posrecip(z0), x1)) → c72(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndspos(negrecip(z0), x1)) → c72(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndspos(cons(z0, z1), x1)) → c72(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndspos(cons2(z0, z1), x1)) → c72(2NDSPOS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(2ndspos(rcons(z0, z1), x1)) → c72(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndspos(from(z0), x1)) → c72(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c72(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c72(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndspos(pi(z0), x1)) → c72(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndspos(plus(z0, z1), x1)) → c72(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndspos(times(z0, z1), x1)) → c72(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndspos(square(z0), x1)) → c72(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndspos(x0, 0)) → c72(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndspos(x0, nil)) → c72(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndspos(x0, rnil)) → c72(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndspos(0, x1)) → c72(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndspos(nil, x1)) → c72(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndspos(rnil, x1)) → c72(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(x0, s(z0))) → c73(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndsneg(x0, posrecip(z0))) → c73(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndsneg(x0, negrecip(z0))) → c73(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndsneg(x0, cons(z0, z1))) → c73(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndsneg(x0, cons2(z0, z1))) → c73(2NDSNEG(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(2ndsneg(x0, rcons(z0, z1))) → c73(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndsneg(x0, from(z0))) → c73(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c73(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c73(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndsneg(x0, pi(z0))) → c73(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndsneg(x0, plus(z0, z1))) → c73(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndsneg(x0, times(z0, z1))) → c73(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndsneg(x0, square(z0))) → c73(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndsneg(s(z0), x1)) → c73(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndsneg(posrecip(z0), x1)) → c73(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndsneg(negrecip(z0), x1)) → c73(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndsneg(cons(z0, z1), x1)) → c73(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(cons2(z0, z1), x1)) → c73(2NDSNEG(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(2ndsneg(rcons(z0, z1), x1)) → c73(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(from(z0), x1)) → c73(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c73(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c73(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndsneg(pi(z0), x1)) → c73(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndsneg(plus(z0, z1), x1)) → c73(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndsneg(times(z0, z1), x1)) → c73(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndsneg(square(z0), x1)) → c73(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndsneg(x0, 0)) → c73(2NDSNEG(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndsneg(x0, nil)) → c73(2NDSNEG(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndsneg(x0, rnil)) → c73(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndsneg(0, x1)) → c73(2NDSNEG(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndsneg(nil, x1)) → c73(2NDSNEG(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(rnil, x1)) → c73(2NDSNEG(ok(rnil), proper(x1)), PROPER(x1))
PROPER(pi(s(z0))) → c74(PI(s(proper(z0))), PROPER(s(z0)))
PROPER(pi(posrecip(z0))) → c74(PI(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(pi(negrecip(z0))) → c74(PI(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(pi(cons(z0, z1))) → c74(PI(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(pi(cons2(z0, z1))) → c74(PI(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(pi(rcons(z0, z1))) → c74(PI(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(pi(from(z0))) → c74(PI(from(proper(z0))), PROPER(from(z0)))
PROPER(pi(2ndspos(z0, z1))) → c74(PI(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(pi(2ndsneg(z0, z1))) → c74(PI(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(pi(pi(z0))) → c74(PI(pi(proper(z0))), PROPER(pi(z0)))
PROPER(pi(plus(z0, z1))) → c74(PI(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(pi(times(z0, z1))) → c74(PI(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(pi(square(z0))) → c74(PI(square(proper(z0))), PROPER(square(z0)))
PROPER(pi(0)) → c74(PI(ok(0)))
PROPER(pi(nil)) → c74(PI(ok(nil)))
PROPER(pi(rnil)) → c74(PI(ok(rnil)))
PROPER(plus(x0, s(z0))) → c75(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(plus(x0, posrecip(z0))) → c75(PLUS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(plus(x0, negrecip(z0))) → c75(PLUS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(plus(x0, cons(z0, z1))) → c75(PLUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(plus(x0, cons2(z0, z1))) → c75(PLUS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(plus(x0, rcons(z0, z1))) → c75(PLUS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(plus(x0, from(z0))) → c75(PLUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(plus(x0, 2ndspos(z0, z1))) → c75(PLUS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(plus(x0, 2ndsneg(z0, z1))) → c75(PLUS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(plus(x0, pi(z0))) → c75(PLUS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(plus(x0, plus(z0, z1))) → c75(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(plus(x0, times(z0, z1))) → c75(PLUS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(plus(x0, square(z0))) → c75(PLUS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(plus(s(z0), x1)) → c75(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(plus(posrecip(z0), x1)) → c75(PLUS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(plus(negrecip(z0), x1)) → c75(PLUS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(plus(cons(z0, z1), x1)) → c75(PLUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(plus(cons2(z0, z1), x1)) → c75(PLUS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(plus(rcons(z0, z1), x1)) → c75(PLUS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(plus(from(z0), x1)) → c75(PLUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(plus(2ndspos(z0, z1), x1)) → c75(PLUS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(plus(2ndsneg(z0, z1), x1)) → c75(PLUS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(plus(pi(z0), x1)) → c75(PLUS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(plus(plus(z0, z1), x1)) → c75(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(plus(times(z0, z1), x1)) → c75(PLUS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(plus(square(z0), x1)) → c75(PLUS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(plus(x0, 0)) → c75(PLUS(proper(x0), ok(0)), PROPER(x0))
PROPER(plus(x0, nil)) → c75(PLUS(proper(x0), ok(nil)), PROPER(x0))
PROPER(plus(x0, rnil)) → c75(PLUS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(plus(0, x1)) → c75(PLUS(ok(0), proper(x1)), PROPER(x1))
PROPER(plus(nil, x1)) → c75(PLUS(ok(nil), proper(x1)), PROPER(x1))
PROPER(plus(rnil, x1)) → c75(PLUS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(times(x0, 0)) → c76(TIMES(proper(x0), ok(0)), PROPER(x0), PROPER(0))
PROPER(times(x0, s(z0))) → c76(TIMES(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(times(x0, posrecip(z0))) → c76(TIMES(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(times(x0, negrecip(z0))) → c76(TIMES(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(times(x0, nil)) → c76(TIMES(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
PROPER(times(x0, cons(z0, z1))) → c76(TIMES(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(times(x0, cons2(z0, z1))) → c76(TIMES(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(times(x0, rnil)) → c76(TIMES(proper(x0), ok(rnil)), PROPER(x0), PROPER(rnil))
PROPER(times(x0, rcons(z0, z1))) → c76(TIMES(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(times(x0, from(z0))) → c76(TIMES(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(times(x0, 2ndspos(z0, z1))) → c76(TIMES(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(times(x0, 2ndsneg(z0, z1))) → c76(TIMES(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(times(x0, pi(z0))) → c76(TIMES(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(times(x0, plus(z0, z1))) → c76(TIMES(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(times(x0, times(z0, z1))) → c76(TIMES(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(times(x0, square(z0))) → c76(TIMES(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(times(0, x1)) → c76(TIMES(ok(0), proper(x1)), PROPER(0), PROPER(x1))
PROPER(times(s(z0), x1)) → c76(TIMES(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(times(posrecip(z0), x1)) → c76(TIMES(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(times(negrecip(z0), x1)) → c76(TIMES(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(times(nil, x1)) → c76(TIMES(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
PROPER(times(cons(z0, z1), x1)) → c76(TIMES(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(times(cons2(z0, z1), x1)) → c76(TIMES(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(times(rnil, x1)) → c76(TIMES(ok(rnil), proper(x1)), PROPER(rnil), PROPER(x1))
PROPER(times(rcons(z0, z1), x1)) → c76(TIMES(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(times(from(z0), x1)) → c76(TIMES(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(times(2ndspos(z0, z1), x1)) → c76(TIMES(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(times(2ndsneg(z0, z1), x1)) → c76(TIMES(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(times(pi(z0), x1)) → c76(TIMES(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(times(plus(z0, z1), x1)) → c76(TIMES(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(times(times(z0, z1), x1)) → c76(TIMES(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(times(square(z0), x1)) → c76(TIMES(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
S tuples:
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
PROPER(square(z0)) → c77(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c78(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c79(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c9(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(2NDSPOS(s(z0), cons2(z1, z2)))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(2NDSNEG(s(z0), cons2(z1, z2)))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c13(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, z2)))) → c13(S(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(s(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, z2)))) → c13(S(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(s(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c13(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c13(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c13(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c13(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c13(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c13(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c13(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c13(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(cons2(z0, z1))) → c13(S(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c13(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c13(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c13(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c14(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c14(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c14(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c14(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c14(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c14(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c14(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c14(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(cons2(z0, z1))) → c14(POSRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c15(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c15(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c15(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c15(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c15(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c15(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c15(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c15(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(cons2(z0, z1))) → c15(NEGRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndspos(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndspos(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndsneg(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndsneg(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c16(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c16(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c16(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c16(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c16(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c16(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c16(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c16(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(cons2(z0, z1), x1)) → c16(CONS(cons2(z0, active(z1)), x1), ACTIVE(cons2(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, 2ndsneg(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(0, z0))) → c17(CONS2(x0, mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(cons2(x0, plus(s(z0), z1))) → c17(CONS2(x0, mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons2(x0, times(0, z0))) → c17(CONS2(x0, mark(0)), ACTIVE(times(0, z0)))
ACTIVE(cons2(x0, times(s(z0), z1))) → c17(CONS2(x0, mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(cons2(x0, s(z0))) → c17(CONS2(x0, s(active(z0))), ACTIVE(s(z0)))
ACTIVE(cons2(x0, posrecip(z0))) → c17(CONS2(x0, posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(cons2(x0, negrecip(z0))) → c17(CONS2(x0, negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(cons2(x0, cons(z0, z1))) → c17(CONS2(x0, cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(cons2(x0, cons2(z0, z1))) → c17(CONS2(x0, cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, from(active(z0))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, square(active(z0))), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c20(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(from(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(from(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c20(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c20(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c20(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c20(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c20(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c20(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c20(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c20(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c20(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c20(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(cons2(z0, z1))) → c20(FROM(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c20(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c20(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c20(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c25(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c25(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c25(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c25(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c25(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c25(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c25(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c25(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c25(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c25(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c25(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(cons2(z0, z1))) → c25(PI(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c25(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c25(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c25(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c30(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(square(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(square(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c30(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c30(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c30(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c30(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c30(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c30(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c30(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c30(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c30(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(cons2(z0, z1))) → c30(SQUARE(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c30(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c30(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c63(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c63(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c63(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c63(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(cons2(z0, z1))) → c63(S(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(s(rcons(z0, z1))) → c63(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c63(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c63(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c63(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c63(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c63(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c63(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c63(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c63(S(ok(0)))
PROPER(s(nil)) → c63(S(ok(nil)))
PROPER(s(rnil)) → c63(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c64(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c64(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c64(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c64(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(cons2(z0, z1))) → c64(POSRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c64(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c64(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c64(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c64(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c64(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c64(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c64(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c64(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c64(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c64(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c64(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c65(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c65(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c65(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c65(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(cons2(z0, z1))) → c65(NEGRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c65(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c65(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c65(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c65(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c65(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c65(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c65(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c65(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c65(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c65(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c65(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c67(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c67(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c67(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c67(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, cons2(z0, z1))) → c67(CONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c67(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c67(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c67(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c67(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c67(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c67(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c67(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c67(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c67(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c67(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c67(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c67(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(cons2(z0, z1), x1)) → c67(CONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c67(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c67(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c67(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c67(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c67(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c67(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c67(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c67(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c67(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c67(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c67(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c67(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c67(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c67(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(cons2(x0, s(z0))) → c68(CONS2(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons2(x0, posrecip(z0))) → c68(CONS2(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons2(x0, negrecip(z0))) → c68(CONS2(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons2(x0, cons(z0, z1))) → c68(CONS2(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons2(x0, cons2(z0, z1))) → c68(CONS2(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons2(x0, rcons(z0, z1))) → c68(CONS2(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons2(x0, from(z0))) → c68(CONS2(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons2(x0, 2ndspos(z0, z1))) → c68(CONS2(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons2(x0, 2ndsneg(z0, z1))) → c68(CONS2(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons2(x0, pi(z0))) → c68(CONS2(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons2(x0, plus(z0, z1))) → c68(CONS2(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons2(x0, times(z0, z1))) → c68(CONS2(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons2(x0, square(z0))) → c68(CONS2(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons2(s(z0), x1)) → c68(CONS2(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons2(posrecip(z0), x1)) → c68(CONS2(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons2(negrecip(z0), x1)) → c68(CONS2(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons2(cons(z0, z1), x1)) → c68(CONS2(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons2(cons2(z0, z1), x1)) → c68(CONS2(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons2(rcons(z0, z1), x1)) → c68(CONS2(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons2(from(z0), x1)) → c68(CONS2(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons2(2ndspos(z0, z1), x1)) → c68(CONS2(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons2(2ndsneg(z0, z1), x1)) → c68(CONS2(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons2(pi(z0), x1)) → c68(CONS2(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons2(plus(z0, z1), x1)) → c68(CONS2(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons2(times(z0, z1), x1)) → c68(CONS2(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons2(square(z0), x1)) → c68(CONS2(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons2(x0, 0)) → c68(CONS2(proper(x0), ok(0)), PROPER(x0))
PROPER(cons2(x0, nil)) → c68(CONS2(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons2(x0, rnil)) → c68(CONS2(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons2(0, x1)) → c68(CONS2(ok(0), proper(x1)), PROPER(x1))
PROPER(cons2(nil, x1)) → c68(CONS2(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons2(rnil, x1)) → c68(CONS2(ok(rnil), proper(x1)), PROPER(x1))
PROPER(rcons(x0, s(z0))) → c70(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c70(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c70(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, cons(z0, z1))) → c70(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, cons2(z0, z1))) → c70(RCONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(rcons(x0, rcons(z0, z1))) → c70(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c70(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c70(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c70(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c70(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c70(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c70(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c70(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(s(z0), x1)) → c70(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c70(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c70(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c70(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(cons2(z0, z1), x1)) → c70(RCONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c70(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c70(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c70(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c70(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c70(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c70(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c70(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c70(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(rcons(x0, 0)) → c70(RCONS(proper(x0), ok(0)), PROPER(x0))
PROPER(rcons(x0, nil)) → c70(RCONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(rcons(x0, rnil)) → c70(RCONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(rcons(0, x1)) → c70(RCONS(ok(0), proper(x1)), PROPER(x1))
PROPER(rcons(nil, x1)) → c70(RCONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c70(RCONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(from(s(z0))) → c71(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(posrecip(z0))) → c71(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(from(negrecip(z0))) → c71(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(from(cons(z0, z1))) → c71(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(cons2(z0, z1))) → c71(FROM(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(from(rcons(z0, z1))) → c71(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(from(from(z0))) → c71(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(2ndspos(z0, z1))) → c71(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(from(2ndsneg(z0, z1))) → c71(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(from(pi(z0))) → c71(FROM(pi(proper(z0))), PROPER(pi(z0)))
PROPER(from(plus(z0, z1))) → c71(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(from(times(z0, z1))) → c71(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(from(square(z0))) → c71(FROM(square(proper(z0))), PROPER(square(z0)))
PROPER(from(0)) → c71(FROM(ok(0)))
PROPER(from(nil)) → c71(FROM(ok(nil)))
PROPER(from(rnil)) → c71(FROM(ok(rnil)))
PROPER(2ndspos(x0, s(z0))) → c72(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndspos(x0, posrecip(z0))) → c72(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndspos(x0, negrecip(z0))) → c72(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndspos(x0, cons(z0, z1))) → c72(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndspos(x0, cons2(z0, z1))) → c72(2NDSPOS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(2ndspos(x0, rcons(z0, z1))) → c72(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndspos(x0, from(z0))) → c72(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c72(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c72(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndspos(x0, pi(z0))) → c72(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndspos(x0, plus(z0, z1))) → c72(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndspos(x0, times(z0, z1))) → c72(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndspos(x0, square(z0))) → c72(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndspos(s(z0), x1)) → c72(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndspos(posrecip(z0), x1)) → c72(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndspos(negrecip(z0), x1)) → c72(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndspos(cons(z0, z1), x1)) → c72(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndspos(cons2(z0, z1), x1)) → c72(2NDSPOS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(2ndspos(rcons(z0, z1), x1)) → c72(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndspos(from(z0), x1)) → c72(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c72(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c72(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndspos(pi(z0), x1)) → c72(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndspos(plus(z0, z1), x1)) → c72(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndspos(times(z0, z1), x1)) → c72(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndspos(square(z0), x1)) → c72(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndspos(x0, 0)) → c72(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndspos(x0, nil)) → c72(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndspos(x0, rnil)) → c72(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndspos(0, x1)) → c72(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndspos(nil, x1)) → c72(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndspos(rnil, x1)) → c72(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(x0, s(z0))) → c73(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndsneg(x0, posrecip(z0))) → c73(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndsneg(x0, negrecip(z0))) → c73(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndsneg(x0, cons(z0, z1))) → c73(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndsneg(x0, cons2(z0, z1))) → c73(2NDSNEG(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(2ndsneg(x0, rcons(z0, z1))) → c73(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndsneg(x0, from(z0))) → c73(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c73(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c73(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndsneg(x0, pi(z0))) → c73(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndsneg(x0, plus(z0, z1))) → c73(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndsneg(x0, times(z0, z1))) → c73(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndsneg(x0, square(z0))) → c73(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndsneg(s(z0), x1)) → c73(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndsneg(posrecip(z0), x1)) → c73(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndsneg(negrecip(z0), x1)) → c73(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndsneg(cons(z0, z1), x1)) → c73(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(cons2(z0, z1), x1)) → c73(2NDSNEG(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(2ndsneg(rcons(z0, z1), x1)) → c73(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(from(z0), x1)) → c73(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c73(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c73(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndsneg(pi(z0), x1)) → c73(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndsneg(plus(z0, z1), x1)) → c73(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndsneg(times(z0, z1), x1)) → c73(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndsneg(square(z0), x1)) → c73(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndsneg(x0, 0)) → c73(2NDSNEG(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndsneg(x0, nil)) → c73(2NDSNEG(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndsneg(x0, rnil)) → c73(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndsneg(0, x1)) → c73(2NDSNEG(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndsneg(nil, x1)) → c73(2NDSNEG(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(rnil, x1)) → c73(2NDSNEG(ok(rnil), proper(x1)), PROPER(x1))
PROPER(pi(s(z0))) → c74(PI(s(proper(z0))), PROPER(s(z0)))
PROPER(pi(posrecip(z0))) → c74(PI(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(pi(negrecip(z0))) → c74(PI(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(pi(cons(z0, z1))) → c74(PI(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(pi(cons2(z0, z1))) → c74(PI(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(pi(rcons(z0, z1))) → c74(PI(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(pi(from(z0))) → c74(PI(from(proper(z0))), PROPER(from(z0)))
PROPER(pi(2ndspos(z0, z1))) → c74(PI(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(pi(2ndsneg(z0, z1))) → c74(PI(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(pi(pi(z0))) → c74(PI(pi(proper(z0))), PROPER(pi(z0)))
PROPER(pi(plus(z0, z1))) → c74(PI(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(pi(times(z0, z1))) → c74(PI(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(pi(square(z0))) → c74(PI(square(proper(z0))), PROPER(square(z0)))
PROPER(pi(0)) → c74(PI(ok(0)))
PROPER(pi(nil)) → c74(PI(ok(nil)))
PROPER(pi(rnil)) → c74(PI(ok(rnil)))
PROPER(plus(x0, s(z0))) → c75(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(plus(x0, posrecip(z0))) → c75(PLUS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(plus(x0, negrecip(z0))) → c75(PLUS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(plus(x0, cons(z0, z1))) → c75(PLUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(plus(x0, cons2(z0, z1))) → c75(PLUS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(plus(x0, rcons(z0, z1))) → c75(PLUS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(plus(x0, from(z0))) → c75(PLUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(plus(x0, 2ndspos(z0, z1))) → c75(PLUS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(plus(x0, 2ndsneg(z0, z1))) → c75(PLUS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(plus(x0, pi(z0))) → c75(PLUS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(plus(x0, plus(z0, z1))) → c75(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(plus(x0, times(z0, z1))) → c75(PLUS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(plus(x0, square(z0))) → c75(PLUS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(plus(s(z0), x1)) → c75(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(plus(posrecip(z0), x1)) → c75(PLUS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(plus(negrecip(z0), x1)) → c75(PLUS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(plus(cons(z0, z1), x1)) → c75(PLUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(plus(cons2(z0, z1), x1)) → c75(PLUS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(plus(rcons(z0, z1), x1)) → c75(PLUS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(plus(from(z0), x1)) → c75(PLUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(plus(2ndspos(z0, z1), x1)) → c75(PLUS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(plus(2ndsneg(z0, z1), x1)) → c75(PLUS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(plus(pi(z0), x1)) → c75(PLUS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(plus(plus(z0, z1), x1)) → c75(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(plus(times(z0, z1), x1)) → c75(PLUS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(plus(square(z0), x1)) → c75(PLUS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(plus(x0, 0)) → c75(PLUS(proper(x0), ok(0)), PROPER(x0))
PROPER(plus(x0, nil)) → c75(PLUS(proper(x0), ok(nil)), PROPER(x0))
PROPER(plus(x0, rnil)) → c75(PLUS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(plus(0, x1)) → c75(PLUS(ok(0), proper(x1)), PROPER(x1))
PROPER(plus(nil, x1)) → c75(PLUS(ok(nil), proper(x1)), PROPER(x1))
PROPER(plus(rnil, x1)) → c75(PLUS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(times(x0, 0)) → c76(TIMES(proper(x0), ok(0)), PROPER(x0), PROPER(0))
PROPER(times(x0, s(z0))) → c76(TIMES(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(times(x0, posrecip(z0))) → c76(TIMES(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(times(x0, negrecip(z0))) → c76(TIMES(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(times(x0, nil)) → c76(TIMES(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
PROPER(times(x0, cons(z0, z1))) → c76(TIMES(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(times(x0, cons2(z0, z1))) → c76(TIMES(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(times(x0, rnil)) → c76(TIMES(proper(x0), ok(rnil)), PROPER(x0), PROPER(rnil))
PROPER(times(x0, rcons(z0, z1))) → c76(TIMES(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(times(x0, from(z0))) → c76(TIMES(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(times(x0, 2ndspos(z0, z1))) → c76(TIMES(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(times(x0, 2ndsneg(z0, z1))) → c76(TIMES(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(times(x0, pi(z0))) → c76(TIMES(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(times(x0, plus(z0, z1))) → c76(TIMES(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(times(x0, times(z0, z1))) → c76(TIMES(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(times(x0, square(z0))) → c76(TIMES(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(times(0, x1)) → c76(TIMES(ok(0), proper(x1)), PROPER(0), PROPER(x1))
PROPER(times(s(z0), x1)) → c76(TIMES(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(times(posrecip(z0), x1)) → c76(TIMES(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(times(negrecip(z0), x1)) → c76(TIMES(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(times(nil, x1)) → c76(TIMES(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
PROPER(times(cons(z0, z1), x1)) → c76(TIMES(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(times(cons2(z0, z1), x1)) → c76(TIMES(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(times(rnil, x1)) → c76(TIMES(ok(rnil), proper(x1)), PROPER(rnil), PROPER(x1))
PROPER(times(rcons(z0, z1), x1)) → c76(TIMES(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(times(from(z0), x1)) → c76(TIMES(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(times(2ndspos(z0, z1), x1)) → c76(TIMES(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(times(2ndsneg(z0, z1), x1)) → c76(TIMES(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(times(pi(z0), x1)) → c76(TIMES(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(times(plus(z0, z1), x1)) → c76(TIMES(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(times(times(z0, z1), x1)) → c76(TIMES(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(times(square(z0), x1)) → c76(TIMES(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
K tuples:none
Defined Rule Symbols:
active, 2ndspos, cons2, rcons, posrecip, 2ndsneg, negrecip, s, cons, from, pi, plus, times, square, proper
Defined Pair Symbols:
ACTIVE, S, POSRECIP, NEGRECIP, CONS, CONS2, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP
Compound Symbols:
c12, c18, c19, c21, c22, c23, c24, c26, c27, c28, c29, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c77, c78, c79, c, c7, c9, c11, c1, c13, c14, c15, c16, c17, c20, c25, c30, c63, c63, c64, c64, c65, c65, c67, c67, c68, c68, c70, c70, c71, c71, c72, c72, c73, c73, c74, c74, c75, c75, c76
(73) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 6 trailing tuple parts
(74) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(2ndspos(0, z0)) → mark(rnil)
active(2ndspos(s(z0), cons(z1, z2))) → mark(2ndspos(s(z0), cons2(z1, z2)))
active(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(z1, z2))) → mark(2ndsneg(s(z0), cons2(z1, z2)))
active(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
active(pi(z0)) → mark(2ndspos(z0, from(0)))
active(plus(0, z0)) → mark(z0)
active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
active(times(0, z0)) → mark(0)
active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
active(square(z0)) → mark(times(z0, z0))
active(s(z0)) → s(active(z0))
active(posrecip(z0)) → posrecip(active(z0))
active(negrecip(z0)) → negrecip(active(z0))
active(cons(z0, z1)) → cons(active(z0), z1)
active(cons2(z0, z1)) → cons2(z0, active(z1))
active(rcons(z0, z1)) → rcons(active(z0), z1)
active(rcons(z0, z1)) → rcons(z0, active(z1))
active(from(z0)) → from(active(z0))
active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
active(pi(z0)) → pi(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(times(z0, z1)) → times(active(z0), z1)
active(times(z0, z1)) → times(z0, active(z1))
active(square(z0)) → square(active(z0))
2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
cons2(z0, mark(z1)) → mark(cons2(z0, z1))
cons2(ok(z0), ok(z1)) → ok(cons2(z0, z1))
rcons(mark(z0), z1) → mark(rcons(z0, z1))
rcons(z0, mark(z1)) → mark(rcons(z0, z1))
rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
posrecip(ok(z0)) → ok(posrecip(z0))
posrecip(mark(z0)) → mark(posrecip(z0))
2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
negrecip(ok(z0)) → ok(negrecip(z0))
negrecip(mark(z0)) → mark(negrecip(z0))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
cons(mark(z0), z1) → mark(cons(z0, z1))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
from(mark(z0)) → mark(from(z0))
from(ok(z0)) → ok(from(z0))
pi(mark(z0)) → mark(pi(z0))
pi(ok(z0)) → ok(pi(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
times(mark(z0), z1) → mark(times(z0, z1))
times(ok(z0), ok(z1)) → ok(times(z0, z1))
times(z0, mark(z1)) → mark(times(z0, z1))
square(mark(z0)) → mark(square(z0))
square(ok(z0)) → ok(square(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(posrecip(z0)) → posrecip(proper(z0))
proper(negrecip(z0)) → negrecip(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(cons2(z0, z1)) → cons2(proper(z0), proper(z1))
proper(rnil) → ok(rnil)
proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
proper(pi(z0)) → pi(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(times(z0, z1)) → times(proper(z0), proper(z1))
proper(square(z0)) → square(proper(z0))
Tuples:
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
PROPER(square(z0)) → c77(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c78(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c79(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c9(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(2NDSPOS(s(z0), cons2(z1, z2)))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(2NDSNEG(s(z0), cons2(z1, z2)))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c13(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, z2)))) → c13(S(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(s(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, z2)))) → c13(S(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(s(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c13(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c13(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c13(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c13(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c13(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c13(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c13(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c13(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(cons2(z0, z1))) → c13(S(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c13(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c13(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c13(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c14(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c14(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c14(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c14(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c14(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c14(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c14(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c14(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(cons2(z0, z1))) → c14(POSRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c15(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c15(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c15(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c15(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c15(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c15(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c15(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c15(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(cons2(z0, z1))) → c15(NEGRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndspos(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndspos(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndsneg(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndsneg(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c16(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c16(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c16(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c16(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c16(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c16(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c16(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c16(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(cons2(z0, z1), x1)) → c16(CONS(cons2(z0, active(z1)), x1), ACTIVE(cons2(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, 2ndsneg(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(0, z0))) → c17(CONS2(x0, mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(cons2(x0, plus(s(z0), z1))) → c17(CONS2(x0, mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons2(x0, times(0, z0))) → c17(CONS2(x0, mark(0)), ACTIVE(times(0, z0)))
ACTIVE(cons2(x0, times(s(z0), z1))) → c17(CONS2(x0, mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(cons2(x0, s(z0))) → c17(CONS2(x0, s(active(z0))), ACTIVE(s(z0)))
ACTIVE(cons2(x0, posrecip(z0))) → c17(CONS2(x0, posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(cons2(x0, negrecip(z0))) → c17(CONS2(x0, negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(cons2(x0, cons(z0, z1))) → c17(CONS2(x0, cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(cons2(x0, cons2(z0, z1))) → c17(CONS2(x0, cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, from(active(z0))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, square(active(z0))), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c20(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(from(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(from(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c20(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c20(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c20(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c20(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c20(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c20(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c20(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c20(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c20(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c20(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(cons2(z0, z1))) → c20(FROM(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c20(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c20(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c20(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c25(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c25(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c25(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c25(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c25(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c25(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c25(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c25(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c25(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c25(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c25(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(cons2(z0, z1))) → c25(PI(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c25(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c25(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c25(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c30(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(square(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(square(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c30(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c30(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c30(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c30(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c30(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c30(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c30(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c30(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c30(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(cons2(z0, z1))) → c30(SQUARE(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c30(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c30(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c63(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c63(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c63(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c63(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(cons2(z0, z1))) → c63(S(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(s(rcons(z0, z1))) → c63(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c63(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c63(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c63(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c63(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c63(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c63(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c63(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c63(S(ok(0)))
PROPER(s(nil)) → c63(S(ok(nil)))
PROPER(s(rnil)) → c63(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c64(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c64(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c64(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c64(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(cons2(z0, z1))) → c64(POSRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c64(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c64(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c64(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c64(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c64(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c64(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c64(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c64(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c64(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c64(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c64(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c65(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c65(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c65(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c65(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(cons2(z0, z1))) → c65(NEGRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c65(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c65(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c65(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c65(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c65(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c65(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c65(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c65(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c65(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c65(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c65(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c67(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c67(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c67(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c67(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, cons2(z0, z1))) → c67(CONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c67(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c67(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c67(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c67(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c67(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c67(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c67(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c67(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c67(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c67(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c67(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c67(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(cons2(z0, z1), x1)) → c67(CONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c67(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c67(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c67(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c67(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c67(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c67(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c67(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c67(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c67(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c67(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c67(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c67(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c67(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c67(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(cons2(x0, s(z0))) → c68(CONS2(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons2(x0, posrecip(z0))) → c68(CONS2(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons2(x0, negrecip(z0))) → c68(CONS2(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons2(x0, cons(z0, z1))) → c68(CONS2(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons2(x0, cons2(z0, z1))) → c68(CONS2(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons2(x0, rcons(z0, z1))) → c68(CONS2(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons2(x0, from(z0))) → c68(CONS2(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons2(x0, 2ndspos(z0, z1))) → c68(CONS2(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons2(x0, 2ndsneg(z0, z1))) → c68(CONS2(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons2(x0, pi(z0))) → c68(CONS2(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons2(x0, plus(z0, z1))) → c68(CONS2(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons2(x0, times(z0, z1))) → c68(CONS2(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons2(x0, square(z0))) → c68(CONS2(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons2(s(z0), x1)) → c68(CONS2(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons2(posrecip(z0), x1)) → c68(CONS2(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons2(negrecip(z0), x1)) → c68(CONS2(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons2(cons(z0, z1), x1)) → c68(CONS2(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons2(cons2(z0, z1), x1)) → c68(CONS2(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons2(rcons(z0, z1), x1)) → c68(CONS2(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons2(from(z0), x1)) → c68(CONS2(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons2(2ndspos(z0, z1), x1)) → c68(CONS2(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons2(2ndsneg(z0, z1), x1)) → c68(CONS2(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons2(pi(z0), x1)) → c68(CONS2(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons2(plus(z0, z1), x1)) → c68(CONS2(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons2(times(z0, z1), x1)) → c68(CONS2(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons2(square(z0), x1)) → c68(CONS2(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons2(x0, 0)) → c68(CONS2(proper(x0), ok(0)), PROPER(x0))
PROPER(cons2(x0, nil)) → c68(CONS2(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons2(x0, rnil)) → c68(CONS2(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons2(0, x1)) → c68(CONS2(ok(0), proper(x1)), PROPER(x1))
PROPER(cons2(nil, x1)) → c68(CONS2(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons2(rnil, x1)) → c68(CONS2(ok(rnil), proper(x1)), PROPER(x1))
PROPER(rcons(x0, s(z0))) → c70(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c70(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c70(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, cons(z0, z1))) → c70(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, cons2(z0, z1))) → c70(RCONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(rcons(x0, rcons(z0, z1))) → c70(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c70(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c70(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c70(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c70(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c70(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c70(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c70(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(s(z0), x1)) → c70(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c70(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c70(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c70(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(cons2(z0, z1), x1)) → c70(RCONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c70(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c70(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c70(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c70(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c70(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c70(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c70(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c70(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(rcons(x0, 0)) → c70(RCONS(proper(x0), ok(0)), PROPER(x0))
PROPER(rcons(x0, nil)) → c70(RCONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(rcons(x0, rnil)) → c70(RCONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(rcons(0, x1)) → c70(RCONS(ok(0), proper(x1)), PROPER(x1))
PROPER(rcons(nil, x1)) → c70(RCONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c70(RCONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(from(s(z0))) → c71(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(posrecip(z0))) → c71(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(from(negrecip(z0))) → c71(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(from(cons(z0, z1))) → c71(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(cons2(z0, z1))) → c71(FROM(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(from(rcons(z0, z1))) → c71(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(from(from(z0))) → c71(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(2ndspos(z0, z1))) → c71(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(from(2ndsneg(z0, z1))) → c71(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(from(pi(z0))) → c71(FROM(pi(proper(z0))), PROPER(pi(z0)))
PROPER(from(plus(z0, z1))) → c71(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(from(times(z0, z1))) → c71(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(from(square(z0))) → c71(FROM(square(proper(z0))), PROPER(square(z0)))
PROPER(from(0)) → c71(FROM(ok(0)))
PROPER(from(nil)) → c71(FROM(ok(nil)))
PROPER(from(rnil)) → c71(FROM(ok(rnil)))
PROPER(2ndspos(x0, s(z0))) → c72(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndspos(x0, posrecip(z0))) → c72(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndspos(x0, negrecip(z0))) → c72(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndspos(x0, cons(z0, z1))) → c72(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndspos(x0, cons2(z0, z1))) → c72(2NDSPOS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(2ndspos(x0, rcons(z0, z1))) → c72(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndspos(x0, from(z0))) → c72(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c72(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c72(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndspos(x0, pi(z0))) → c72(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndspos(x0, plus(z0, z1))) → c72(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndspos(x0, times(z0, z1))) → c72(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndspos(x0, square(z0))) → c72(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndspos(s(z0), x1)) → c72(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndspos(posrecip(z0), x1)) → c72(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndspos(negrecip(z0), x1)) → c72(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndspos(cons(z0, z1), x1)) → c72(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndspos(cons2(z0, z1), x1)) → c72(2NDSPOS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(2ndspos(rcons(z0, z1), x1)) → c72(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndspos(from(z0), x1)) → c72(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c72(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c72(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndspos(pi(z0), x1)) → c72(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndspos(plus(z0, z1), x1)) → c72(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndspos(times(z0, z1), x1)) → c72(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndspos(square(z0), x1)) → c72(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndspos(x0, 0)) → c72(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndspos(x0, nil)) → c72(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndspos(x0, rnil)) → c72(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndspos(0, x1)) → c72(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndspos(nil, x1)) → c72(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndspos(rnil, x1)) → c72(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(x0, s(z0))) → c73(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndsneg(x0, posrecip(z0))) → c73(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndsneg(x0, negrecip(z0))) → c73(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndsneg(x0, cons(z0, z1))) → c73(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndsneg(x0, cons2(z0, z1))) → c73(2NDSNEG(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(2ndsneg(x0, rcons(z0, z1))) → c73(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndsneg(x0, from(z0))) → c73(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c73(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c73(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndsneg(x0, pi(z0))) → c73(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndsneg(x0, plus(z0, z1))) → c73(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndsneg(x0, times(z0, z1))) → c73(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndsneg(x0, square(z0))) → c73(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndsneg(s(z0), x1)) → c73(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndsneg(posrecip(z0), x1)) → c73(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndsneg(negrecip(z0), x1)) → c73(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndsneg(cons(z0, z1), x1)) → c73(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(cons2(z0, z1), x1)) → c73(2NDSNEG(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(2ndsneg(rcons(z0, z1), x1)) → c73(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(from(z0), x1)) → c73(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c73(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c73(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndsneg(pi(z0), x1)) → c73(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndsneg(plus(z0, z1), x1)) → c73(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndsneg(times(z0, z1), x1)) → c73(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndsneg(square(z0), x1)) → c73(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndsneg(x0, 0)) → c73(2NDSNEG(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndsneg(x0, nil)) → c73(2NDSNEG(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndsneg(x0, rnil)) → c73(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndsneg(0, x1)) → c73(2NDSNEG(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndsneg(nil, x1)) → c73(2NDSNEG(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(rnil, x1)) → c73(2NDSNEG(ok(rnil), proper(x1)), PROPER(x1))
PROPER(pi(s(z0))) → c74(PI(s(proper(z0))), PROPER(s(z0)))
PROPER(pi(posrecip(z0))) → c74(PI(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(pi(negrecip(z0))) → c74(PI(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(pi(cons(z0, z1))) → c74(PI(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(pi(cons2(z0, z1))) → c74(PI(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(pi(rcons(z0, z1))) → c74(PI(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(pi(from(z0))) → c74(PI(from(proper(z0))), PROPER(from(z0)))
PROPER(pi(2ndspos(z0, z1))) → c74(PI(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(pi(2ndsneg(z0, z1))) → c74(PI(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(pi(pi(z0))) → c74(PI(pi(proper(z0))), PROPER(pi(z0)))
PROPER(pi(plus(z0, z1))) → c74(PI(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(pi(times(z0, z1))) → c74(PI(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(pi(square(z0))) → c74(PI(square(proper(z0))), PROPER(square(z0)))
PROPER(pi(0)) → c74(PI(ok(0)))
PROPER(pi(nil)) → c74(PI(ok(nil)))
PROPER(pi(rnil)) → c74(PI(ok(rnil)))
PROPER(plus(x0, s(z0))) → c75(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(plus(x0, posrecip(z0))) → c75(PLUS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(plus(x0, negrecip(z0))) → c75(PLUS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(plus(x0, cons(z0, z1))) → c75(PLUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(plus(x0, cons2(z0, z1))) → c75(PLUS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(plus(x0, rcons(z0, z1))) → c75(PLUS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(plus(x0, from(z0))) → c75(PLUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(plus(x0, 2ndspos(z0, z1))) → c75(PLUS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(plus(x0, 2ndsneg(z0, z1))) → c75(PLUS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(plus(x0, pi(z0))) → c75(PLUS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(plus(x0, plus(z0, z1))) → c75(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(plus(x0, times(z0, z1))) → c75(PLUS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(plus(x0, square(z0))) → c75(PLUS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(plus(s(z0), x1)) → c75(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(plus(posrecip(z0), x1)) → c75(PLUS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(plus(negrecip(z0), x1)) → c75(PLUS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(plus(cons(z0, z1), x1)) → c75(PLUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(plus(cons2(z0, z1), x1)) → c75(PLUS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(plus(rcons(z0, z1), x1)) → c75(PLUS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(plus(from(z0), x1)) → c75(PLUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(plus(2ndspos(z0, z1), x1)) → c75(PLUS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(plus(2ndsneg(z0, z1), x1)) → c75(PLUS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(plus(pi(z0), x1)) → c75(PLUS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(plus(plus(z0, z1), x1)) → c75(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(plus(times(z0, z1), x1)) → c75(PLUS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(plus(square(z0), x1)) → c75(PLUS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(plus(x0, 0)) → c75(PLUS(proper(x0), ok(0)), PROPER(x0))
PROPER(plus(x0, nil)) → c75(PLUS(proper(x0), ok(nil)), PROPER(x0))
PROPER(plus(x0, rnil)) → c75(PLUS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(plus(0, x1)) → c75(PLUS(ok(0), proper(x1)), PROPER(x1))
PROPER(plus(nil, x1)) → c75(PLUS(ok(nil), proper(x1)), PROPER(x1))
PROPER(plus(rnil, x1)) → c75(PLUS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(times(x0, s(z0))) → c76(TIMES(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(times(x0, posrecip(z0))) → c76(TIMES(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(times(x0, negrecip(z0))) → c76(TIMES(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(times(x0, cons(z0, z1))) → c76(TIMES(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(times(x0, cons2(z0, z1))) → c76(TIMES(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(times(x0, rcons(z0, z1))) → c76(TIMES(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(times(x0, from(z0))) → c76(TIMES(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(times(x0, 2ndspos(z0, z1))) → c76(TIMES(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(times(x0, 2ndsneg(z0, z1))) → c76(TIMES(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(times(x0, pi(z0))) → c76(TIMES(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(times(x0, plus(z0, z1))) → c76(TIMES(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(times(x0, times(z0, z1))) → c76(TIMES(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(times(x0, square(z0))) → c76(TIMES(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(times(s(z0), x1)) → c76(TIMES(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(times(posrecip(z0), x1)) → c76(TIMES(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(times(negrecip(z0), x1)) → c76(TIMES(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(times(cons(z0, z1), x1)) → c76(TIMES(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(times(cons2(z0, z1), x1)) → c76(TIMES(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(times(rcons(z0, z1), x1)) → c76(TIMES(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(times(from(z0), x1)) → c76(TIMES(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(times(2ndspos(z0, z1), x1)) → c76(TIMES(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(times(2ndsneg(z0, z1), x1)) → c76(TIMES(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(times(pi(z0), x1)) → c76(TIMES(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(times(plus(z0, z1), x1)) → c76(TIMES(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(times(times(z0, z1), x1)) → c76(TIMES(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(times(square(z0), x1)) → c76(TIMES(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(times(x0, 0)) → c76(TIMES(proper(x0), ok(0)), PROPER(x0))
PROPER(times(x0, nil)) → c76(TIMES(proper(x0), ok(nil)), PROPER(x0))
PROPER(times(x0, rnil)) → c76(TIMES(proper(x0), ok(rnil)), PROPER(x0))
PROPER(times(0, x1)) → c76(TIMES(ok(0), proper(x1)), PROPER(x1))
PROPER(times(nil, x1)) → c76(TIMES(ok(nil), proper(x1)), PROPER(x1))
PROPER(times(rnil, x1)) → c76(TIMES(ok(rnil), proper(x1)), PROPER(x1))
S tuples:
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
PROPER(square(z0)) → c77(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c78(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c79(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c9(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(2NDSPOS(s(z0), cons2(z1, z2)))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(2NDSNEG(s(z0), cons2(z1, z2)))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c13(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, z2)))) → c13(S(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(s(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, z2)))) → c13(S(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(s(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c13(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c13(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c13(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c13(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c13(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c13(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c13(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c13(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(cons2(z0, z1))) → c13(S(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c13(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c13(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c13(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c14(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c14(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c14(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c14(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c14(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c14(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c14(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c14(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(cons2(z0, z1))) → c14(POSRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c15(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c15(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c15(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c15(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c15(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c15(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c15(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c15(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(cons2(z0, z1))) → c15(NEGRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndspos(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndspos(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndsneg(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndsneg(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c16(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c16(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c16(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c16(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c16(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c16(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c16(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c16(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(cons2(z0, z1), x1)) → c16(CONS(cons2(z0, active(z1)), x1), ACTIVE(cons2(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, 2ndsneg(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(0, z0))) → c17(CONS2(x0, mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(cons2(x0, plus(s(z0), z1))) → c17(CONS2(x0, mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons2(x0, times(0, z0))) → c17(CONS2(x0, mark(0)), ACTIVE(times(0, z0)))
ACTIVE(cons2(x0, times(s(z0), z1))) → c17(CONS2(x0, mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(cons2(x0, s(z0))) → c17(CONS2(x0, s(active(z0))), ACTIVE(s(z0)))
ACTIVE(cons2(x0, posrecip(z0))) → c17(CONS2(x0, posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(cons2(x0, negrecip(z0))) → c17(CONS2(x0, negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(cons2(x0, cons(z0, z1))) → c17(CONS2(x0, cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(cons2(x0, cons2(z0, z1))) → c17(CONS2(x0, cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, from(active(z0))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, square(active(z0))), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c20(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(from(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(from(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c20(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c20(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c20(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c20(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c20(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c20(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c20(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c20(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c20(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c20(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(cons2(z0, z1))) → c20(FROM(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c20(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c20(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c20(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c25(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c25(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c25(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c25(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c25(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c25(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c25(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c25(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c25(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c25(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c25(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(cons2(z0, z1))) → c25(PI(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c25(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c25(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c25(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c30(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(square(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(square(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c30(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c30(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c30(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c30(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c30(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c30(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c30(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c30(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c30(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(cons2(z0, z1))) → c30(SQUARE(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c30(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c30(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c63(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c63(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c63(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c63(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(cons2(z0, z1))) → c63(S(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(s(rcons(z0, z1))) → c63(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c63(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c63(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c63(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c63(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c63(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c63(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c63(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c63(S(ok(0)))
PROPER(s(nil)) → c63(S(ok(nil)))
PROPER(s(rnil)) → c63(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c64(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c64(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c64(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c64(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(cons2(z0, z1))) → c64(POSRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c64(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c64(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c64(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c64(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c64(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c64(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c64(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c64(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c64(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c64(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c64(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c65(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c65(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c65(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c65(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(cons2(z0, z1))) → c65(NEGRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c65(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c65(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c65(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c65(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c65(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c65(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c65(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c65(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c65(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c65(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c65(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c67(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c67(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c67(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c67(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, cons2(z0, z1))) → c67(CONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c67(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c67(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c67(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c67(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c67(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c67(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c67(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c67(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c67(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c67(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c67(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c67(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(cons2(z0, z1), x1)) → c67(CONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c67(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c67(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c67(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c67(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c67(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c67(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c67(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c67(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c67(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c67(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c67(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c67(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c67(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c67(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(cons2(x0, s(z0))) → c68(CONS2(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons2(x0, posrecip(z0))) → c68(CONS2(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons2(x0, negrecip(z0))) → c68(CONS2(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons2(x0, cons(z0, z1))) → c68(CONS2(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons2(x0, cons2(z0, z1))) → c68(CONS2(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons2(x0, rcons(z0, z1))) → c68(CONS2(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons2(x0, from(z0))) → c68(CONS2(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons2(x0, 2ndspos(z0, z1))) → c68(CONS2(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons2(x0, 2ndsneg(z0, z1))) → c68(CONS2(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons2(x0, pi(z0))) → c68(CONS2(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons2(x0, plus(z0, z1))) → c68(CONS2(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons2(x0, times(z0, z1))) → c68(CONS2(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons2(x0, square(z0))) → c68(CONS2(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons2(s(z0), x1)) → c68(CONS2(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons2(posrecip(z0), x1)) → c68(CONS2(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons2(negrecip(z0), x1)) → c68(CONS2(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons2(cons(z0, z1), x1)) → c68(CONS2(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons2(cons2(z0, z1), x1)) → c68(CONS2(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons2(rcons(z0, z1), x1)) → c68(CONS2(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons2(from(z0), x1)) → c68(CONS2(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons2(2ndspos(z0, z1), x1)) → c68(CONS2(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons2(2ndsneg(z0, z1), x1)) → c68(CONS2(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons2(pi(z0), x1)) → c68(CONS2(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons2(plus(z0, z1), x1)) → c68(CONS2(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons2(times(z0, z1), x1)) → c68(CONS2(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons2(square(z0), x1)) → c68(CONS2(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons2(x0, 0)) → c68(CONS2(proper(x0), ok(0)), PROPER(x0))
PROPER(cons2(x0, nil)) → c68(CONS2(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons2(x0, rnil)) → c68(CONS2(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons2(0, x1)) → c68(CONS2(ok(0), proper(x1)), PROPER(x1))
PROPER(cons2(nil, x1)) → c68(CONS2(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons2(rnil, x1)) → c68(CONS2(ok(rnil), proper(x1)), PROPER(x1))
PROPER(rcons(x0, s(z0))) → c70(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c70(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c70(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, cons(z0, z1))) → c70(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, cons2(z0, z1))) → c70(RCONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(rcons(x0, rcons(z0, z1))) → c70(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c70(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c70(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c70(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c70(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c70(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c70(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c70(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(s(z0), x1)) → c70(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c70(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c70(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c70(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(cons2(z0, z1), x1)) → c70(RCONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c70(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c70(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c70(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c70(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c70(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c70(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c70(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c70(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(rcons(x0, 0)) → c70(RCONS(proper(x0), ok(0)), PROPER(x0))
PROPER(rcons(x0, nil)) → c70(RCONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(rcons(x0, rnil)) → c70(RCONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(rcons(0, x1)) → c70(RCONS(ok(0), proper(x1)), PROPER(x1))
PROPER(rcons(nil, x1)) → c70(RCONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c70(RCONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(from(s(z0))) → c71(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(posrecip(z0))) → c71(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(from(negrecip(z0))) → c71(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(from(cons(z0, z1))) → c71(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(cons2(z0, z1))) → c71(FROM(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(from(rcons(z0, z1))) → c71(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(from(from(z0))) → c71(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(2ndspos(z0, z1))) → c71(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(from(2ndsneg(z0, z1))) → c71(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(from(pi(z0))) → c71(FROM(pi(proper(z0))), PROPER(pi(z0)))
PROPER(from(plus(z0, z1))) → c71(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(from(times(z0, z1))) → c71(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(from(square(z0))) → c71(FROM(square(proper(z0))), PROPER(square(z0)))
PROPER(from(0)) → c71(FROM(ok(0)))
PROPER(from(nil)) → c71(FROM(ok(nil)))
PROPER(from(rnil)) → c71(FROM(ok(rnil)))
PROPER(2ndspos(x0, s(z0))) → c72(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndspos(x0, posrecip(z0))) → c72(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndspos(x0, negrecip(z0))) → c72(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndspos(x0, cons(z0, z1))) → c72(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndspos(x0, cons2(z0, z1))) → c72(2NDSPOS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(2ndspos(x0, rcons(z0, z1))) → c72(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndspos(x0, from(z0))) → c72(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c72(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c72(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndspos(x0, pi(z0))) → c72(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndspos(x0, plus(z0, z1))) → c72(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndspos(x0, times(z0, z1))) → c72(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndspos(x0, square(z0))) → c72(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndspos(s(z0), x1)) → c72(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndspos(posrecip(z0), x1)) → c72(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndspos(negrecip(z0), x1)) → c72(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndspos(cons(z0, z1), x1)) → c72(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndspos(cons2(z0, z1), x1)) → c72(2NDSPOS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(2ndspos(rcons(z0, z1), x1)) → c72(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndspos(from(z0), x1)) → c72(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c72(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c72(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndspos(pi(z0), x1)) → c72(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndspos(plus(z0, z1), x1)) → c72(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndspos(times(z0, z1), x1)) → c72(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndspos(square(z0), x1)) → c72(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndspos(x0, 0)) → c72(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndspos(x0, nil)) → c72(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndspos(x0, rnil)) → c72(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndspos(0, x1)) → c72(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndspos(nil, x1)) → c72(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndspos(rnil, x1)) → c72(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(x0, s(z0))) → c73(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndsneg(x0, posrecip(z0))) → c73(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndsneg(x0, negrecip(z0))) → c73(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndsneg(x0, cons(z0, z1))) → c73(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndsneg(x0, cons2(z0, z1))) → c73(2NDSNEG(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(2ndsneg(x0, rcons(z0, z1))) → c73(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndsneg(x0, from(z0))) → c73(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c73(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c73(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndsneg(x0, pi(z0))) → c73(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndsneg(x0, plus(z0, z1))) → c73(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndsneg(x0, times(z0, z1))) → c73(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndsneg(x0, square(z0))) → c73(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndsneg(s(z0), x1)) → c73(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndsneg(posrecip(z0), x1)) → c73(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndsneg(negrecip(z0), x1)) → c73(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndsneg(cons(z0, z1), x1)) → c73(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(cons2(z0, z1), x1)) → c73(2NDSNEG(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(2ndsneg(rcons(z0, z1), x1)) → c73(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(from(z0), x1)) → c73(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c73(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c73(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndsneg(pi(z0), x1)) → c73(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndsneg(plus(z0, z1), x1)) → c73(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndsneg(times(z0, z1), x1)) → c73(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndsneg(square(z0), x1)) → c73(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndsneg(x0, 0)) → c73(2NDSNEG(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndsneg(x0, nil)) → c73(2NDSNEG(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndsneg(x0, rnil)) → c73(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndsneg(0, x1)) → c73(2NDSNEG(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndsneg(nil, x1)) → c73(2NDSNEG(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(rnil, x1)) → c73(2NDSNEG(ok(rnil), proper(x1)), PROPER(x1))
PROPER(pi(s(z0))) → c74(PI(s(proper(z0))), PROPER(s(z0)))
PROPER(pi(posrecip(z0))) → c74(PI(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(pi(negrecip(z0))) → c74(PI(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(pi(cons(z0, z1))) → c74(PI(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(pi(cons2(z0, z1))) → c74(PI(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(pi(rcons(z0, z1))) → c74(PI(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(pi(from(z0))) → c74(PI(from(proper(z0))), PROPER(from(z0)))
PROPER(pi(2ndspos(z0, z1))) → c74(PI(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(pi(2ndsneg(z0, z1))) → c74(PI(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(pi(pi(z0))) → c74(PI(pi(proper(z0))), PROPER(pi(z0)))
PROPER(pi(plus(z0, z1))) → c74(PI(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(pi(times(z0, z1))) → c74(PI(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(pi(square(z0))) → c74(PI(square(proper(z0))), PROPER(square(z0)))
PROPER(pi(0)) → c74(PI(ok(0)))
PROPER(pi(nil)) → c74(PI(ok(nil)))
PROPER(pi(rnil)) → c74(PI(ok(rnil)))
PROPER(plus(x0, s(z0))) → c75(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(plus(x0, posrecip(z0))) → c75(PLUS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(plus(x0, negrecip(z0))) → c75(PLUS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(plus(x0, cons(z0, z1))) → c75(PLUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(plus(x0, cons2(z0, z1))) → c75(PLUS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(plus(x0, rcons(z0, z1))) → c75(PLUS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(plus(x0, from(z0))) → c75(PLUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(plus(x0, 2ndspos(z0, z1))) → c75(PLUS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(plus(x0, 2ndsneg(z0, z1))) → c75(PLUS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(plus(x0, pi(z0))) → c75(PLUS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(plus(x0, plus(z0, z1))) → c75(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(plus(x0, times(z0, z1))) → c75(PLUS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(plus(x0, square(z0))) → c75(PLUS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(plus(s(z0), x1)) → c75(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(plus(posrecip(z0), x1)) → c75(PLUS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(plus(negrecip(z0), x1)) → c75(PLUS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(plus(cons(z0, z1), x1)) → c75(PLUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(plus(cons2(z0, z1), x1)) → c75(PLUS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(plus(rcons(z0, z1), x1)) → c75(PLUS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(plus(from(z0), x1)) → c75(PLUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(plus(2ndspos(z0, z1), x1)) → c75(PLUS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(plus(2ndsneg(z0, z1), x1)) → c75(PLUS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(plus(pi(z0), x1)) → c75(PLUS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(plus(plus(z0, z1), x1)) → c75(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(plus(times(z0, z1), x1)) → c75(PLUS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(plus(square(z0), x1)) → c75(PLUS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(plus(x0, 0)) → c75(PLUS(proper(x0), ok(0)), PROPER(x0))
PROPER(plus(x0, nil)) → c75(PLUS(proper(x0), ok(nil)), PROPER(x0))
PROPER(plus(x0, rnil)) → c75(PLUS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(plus(0, x1)) → c75(PLUS(ok(0), proper(x1)), PROPER(x1))
PROPER(plus(nil, x1)) → c75(PLUS(ok(nil), proper(x1)), PROPER(x1))
PROPER(plus(rnil, x1)) → c75(PLUS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(times(x0, s(z0))) → c76(TIMES(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(times(x0, posrecip(z0))) → c76(TIMES(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(times(x0, negrecip(z0))) → c76(TIMES(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(times(x0, cons(z0, z1))) → c76(TIMES(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(times(x0, cons2(z0, z1))) → c76(TIMES(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(times(x0, rcons(z0, z1))) → c76(TIMES(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(times(x0, from(z0))) → c76(TIMES(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(times(x0, 2ndspos(z0, z1))) → c76(TIMES(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(times(x0, 2ndsneg(z0, z1))) → c76(TIMES(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(times(x0, pi(z0))) → c76(TIMES(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(times(x0, plus(z0, z1))) → c76(TIMES(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(times(x0, times(z0, z1))) → c76(TIMES(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(times(x0, square(z0))) → c76(TIMES(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(times(s(z0), x1)) → c76(TIMES(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(times(posrecip(z0), x1)) → c76(TIMES(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(times(negrecip(z0), x1)) → c76(TIMES(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(times(cons(z0, z1), x1)) → c76(TIMES(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(times(cons2(z0, z1), x1)) → c76(TIMES(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(times(rcons(z0, z1), x1)) → c76(TIMES(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(times(from(z0), x1)) → c76(TIMES(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(times(2ndspos(z0, z1), x1)) → c76(TIMES(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(times(2ndsneg(z0, z1), x1)) → c76(TIMES(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(times(pi(z0), x1)) → c76(TIMES(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(times(plus(z0, z1), x1)) → c76(TIMES(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(times(times(z0, z1), x1)) → c76(TIMES(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(times(square(z0), x1)) → c76(TIMES(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(times(x0, 0)) → c76(TIMES(proper(x0), ok(0)), PROPER(x0))
PROPER(times(x0, nil)) → c76(TIMES(proper(x0), ok(nil)), PROPER(x0))
PROPER(times(x0, rnil)) → c76(TIMES(proper(x0), ok(rnil)), PROPER(x0))
PROPER(times(0, x1)) → c76(TIMES(ok(0), proper(x1)), PROPER(x1))
PROPER(times(nil, x1)) → c76(TIMES(ok(nil), proper(x1)), PROPER(x1))
PROPER(times(rnil, x1)) → c76(TIMES(ok(rnil), proper(x1)), PROPER(x1))
K tuples:none
Defined Rule Symbols:
active, 2ndspos, cons2, rcons, posrecip, 2ndsneg, negrecip, s, cons, from, pi, plus, times, square, proper
Defined Pair Symbols:
ACTIVE, S, POSRECIP, NEGRECIP, CONS, CONS2, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP
Compound Symbols:
c12, c18, c19, c21, c22, c23, c24, c26, c27, c28, c29, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c77, c78, c79, c, c7, c9, c11, c1, c13, c14, c15, c16, c17, c20, c25, c30, c63, c63, c64, c64, c65, c65, c67, c67, c68, c68, c70, c70, c71, c71, c72, c72, c73, c73, c74, c74, c75, c75, c76, c76
(75) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
PROPER(
square(
z0)) →
c77(
SQUARE(
proper(
z0)),
PROPER(
z0)) by
PROPER(square(0)) → c77(SQUARE(ok(0)), PROPER(0))
PROPER(square(s(z0))) → c77(SQUARE(s(proper(z0))), PROPER(s(z0)))
PROPER(square(posrecip(z0))) → c77(SQUARE(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(square(negrecip(z0))) → c77(SQUARE(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(square(nil)) → c77(SQUARE(ok(nil)), PROPER(nil))
PROPER(square(cons(z0, z1))) → c77(SQUARE(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(square(cons2(z0, z1))) → c77(SQUARE(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(square(rnil)) → c77(SQUARE(ok(rnil)), PROPER(rnil))
PROPER(square(rcons(z0, z1))) → c77(SQUARE(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(square(from(z0))) → c77(SQUARE(from(proper(z0))), PROPER(from(z0)))
PROPER(square(2ndspos(z0, z1))) → c77(SQUARE(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(square(2ndsneg(z0, z1))) → c77(SQUARE(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(square(pi(z0))) → c77(SQUARE(pi(proper(z0))), PROPER(pi(z0)))
PROPER(square(plus(z0, z1))) → c77(SQUARE(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(square(times(z0, z1))) → c77(SQUARE(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(square(square(z0))) → c77(SQUARE(square(proper(z0))), PROPER(square(z0)))
(76) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(2ndspos(0, z0)) → mark(rnil)
active(2ndspos(s(z0), cons(z1, z2))) → mark(2ndspos(s(z0), cons2(z1, z2)))
active(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(z1, z2))) → mark(2ndsneg(s(z0), cons2(z1, z2)))
active(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
active(pi(z0)) → mark(2ndspos(z0, from(0)))
active(plus(0, z0)) → mark(z0)
active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
active(times(0, z0)) → mark(0)
active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
active(square(z0)) → mark(times(z0, z0))
active(s(z0)) → s(active(z0))
active(posrecip(z0)) → posrecip(active(z0))
active(negrecip(z0)) → negrecip(active(z0))
active(cons(z0, z1)) → cons(active(z0), z1)
active(cons2(z0, z1)) → cons2(z0, active(z1))
active(rcons(z0, z1)) → rcons(active(z0), z1)
active(rcons(z0, z1)) → rcons(z0, active(z1))
active(from(z0)) → from(active(z0))
active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
active(pi(z0)) → pi(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(times(z0, z1)) → times(active(z0), z1)
active(times(z0, z1)) → times(z0, active(z1))
active(square(z0)) → square(active(z0))
2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
cons2(z0, mark(z1)) → mark(cons2(z0, z1))
cons2(ok(z0), ok(z1)) → ok(cons2(z0, z1))
rcons(mark(z0), z1) → mark(rcons(z0, z1))
rcons(z0, mark(z1)) → mark(rcons(z0, z1))
rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
posrecip(ok(z0)) → ok(posrecip(z0))
posrecip(mark(z0)) → mark(posrecip(z0))
2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
negrecip(ok(z0)) → ok(negrecip(z0))
negrecip(mark(z0)) → mark(negrecip(z0))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
cons(mark(z0), z1) → mark(cons(z0, z1))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
from(mark(z0)) → mark(from(z0))
from(ok(z0)) → ok(from(z0))
pi(mark(z0)) → mark(pi(z0))
pi(ok(z0)) → ok(pi(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
times(mark(z0), z1) → mark(times(z0, z1))
times(ok(z0), ok(z1)) → ok(times(z0, z1))
times(z0, mark(z1)) → mark(times(z0, z1))
square(mark(z0)) → mark(square(z0))
square(ok(z0)) → ok(square(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(posrecip(z0)) → posrecip(proper(z0))
proper(negrecip(z0)) → negrecip(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(cons2(z0, z1)) → cons2(proper(z0), proper(z1))
proper(rnil) → ok(rnil)
proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
proper(pi(z0)) → pi(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(times(z0, z1)) → times(proper(z0), proper(z1))
proper(square(z0)) → square(proper(z0))
Tuples:
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
TOP(mark(z0)) → c78(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c79(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c9(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(2NDSPOS(s(z0), cons2(z1, z2)))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(2NDSNEG(s(z0), cons2(z1, z2)))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c13(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, z2)))) → c13(S(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(s(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, z2)))) → c13(S(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(s(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c13(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c13(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c13(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c13(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c13(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c13(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c13(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c13(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(cons2(z0, z1))) → c13(S(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c13(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c13(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c13(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c14(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c14(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c14(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c14(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c14(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c14(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c14(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c14(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(cons2(z0, z1))) → c14(POSRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c15(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c15(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c15(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c15(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c15(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c15(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c15(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c15(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(cons2(z0, z1))) → c15(NEGRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndspos(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndspos(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndsneg(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndsneg(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c16(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c16(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c16(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c16(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c16(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c16(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c16(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c16(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(cons2(z0, z1), x1)) → c16(CONS(cons2(z0, active(z1)), x1), ACTIVE(cons2(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, 2ndsneg(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(0, z0))) → c17(CONS2(x0, mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(cons2(x0, plus(s(z0), z1))) → c17(CONS2(x0, mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons2(x0, times(0, z0))) → c17(CONS2(x0, mark(0)), ACTIVE(times(0, z0)))
ACTIVE(cons2(x0, times(s(z0), z1))) → c17(CONS2(x0, mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(cons2(x0, s(z0))) → c17(CONS2(x0, s(active(z0))), ACTIVE(s(z0)))
ACTIVE(cons2(x0, posrecip(z0))) → c17(CONS2(x0, posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(cons2(x0, negrecip(z0))) → c17(CONS2(x0, negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(cons2(x0, cons(z0, z1))) → c17(CONS2(x0, cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(cons2(x0, cons2(z0, z1))) → c17(CONS2(x0, cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, from(active(z0))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, square(active(z0))), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c20(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(from(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(from(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c20(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c20(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c20(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c20(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c20(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c20(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c20(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c20(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c20(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c20(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(cons2(z0, z1))) → c20(FROM(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c20(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c20(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c20(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c25(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c25(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c25(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c25(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c25(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c25(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c25(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c25(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c25(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c25(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c25(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(cons2(z0, z1))) → c25(PI(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c25(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c25(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c25(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c30(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(square(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(square(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c30(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c30(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c30(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c30(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c30(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c30(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c30(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c30(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c30(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(cons2(z0, z1))) → c30(SQUARE(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c30(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c30(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c63(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c63(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c63(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c63(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(cons2(z0, z1))) → c63(S(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(s(rcons(z0, z1))) → c63(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c63(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c63(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c63(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c63(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c63(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c63(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c63(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c63(S(ok(0)))
PROPER(s(nil)) → c63(S(ok(nil)))
PROPER(s(rnil)) → c63(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c64(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c64(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c64(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c64(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(cons2(z0, z1))) → c64(POSRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c64(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c64(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c64(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c64(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c64(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c64(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c64(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c64(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c64(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c64(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c64(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c65(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c65(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c65(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c65(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(cons2(z0, z1))) → c65(NEGRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c65(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c65(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c65(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c65(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c65(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c65(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c65(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c65(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c65(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c65(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c65(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c67(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c67(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c67(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c67(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, cons2(z0, z1))) → c67(CONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c67(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c67(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c67(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c67(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c67(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c67(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c67(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c67(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c67(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c67(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c67(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c67(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(cons2(z0, z1), x1)) → c67(CONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c67(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c67(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c67(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c67(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c67(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c67(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c67(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c67(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c67(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c67(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c67(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c67(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c67(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c67(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(cons2(x0, s(z0))) → c68(CONS2(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons2(x0, posrecip(z0))) → c68(CONS2(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons2(x0, negrecip(z0))) → c68(CONS2(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons2(x0, cons(z0, z1))) → c68(CONS2(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons2(x0, cons2(z0, z1))) → c68(CONS2(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons2(x0, rcons(z0, z1))) → c68(CONS2(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons2(x0, from(z0))) → c68(CONS2(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons2(x0, 2ndspos(z0, z1))) → c68(CONS2(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons2(x0, 2ndsneg(z0, z1))) → c68(CONS2(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons2(x0, pi(z0))) → c68(CONS2(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons2(x0, plus(z0, z1))) → c68(CONS2(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons2(x0, times(z0, z1))) → c68(CONS2(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons2(x0, square(z0))) → c68(CONS2(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons2(s(z0), x1)) → c68(CONS2(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons2(posrecip(z0), x1)) → c68(CONS2(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons2(negrecip(z0), x1)) → c68(CONS2(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons2(cons(z0, z1), x1)) → c68(CONS2(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons2(cons2(z0, z1), x1)) → c68(CONS2(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons2(rcons(z0, z1), x1)) → c68(CONS2(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons2(from(z0), x1)) → c68(CONS2(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons2(2ndspos(z0, z1), x1)) → c68(CONS2(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons2(2ndsneg(z0, z1), x1)) → c68(CONS2(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons2(pi(z0), x1)) → c68(CONS2(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons2(plus(z0, z1), x1)) → c68(CONS2(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons2(times(z0, z1), x1)) → c68(CONS2(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons2(square(z0), x1)) → c68(CONS2(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons2(x0, 0)) → c68(CONS2(proper(x0), ok(0)), PROPER(x0))
PROPER(cons2(x0, nil)) → c68(CONS2(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons2(x0, rnil)) → c68(CONS2(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons2(0, x1)) → c68(CONS2(ok(0), proper(x1)), PROPER(x1))
PROPER(cons2(nil, x1)) → c68(CONS2(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons2(rnil, x1)) → c68(CONS2(ok(rnil), proper(x1)), PROPER(x1))
PROPER(rcons(x0, s(z0))) → c70(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c70(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c70(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, cons(z0, z1))) → c70(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, cons2(z0, z1))) → c70(RCONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(rcons(x0, rcons(z0, z1))) → c70(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c70(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c70(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c70(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c70(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c70(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c70(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c70(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(s(z0), x1)) → c70(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c70(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c70(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c70(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(cons2(z0, z1), x1)) → c70(RCONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c70(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c70(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c70(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c70(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c70(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c70(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c70(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c70(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(rcons(x0, 0)) → c70(RCONS(proper(x0), ok(0)), PROPER(x0))
PROPER(rcons(x0, nil)) → c70(RCONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(rcons(x0, rnil)) → c70(RCONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(rcons(0, x1)) → c70(RCONS(ok(0), proper(x1)), PROPER(x1))
PROPER(rcons(nil, x1)) → c70(RCONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c70(RCONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(from(s(z0))) → c71(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(posrecip(z0))) → c71(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(from(negrecip(z0))) → c71(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(from(cons(z0, z1))) → c71(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(cons2(z0, z1))) → c71(FROM(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(from(rcons(z0, z1))) → c71(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(from(from(z0))) → c71(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(2ndspos(z0, z1))) → c71(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(from(2ndsneg(z0, z1))) → c71(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(from(pi(z0))) → c71(FROM(pi(proper(z0))), PROPER(pi(z0)))
PROPER(from(plus(z0, z1))) → c71(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(from(times(z0, z1))) → c71(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(from(square(z0))) → c71(FROM(square(proper(z0))), PROPER(square(z0)))
PROPER(from(0)) → c71(FROM(ok(0)))
PROPER(from(nil)) → c71(FROM(ok(nil)))
PROPER(from(rnil)) → c71(FROM(ok(rnil)))
PROPER(2ndspos(x0, s(z0))) → c72(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndspos(x0, posrecip(z0))) → c72(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndspos(x0, negrecip(z0))) → c72(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndspos(x0, cons(z0, z1))) → c72(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndspos(x0, cons2(z0, z1))) → c72(2NDSPOS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(2ndspos(x0, rcons(z0, z1))) → c72(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndspos(x0, from(z0))) → c72(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c72(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c72(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndspos(x0, pi(z0))) → c72(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndspos(x0, plus(z0, z1))) → c72(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndspos(x0, times(z0, z1))) → c72(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndspos(x0, square(z0))) → c72(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndspos(s(z0), x1)) → c72(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndspos(posrecip(z0), x1)) → c72(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndspos(negrecip(z0), x1)) → c72(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndspos(cons(z0, z1), x1)) → c72(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndspos(cons2(z0, z1), x1)) → c72(2NDSPOS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(2ndspos(rcons(z0, z1), x1)) → c72(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndspos(from(z0), x1)) → c72(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c72(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c72(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndspos(pi(z0), x1)) → c72(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndspos(plus(z0, z1), x1)) → c72(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndspos(times(z0, z1), x1)) → c72(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndspos(square(z0), x1)) → c72(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndspos(x0, 0)) → c72(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndspos(x0, nil)) → c72(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndspos(x0, rnil)) → c72(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndspos(0, x1)) → c72(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndspos(nil, x1)) → c72(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndspos(rnil, x1)) → c72(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(x0, s(z0))) → c73(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndsneg(x0, posrecip(z0))) → c73(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndsneg(x0, negrecip(z0))) → c73(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndsneg(x0, cons(z0, z1))) → c73(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndsneg(x0, cons2(z0, z1))) → c73(2NDSNEG(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(2ndsneg(x0, rcons(z0, z1))) → c73(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndsneg(x0, from(z0))) → c73(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c73(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c73(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndsneg(x0, pi(z0))) → c73(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndsneg(x0, plus(z0, z1))) → c73(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndsneg(x0, times(z0, z1))) → c73(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndsneg(x0, square(z0))) → c73(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndsneg(s(z0), x1)) → c73(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndsneg(posrecip(z0), x1)) → c73(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndsneg(negrecip(z0), x1)) → c73(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndsneg(cons(z0, z1), x1)) → c73(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(cons2(z0, z1), x1)) → c73(2NDSNEG(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(2ndsneg(rcons(z0, z1), x1)) → c73(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(from(z0), x1)) → c73(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c73(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c73(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndsneg(pi(z0), x1)) → c73(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndsneg(plus(z0, z1), x1)) → c73(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndsneg(times(z0, z1), x1)) → c73(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndsneg(square(z0), x1)) → c73(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndsneg(x0, 0)) → c73(2NDSNEG(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndsneg(x0, nil)) → c73(2NDSNEG(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndsneg(x0, rnil)) → c73(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndsneg(0, x1)) → c73(2NDSNEG(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndsneg(nil, x1)) → c73(2NDSNEG(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(rnil, x1)) → c73(2NDSNEG(ok(rnil), proper(x1)), PROPER(x1))
PROPER(pi(s(z0))) → c74(PI(s(proper(z0))), PROPER(s(z0)))
PROPER(pi(posrecip(z0))) → c74(PI(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(pi(negrecip(z0))) → c74(PI(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(pi(cons(z0, z1))) → c74(PI(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(pi(cons2(z0, z1))) → c74(PI(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(pi(rcons(z0, z1))) → c74(PI(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(pi(from(z0))) → c74(PI(from(proper(z0))), PROPER(from(z0)))
PROPER(pi(2ndspos(z0, z1))) → c74(PI(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(pi(2ndsneg(z0, z1))) → c74(PI(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(pi(pi(z0))) → c74(PI(pi(proper(z0))), PROPER(pi(z0)))
PROPER(pi(plus(z0, z1))) → c74(PI(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(pi(times(z0, z1))) → c74(PI(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(pi(square(z0))) → c74(PI(square(proper(z0))), PROPER(square(z0)))
PROPER(pi(0)) → c74(PI(ok(0)))
PROPER(pi(nil)) → c74(PI(ok(nil)))
PROPER(pi(rnil)) → c74(PI(ok(rnil)))
PROPER(plus(x0, s(z0))) → c75(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(plus(x0, posrecip(z0))) → c75(PLUS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(plus(x0, negrecip(z0))) → c75(PLUS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(plus(x0, cons(z0, z1))) → c75(PLUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(plus(x0, cons2(z0, z1))) → c75(PLUS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(plus(x0, rcons(z0, z1))) → c75(PLUS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(plus(x0, from(z0))) → c75(PLUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(plus(x0, 2ndspos(z0, z1))) → c75(PLUS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(plus(x0, 2ndsneg(z0, z1))) → c75(PLUS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(plus(x0, pi(z0))) → c75(PLUS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(plus(x0, plus(z0, z1))) → c75(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(plus(x0, times(z0, z1))) → c75(PLUS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(plus(x0, square(z0))) → c75(PLUS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(plus(s(z0), x1)) → c75(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(plus(posrecip(z0), x1)) → c75(PLUS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(plus(negrecip(z0), x1)) → c75(PLUS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(plus(cons(z0, z1), x1)) → c75(PLUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(plus(cons2(z0, z1), x1)) → c75(PLUS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(plus(rcons(z0, z1), x1)) → c75(PLUS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(plus(from(z0), x1)) → c75(PLUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(plus(2ndspos(z0, z1), x1)) → c75(PLUS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(plus(2ndsneg(z0, z1), x1)) → c75(PLUS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(plus(pi(z0), x1)) → c75(PLUS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(plus(plus(z0, z1), x1)) → c75(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(plus(times(z0, z1), x1)) → c75(PLUS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(plus(square(z0), x1)) → c75(PLUS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(plus(x0, 0)) → c75(PLUS(proper(x0), ok(0)), PROPER(x0))
PROPER(plus(x0, nil)) → c75(PLUS(proper(x0), ok(nil)), PROPER(x0))
PROPER(plus(x0, rnil)) → c75(PLUS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(plus(0, x1)) → c75(PLUS(ok(0), proper(x1)), PROPER(x1))
PROPER(plus(nil, x1)) → c75(PLUS(ok(nil), proper(x1)), PROPER(x1))
PROPER(plus(rnil, x1)) → c75(PLUS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(times(x0, s(z0))) → c76(TIMES(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(times(x0, posrecip(z0))) → c76(TIMES(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(times(x0, negrecip(z0))) → c76(TIMES(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(times(x0, cons(z0, z1))) → c76(TIMES(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(times(x0, cons2(z0, z1))) → c76(TIMES(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(times(x0, rcons(z0, z1))) → c76(TIMES(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(times(x0, from(z0))) → c76(TIMES(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(times(x0, 2ndspos(z0, z1))) → c76(TIMES(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(times(x0, 2ndsneg(z0, z1))) → c76(TIMES(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(times(x0, pi(z0))) → c76(TIMES(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(times(x0, plus(z0, z1))) → c76(TIMES(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(times(x0, times(z0, z1))) → c76(TIMES(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(times(x0, square(z0))) → c76(TIMES(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(times(s(z0), x1)) → c76(TIMES(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(times(posrecip(z0), x1)) → c76(TIMES(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(times(negrecip(z0), x1)) → c76(TIMES(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(times(cons(z0, z1), x1)) → c76(TIMES(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(times(cons2(z0, z1), x1)) → c76(TIMES(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(times(rcons(z0, z1), x1)) → c76(TIMES(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(times(from(z0), x1)) → c76(TIMES(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(times(2ndspos(z0, z1), x1)) → c76(TIMES(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(times(2ndsneg(z0, z1), x1)) → c76(TIMES(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(times(pi(z0), x1)) → c76(TIMES(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(times(plus(z0, z1), x1)) → c76(TIMES(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(times(times(z0, z1), x1)) → c76(TIMES(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(times(square(z0), x1)) → c76(TIMES(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(times(x0, 0)) → c76(TIMES(proper(x0), ok(0)), PROPER(x0))
PROPER(times(x0, nil)) → c76(TIMES(proper(x0), ok(nil)), PROPER(x0))
PROPER(times(x0, rnil)) → c76(TIMES(proper(x0), ok(rnil)), PROPER(x0))
PROPER(times(0, x1)) → c76(TIMES(ok(0), proper(x1)), PROPER(x1))
PROPER(times(nil, x1)) → c76(TIMES(ok(nil), proper(x1)), PROPER(x1))
PROPER(times(rnil, x1)) → c76(TIMES(ok(rnil), proper(x1)), PROPER(x1))
PROPER(square(0)) → c77(SQUARE(ok(0)), PROPER(0))
PROPER(square(s(z0))) → c77(SQUARE(s(proper(z0))), PROPER(s(z0)))
PROPER(square(posrecip(z0))) → c77(SQUARE(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(square(negrecip(z0))) → c77(SQUARE(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(square(nil)) → c77(SQUARE(ok(nil)), PROPER(nil))
PROPER(square(cons(z0, z1))) → c77(SQUARE(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(square(cons2(z0, z1))) → c77(SQUARE(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(square(rnil)) → c77(SQUARE(ok(rnil)), PROPER(rnil))
PROPER(square(rcons(z0, z1))) → c77(SQUARE(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(square(from(z0))) → c77(SQUARE(from(proper(z0))), PROPER(from(z0)))
PROPER(square(2ndspos(z0, z1))) → c77(SQUARE(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(square(2ndsneg(z0, z1))) → c77(SQUARE(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(square(pi(z0))) → c77(SQUARE(pi(proper(z0))), PROPER(pi(z0)))
PROPER(square(plus(z0, z1))) → c77(SQUARE(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(square(times(z0, z1))) → c77(SQUARE(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(square(square(z0))) → c77(SQUARE(square(proper(z0))), PROPER(square(z0)))
S tuples:
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
TOP(mark(z0)) → c78(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c79(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c9(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(2NDSPOS(s(z0), cons2(z1, z2)))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(2NDSNEG(s(z0), cons2(z1, z2)))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c13(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, z2)))) → c13(S(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(s(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, z2)))) → c13(S(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(s(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c13(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c13(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c13(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c13(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c13(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c13(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c13(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c13(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(cons2(z0, z1))) → c13(S(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c13(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c13(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c13(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c14(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c14(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c14(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c14(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c14(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c14(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c14(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c14(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(cons2(z0, z1))) → c14(POSRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c15(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c15(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c15(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c15(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c15(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c15(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c15(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c15(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(cons2(z0, z1))) → c15(NEGRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndspos(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndspos(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndsneg(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndsneg(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c16(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c16(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c16(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c16(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c16(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c16(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c16(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c16(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(cons2(z0, z1), x1)) → c16(CONS(cons2(z0, active(z1)), x1), ACTIVE(cons2(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, 2ndsneg(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(0, z0))) → c17(CONS2(x0, mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(cons2(x0, plus(s(z0), z1))) → c17(CONS2(x0, mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons2(x0, times(0, z0))) → c17(CONS2(x0, mark(0)), ACTIVE(times(0, z0)))
ACTIVE(cons2(x0, times(s(z0), z1))) → c17(CONS2(x0, mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(cons2(x0, s(z0))) → c17(CONS2(x0, s(active(z0))), ACTIVE(s(z0)))
ACTIVE(cons2(x0, posrecip(z0))) → c17(CONS2(x0, posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(cons2(x0, negrecip(z0))) → c17(CONS2(x0, negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(cons2(x0, cons(z0, z1))) → c17(CONS2(x0, cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(cons2(x0, cons2(z0, z1))) → c17(CONS2(x0, cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, from(active(z0))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, square(active(z0))), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c20(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(from(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(from(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c20(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c20(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c20(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c20(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c20(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c20(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c20(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c20(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c20(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c20(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(cons2(z0, z1))) → c20(FROM(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c20(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c20(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c20(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c25(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c25(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c25(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c25(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c25(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c25(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c25(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c25(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c25(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c25(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c25(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(cons2(z0, z1))) → c25(PI(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c25(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c25(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c25(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c30(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(square(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(square(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c30(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c30(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c30(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c30(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c30(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c30(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c30(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c30(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c30(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(cons2(z0, z1))) → c30(SQUARE(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c30(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c30(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c63(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c63(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c63(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c63(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(cons2(z0, z1))) → c63(S(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(s(rcons(z0, z1))) → c63(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c63(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c63(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c63(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c63(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c63(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c63(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c63(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c63(S(ok(0)))
PROPER(s(nil)) → c63(S(ok(nil)))
PROPER(s(rnil)) → c63(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c64(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c64(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c64(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c64(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(cons2(z0, z1))) → c64(POSRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c64(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c64(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c64(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c64(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c64(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c64(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c64(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c64(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c64(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c64(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c64(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c65(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c65(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c65(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c65(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(cons2(z0, z1))) → c65(NEGRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c65(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c65(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c65(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c65(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c65(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c65(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c65(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c65(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c65(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c65(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c65(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c67(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c67(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c67(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c67(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, cons2(z0, z1))) → c67(CONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c67(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c67(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c67(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c67(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c67(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c67(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c67(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c67(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c67(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c67(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c67(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c67(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(cons2(z0, z1), x1)) → c67(CONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c67(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c67(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c67(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c67(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c67(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c67(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c67(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c67(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c67(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c67(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c67(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c67(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c67(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c67(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(cons2(x0, s(z0))) → c68(CONS2(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons2(x0, posrecip(z0))) → c68(CONS2(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons2(x0, negrecip(z0))) → c68(CONS2(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons2(x0, cons(z0, z1))) → c68(CONS2(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons2(x0, cons2(z0, z1))) → c68(CONS2(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons2(x0, rcons(z0, z1))) → c68(CONS2(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons2(x0, from(z0))) → c68(CONS2(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons2(x0, 2ndspos(z0, z1))) → c68(CONS2(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons2(x0, 2ndsneg(z0, z1))) → c68(CONS2(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons2(x0, pi(z0))) → c68(CONS2(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons2(x0, plus(z0, z1))) → c68(CONS2(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons2(x0, times(z0, z1))) → c68(CONS2(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons2(x0, square(z0))) → c68(CONS2(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons2(s(z0), x1)) → c68(CONS2(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons2(posrecip(z0), x1)) → c68(CONS2(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons2(negrecip(z0), x1)) → c68(CONS2(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons2(cons(z0, z1), x1)) → c68(CONS2(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons2(cons2(z0, z1), x1)) → c68(CONS2(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons2(rcons(z0, z1), x1)) → c68(CONS2(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons2(from(z0), x1)) → c68(CONS2(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons2(2ndspos(z0, z1), x1)) → c68(CONS2(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons2(2ndsneg(z0, z1), x1)) → c68(CONS2(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons2(pi(z0), x1)) → c68(CONS2(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons2(plus(z0, z1), x1)) → c68(CONS2(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons2(times(z0, z1), x1)) → c68(CONS2(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons2(square(z0), x1)) → c68(CONS2(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons2(x0, 0)) → c68(CONS2(proper(x0), ok(0)), PROPER(x0))
PROPER(cons2(x0, nil)) → c68(CONS2(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons2(x0, rnil)) → c68(CONS2(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons2(0, x1)) → c68(CONS2(ok(0), proper(x1)), PROPER(x1))
PROPER(cons2(nil, x1)) → c68(CONS2(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons2(rnil, x1)) → c68(CONS2(ok(rnil), proper(x1)), PROPER(x1))
PROPER(rcons(x0, s(z0))) → c70(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c70(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c70(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, cons(z0, z1))) → c70(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, cons2(z0, z1))) → c70(RCONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(rcons(x0, rcons(z0, z1))) → c70(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c70(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c70(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c70(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c70(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c70(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c70(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c70(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(s(z0), x1)) → c70(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c70(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c70(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c70(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(cons2(z0, z1), x1)) → c70(RCONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c70(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c70(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c70(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c70(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c70(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c70(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c70(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c70(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(rcons(x0, 0)) → c70(RCONS(proper(x0), ok(0)), PROPER(x0))
PROPER(rcons(x0, nil)) → c70(RCONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(rcons(x0, rnil)) → c70(RCONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(rcons(0, x1)) → c70(RCONS(ok(0), proper(x1)), PROPER(x1))
PROPER(rcons(nil, x1)) → c70(RCONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c70(RCONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(from(s(z0))) → c71(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(posrecip(z0))) → c71(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(from(negrecip(z0))) → c71(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(from(cons(z0, z1))) → c71(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(cons2(z0, z1))) → c71(FROM(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(from(rcons(z0, z1))) → c71(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(from(from(z0))) → c71(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(2ndspos(z0, z1))) → c71(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(from(2ndsneg(z0, z1))) → c71(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(from(pi(z0))) → c71(FROM(pi(proper(z0))), PROPER(pi(z0)))
PROPER(from(plus(z0, z1))) → c71(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(from(times(z0, z1))) → c71(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(from(square(z0))) → c71(FROM(square(proper(z0))), PROPER(square(z0)))
PROPER(from(0)) → c71(FROM(ok(0)))
PROPER(from(nil)) → c71(FROM(ok(nil)))
PROPER(from(rnil)) → c71(FROM(ok(rnil)))
PROPER(2ndspos(x0, s(z0))) → c72(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndspos(x0, posrecip(z0))) → c72(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndspos(x0, negrecip(z0))) → c72(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndspos(x0, cons(z0, z1))) → c72(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndspos(x0, cons2(z0, z1))) → c72(2NDSPOS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(2ndspos(x0, rcons(z0, z1))) → c72(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndspos(x0, from(z0))) → c72(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c72(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c72(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndspos(x0, pi(z0))) → c72(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndspos(x0, plus(z0, z1))) → c72(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndspos(x0, times(z0, z1))) → c72(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndspos(x0, square(z0))) → c72(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndspos(s(z0), x1)) → c72(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndspos(posrecip(z0), x1)) → c72(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndspos(negrecip(z0), x1)) → c72(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndspos(cons(z0, z1), x1)) → c72(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndspos(cons2(z0, z1), x1)) → c72(2NDSPOS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(2ndspos(rcons(z0, z1), x1)) → c72(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndspos(from(z0), x1)) → c72(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c72(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c72(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndspos(pi(z0), x1)) → c72(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndspos(plus(z0, z1), x1)) → c72(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndspos(times(z0, z1), x1)) → c72(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndspos(square(z0), x1)) → c72(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndspos(x0, 0)) → c72(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndspos(x0, nil)) → c72(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndspos(x0, rnil)) → c72(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndspos(0, x1)) → c72(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndspos(nil, x1)) → c72(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndspos(rnil, x1)) → c72(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(x0, s(z0))) → c73(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndsneg(x0, posrecip(z0))) → c73(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndsneg(x0, negrecip(z0))) → c73(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndsneg(x0, cons(z0, z1))) → c73(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndsneg(x0, cons2(z0, z1))) → c73(2NDSNEG(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(2ndsneg(x0, rcons(z0, z1))) → c73(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndsneg(x0, from(z0))) → c73(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c73(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c73(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndsneg(x0, pi(z0))) → c73(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndsneg(x0, plus(z0, z1))) → c73(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndsneg(x0, times(z0, z1))) → c73(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndsneg(x0, square(z0))) → c73(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndsneg(s(z0), x1)) → c73(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndsneg(posrecip(z0), x1)) → c73(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndsneg(negrecip(z0), x1)) → c73(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndsneg(cons(z0, z1), x1)) → c73(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(cons2(z0, z1), x1)) → c73(2NDSNEG(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(2ndsneg(rcons(z0, z1), x1)) → c73(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(from(z0), x1)) → c73(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c73(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c73(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndsneg(pi(z0), x1)) → c73(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndsneg(plus(z0, z1), x1)) → c73(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndsneg(times(z0, z1), x1)) → c73(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndsneg(square(z0), x1)) → c73(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndsneg(x0, 0)) → c73(2NDSNEG(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndsneg(x0, nil)) → c73(2NDSNEG(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndsneg(x0, rnil)) → c73(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndsneg(0, x1)) → c73(2NDSNEG(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndsneg(nil, x1)) → c73(2NDSNEG(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(rnil, x1)) → c73(2NDSNEG(ok(rnil), proper(x1)), PROPER(x1))
PROPER(pi(s(z0))) → c74(PI(s(proper(z0))), PROPER(s(z0)))
PROPER(pi(posrecip(z0))) → c74(PI(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(pi(negrecip(z0))) → c74(PI(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(pi(cons(z0, z1))) → c74(PI(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(pi(cons2(z0, z1))) → c74(PI(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(pi(rcons(z0, z1))) → c74(PI(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(pi(from(z0))) → c74(PI(from(proper(z0))), PROPER(from(z0)))
PROPER(pi(2ndspos(z0, z1))) → c74(PI(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(pi(2ndsneg(z0, z1))) → c74(PI(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(pi(pi(z0))) → c74(PI(pi(proper(z0))), PROPER(pi(z0)))
PROPER(pi(plus(z0, z1))) → c74(PI(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(pi(times(z0, z1))) → c74(PI(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(pi(square(z0))) → c74(PI(square(proper(z0))), PROPER(square(z0)))
PROPER(pi(0)) → c74(PI(ok(0)))
PROPER(pi(nil)) → c74(PI(ok(nil)))
PROPER(pi(rnil)) → c74(PI(ok(rnil)))
PROPER(plus(x0, s(z0))) → c75(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(plus(x0, posrecip(z0))) → c75(PLUS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(plus(x0, negrecip(z0))) → c75(PLUS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(plus(x0, cons(z0, z1))) → c75(PLUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(plus(x0, cons2(z0, z1))) → c75(PLUS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(plus(x0, rcons(z0, z1))) → c75(PLUS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(plus(x0, from(z0))) → c75(PLUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(plus(x0, 2ndspos(z0, z1))) → c75(PLUS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(plus(x0, 2ndsneg(z0, z1))) → c75(PLUS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(plus(x0, pi(z0))) → c75(PLUS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(plus(x0, plus(z0, z1))) → c75(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(plus(x0, times(z0, z1))) → c75(PLUS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(plus(x0, square(z0))) → c75(PLUS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(plus(s(z0), x1)) → c75(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(plus(posrecip(z0), x1)) → c75(PLUS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(plus(negrecip(z0), x1)) → c75(PLUS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(plus(cons(z0, z1), x1)) → c75(PLUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(plus(cons2(z0, z1), x1)) → c75(PLUS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(plus(rcons(z0, z1), x1)) → c75(PLUS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(plus(from(z0), x1)) → c75(PLUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(plus(2ndspos(z0, z1), x1)) → c75(PLUS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(plus(2ndsneg(z0, z1), x1)) → c75(PLUS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(plus(pi(z0), x1)) → c75(PLUS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(plus(plus(z0, z1), x1)) → c75(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(plus(times(z0, z1), x1)) → c75(PLUS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(plus(square(z0), x1)) → c75(PLUS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(plus(x0, 0)) → c75(PLUS(proper(x0), ok(0)), PROPER(x0))
PROPER(plus(x0, nil)) → c75(PLUS(proper(x0), ok(nil)), PROPER(x0))
PROPER(plus(x0, rnil)) → c75(PLUS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(plus(0, x1)) → c75(PLUS(ok(0), proper(x1)), PROPER(x1))
PROPER(plus(nil, x1)) → c75(PLUS(ok(nil), proper(x1)), PROPER(x1))
PROPER(plus(rnil, x1)) → c75(PLUS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(times(x0, s(z0))) → c76(TIMES(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(times(x0, posrecip(z0))) → c76(TIMES(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(times(x0, negrecip(z0))) → c76(TIMES(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(times(x0, cons(z0, z1))) → c76(TIMES(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(times(x0, cons2(z0, z1))) → c76(TIMES(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(times(x0, rcons(z0, z1))) → c76(TIMES(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(times(x0, from(z0))) → c76(TIMES(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(times(x0, 2ndspos(z0, z1))) → c76(TIMES(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(times(x0, 2ndsneg(z0, z1))) → c76(TIMES(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(times(x0, pi(z0))) → c76(TIMES(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(times(x0, plus(z0, z1))) → c76(TIMES(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(times(x0, times(z0, z1))) → c76(TIMES(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(times(x0, square(z0))) → c76(TIMES(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(times(s(z0), x1)) → c76(TIMES(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(times(posrecip(z0), x1)) → c76(TIMES(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(times(negrecip(z0), x1)) → c76(TIMES(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(times(cons(z0, z1), x1)) → c76(TIMES(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(times(cons2(z0, z1), x1)) → c76(TIMES(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(times(rcons(z0, z1), x1)) → c76(TIMES(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(times(from(z0), x1)) → c76(TIMES(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(times(2ndspos(z0, z1), x1)) → c76(TIMES(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(times(2ndsneg(z0, z1), x1)) → c76(TIMES(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(times(pi(z0), x1)) → c76(TIMES(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(times(plus(z0, z1), x1)) → c76(TIMES(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(times(times(z0, z1), x1)) → c76(TIMES(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(times(square(z0), x1)) → c76(TIMES(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(times(x0, 0)) → c76(TIMES(proper(x0), ok(0)), PROPER(x0))
PROPER(times(x0, nil)) → c76(TIMES(proper(x0), ok(nil)), PROPER(x0))
PROPER(times(x0, rnil)) → c76(TIMES(proper(x0), ok(rnil)), PROPER(x0))
PROPER(times(0, x1)) → c76(TIMES(ok(0), proper(x1)), PROPER(x1))
PROPER(times(nil, x1)) → c76(TIMES(ok(nil), proper(x1)), PROPER(x1))
PROPER(times(rnil, x1)) → c76(TIMES(ok(rnil), proper(x1)), PROPER(x1))
PROPER(square(0)) → c77(SQUARE(ok(0)), PROPER(0))
PROPER(square(s(z0))) → c77(SQUARE(s(proper(z0))), PROPER(s(z0)))
PROPER(square(posrecip(z0))) → c77(SQUARE(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(square(negrecip(z0))) → c77(SQUARE(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(square(nil)) → c77(SQUARE(ok(nil)), PROPER(nil))
PROPER(square(cons(z0, z1))) → c77(SQUARE(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(square(cons2(z0, z1))) → c77(SQUARE(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(square(rnil)) → c77(SQUARE(ok(rnil)), PROPER(rnil))
PROPER(square(rcons(z0, z1))) → c77(SQUARE(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(square(from(z0))) → c77(SQUARE(from(proper(z0))), PROPER(from(z0)))
PROPER(square(2ndspos(z0, z1))) → c77(SQUARE(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(square(2ndsneg(z0, z1))) → c77(SQUARE(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(square(pi(z0))) → c77(SQUARE(pi(proper(z0))), PROPER(pi(z0)))
PROPER(square(plus(z0, z1))) → c77(SQUARE(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(square(times(z0, z1))) → c77(SQUARE(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(square(square(z0))) → c77(SQUARE(square(proper(z0))), PROPER(square(z0)))
K tuples:none
Defined Rule Symbols:
active, 2ndspos, cons2, rcons, posrecip, 2ndsneg, negrecip, s, cons, from, pi, plus, times, square, proper
Defined Pair Symbols:
ACTIVE, S, POSRECIP, NEGRECIP, CONS, CONS2, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, TOP, PROPER
Compound Symbols:
c12, c18, c19, c21, c22, c23, c24, c26, c27, c28, c29, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c78, c79, c, c7, c9, c11, c1, c13, c14, c15, c16, c17, c20, c25, c30, c63, c63, c64, c64, c65, c65, c67, c67, c68, c68, c70, c70, c71, c71, c72, c72, c73, c73, c74, c74, c75, c75, c76, c76, c77
(77) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 3 trailing tuple parts
(78) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(2ndspos(0, z0)) → mark(rnil)
active(2ndspos(s(z0), cons(z1, z2))) → mark(2ndspos(s(z0), cons2(z1, z2)))
active(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(z1, z2))) → mark(2ndsneg(s(z0), cons2(z1, z2)))
active(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
active(pi(z0)) → mark(2ndspos(z0, from(0)))
active(plus(0, z0)) → mark(z0)
active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
active(times(0, z0)) → mark(0)
active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
active(square(z0)) → mark(times(z0, z0))
active(s(z0)) → s(active(z0))
active(posrecip(z0)) → posrecip(active(z0))
active(negrecip(z0)) → negrecip(active(z0))
active(cons(z0, z1)) → cons(active(z0), z1)
active(cons2(z0, z1)) → cons2(z0, active(z1))
active(rcons(z0, z1)) → rcons(active(z0), z1)
active(rcons(z0, z1)) → rcons(z0, active(z1))
active(from(z0)) → from(active(z0))
active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
active(pi(z0)) → pi(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(times(z0, z1)) → times(active(z0), z1)
active(times(z0, z1)) → times(z0, active(z1))
active(square(z0)) → square(active(z0))
2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
cons2(z0, mark(z1)) → mark(cons2(z0, z1))
cons2(ok(z0), ok(z1)) → ok(cons2(z0, z1))
rcons(mark(z0), z1) → mark(rcons(z0, z1))
rcons(z0, mark(z1)) → mark(rcons(z0, z1))
rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
posrecip(ok(z0)) → ok(posrecip(z0))
posrecip(mark(z0)) → mark(posrecip(z0))
2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
negrecip(ok(z0)) → ok(negrecip(z0))
negrecip(mark(z0)) → mark(negrecip(z0))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
cons(mark(z0), z1) → mark(cons(z0, z1))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
from(mark(z0)) → mark(from(z0))
from(ok(z0)) → ok(from(z0))
pi(mark(z0)) → mark(pi(z0))
pi(ok(z0)) → ok(pi(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
times(mark(z0), z1) → mark(times(z0, z1))
times(ok(z0), ok(z1)) → ok(times(z0, z1))
times(z0, mark(z1)) → mark(times(z0, z1))
square(mark(z0)) → mark(square(z0))
square(ok(z0)) → ok(square(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(posrecip(z0)) → posrecip(proper(z0))
proper(negrecip(z0)) → negrecip(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(cons2(z0, z1)) → cons2(proper(z0), proper(z1))
proper(rnil) → ok(rnil)
proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
proper(pi(z0)) → pi(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(times(z0, z1)) → times(proper(z0), proper(z1))
proper(square(z0)) → square(proper(z0))
Tuples:
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
TOP(mark(z0)) → c78(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c79(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c9(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(2NDSPOS(s(z0), cons2(z1, z2)))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(2NDSNEG(s(z0), cons2(z1, z2)))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c13(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, z2)))) → c13(S(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(s(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, z2)))) → c13(S(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(s(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c13(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c13(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c13(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c13(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c13(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c13(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c13(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c13(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(cons2(z0, z1))) → c13(S(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c13(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c13(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c13(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c14(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c14(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c14(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c14(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c14(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c14(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c14(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c14(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(cons2(z0, z1))) → c14(POSRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c15(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c15(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c15(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c15(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c15(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c15(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c15(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c15(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(cons2(z0, z1))) → c15(NEGRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndspos(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndspos(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndsneg(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndsneg(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c16(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c16(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c16(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c16(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c16(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c16(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c16(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c16(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(cons2(z0, z1), x1)) → c16(CONS(cons2(z0, active(z1)), x1), ACTIVE(cons2(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, 2ndsneg(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(0, z0))) → c17(CONS2(x0, mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(cons2(x0, plus(s(z0), z1))) → c17(CONS2(x0, mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons2(x0, times(0, z0))) → c17(CONS2(x0, mark(0)), ACTIVE(times(0, z0)))
ACTIVE(cons2(x0, times(s(z0), z1))) → c17(CONS2(x0, mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(cons2(x0, s(z0))) → c17(CONS2(x0, s(active(z0))), ACTIVE(s(z0)))
ACTIVE(cons2(x0, posrecip(z0))) → c17(CONS2(x0, posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(cons2(x0, negrecip(z0))) → c17(CONS2(x0, negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(cons2(x0, cons(z0, z1))) → c17(CONS2(x0, cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(cons2(x0, cons2(z0, z1))) → c17(CONS2(x0, cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, from(active(z0))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, square(active(z0))), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c20(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(from(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(from(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c20(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c20(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c20(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c20(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c20(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c20(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c20(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c20(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c20(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c20(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(cons2(z0, z1))) → c20(FROM(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c20(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c20(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c20(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c25(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c25(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c25(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c25(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c25(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c25(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c25(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c25(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c25(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c25(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c25(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(cons2(z0, z1))) → c25(PI(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c25(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c25(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c25(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c30(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(square(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(square(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c30(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c30(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c30(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c30(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c30(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c30(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c30(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c30(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c30(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(cons2(z0, z1))) → c30(SQUARE(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c30(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c30(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c63(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c63(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c63(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c63(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(cons2(z0, z1))) → c63(S(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(s(rcons(z0, z1))) → c63(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c63(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c63(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c63(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c63(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c63(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c63(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c63(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c63(S(ok(0)))
PROPER(s(nil)) → c63(S(ok(nil)))
PROPER(s(rnil)) → c63(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c64(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c64(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c64(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c64(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(cons2(z0, z1))) → c64(POSRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c64(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c64(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c64(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c64(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c64(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c64(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c64(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c64(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c64(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c64(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c64(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c65(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c65(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c65(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c65(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(cons2(z0, z1))) → c65(NEGRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c65(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c65(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c65(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c65(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c65(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c65(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c65(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c65(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c65(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c65(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c65(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c67(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c67(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c67(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c67(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, cons2(z0, z1))) → c67(CONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c67(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c67(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c67(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c67(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c67(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c67(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c67(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c67(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c67(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c67(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c67(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c67(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(cons2(z0, z1), x1)) → c67(CONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c67(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c67(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c67(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c67(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c67(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c67(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c67(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c67(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c67(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c67(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c67(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c67(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c67(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c67(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(cons2(x0, s(z0))) → c68(CONS2(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons2(x0, posrecip(z0))) → c68(CONS2(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons2(x0, negrecip(z0))) → c68(CONS2(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons2(x0, cons(z0, z1))) → c68(CONS2(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons2(x0, cons2(z0, z1))) → c68(CONS2(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons2(x0, rcons(z0, z1))) → c68(CONS2(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons2(x0, from(z0))) → c68(CONS2(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons2(x0, 2ndspos(z0, z1))) → c68(CONS2(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons2(x0, 2ndsneg(z0, z1))) → c68(CONS2(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons2(x0, pi(z0))) → c68(CONS2(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons2(x0, plus(z0, z1))) → c68(CONS2(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons2(x0, times(z0, z1))) → c68(CONS2(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons2(x0, square(z0))) → c68(CONS2(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons2(s(z0), x1)) → c68(CONS2(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons2(posrecip(z0), x1)) → c68(CONS2(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons2(negrecip(z0), x1)) → c68(CONS2(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons2(cons(z0, z1), x1)) → c68(CONS2(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons2(cons2(z0, z1), x1)) → c68(CONS2(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons2(rcons(z0, z1), x1)) → c68(CONS2(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons2(from(z0), x1)) → c68(CONS2(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons2(2ndspos(z0, z1), x1)) → c68(CONS2(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons2(2ndsneg(z0, z1), x1)) → c68(CONS2(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons2(pi(z0), x1)) → c68(CONS2(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons2(plus(z0, z1), x1)) → c68(CONS2(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons2(times(z0, z1), x1)) → c68(CONS2(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons2(square(z0), x1)) → c68(CONS2(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons2(x0, 0)) → c68(CONS2(proper(x0), ok(0)), PROPER(x0))
PROPER(cons2(x0, nil)) → c68(CONS2(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons2(x0, rnil)) → c68(CONS2(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons2(0, x1)) → c68(CONS2(ok(0), proper(x1)), PROPER(x1))
PROPER(cons2(nil, x1)) → c68(CONS2(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons2(rnil, x1)) → c68(CONS2(ok(rnil), proper(x1)), PROPER(x1))
PROPER(rcons(x0, s(z0))) → c70(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c70(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c70(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, cons(z0, z1))) → c70(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, cons2(z0, z1))) → c70(RCONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(rcons(x0, rcons(z0, z1))) → c70(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c70(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c70(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c70(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c70(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c70(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c70(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c70(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(s(z0), x1)) → c70(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c70(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c70(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c70(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(cons2(z0, z1), x1)) → c70(RCONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c70(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c70(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c70(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c70(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c70(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c70(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c70(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c70(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(rcons(x0, 0)) → c70(RCONS(proper(x0), ok(0)), PROPER(x0))
PROPER(rcons(x0, nil)) → c70(RCONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(rcons(x0, rnil)) → c70(RCONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(rcons(0, x1)) → c70(RCONS(ok(0), proper(x1)), PROPER(x1))
PROPER(rcons(nil, x1)) → c70(RCONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c70(RCONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(from(s(z0))) → c71(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(posrecip(z0))) → c71(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(from(negrecip(z0))) → c71(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(from(cons(z0, z1))) → c71(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(cons2(z0, z1))) → c71(FROM(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(from(rcons(z0, z1))) → c71(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(from(from(z0))) → c71(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(2ndspos(z0, z1))) → c71(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(from(2ndsneg(z0, z1))) → c71(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(from(pi(z0))) → c71(FROM(pi(proper(z0))), PROPER(pi(z0)))
PROPER(from(plus(z0, z1))) → c71(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(from(times(z0, z1))) → c71(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(from(square(z0))) → c71(FROM(square(proper(z0))), PROPER(square(z0)))
PROPER(from(0)) → c71(FROM(ok(0)))
PROPER(from(nil)) → c71(FROM(ok(nil)))
PROPER(from(rnil)) → c71(FROM(ok(rnil)))
PROPER(2ndspos(x0, s(z0))) → c72(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndspos(x0, posrecip(z0))) → c72(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndspos(x0, negrecip(z0))) → c72(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndspos(x0, cons(z0, z1))) → c72(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndspos(x0, cons2(z0, z1))) → c72(2NDSPOS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(2ndspos(x0, rcons(z0, z1))) → c72(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndspos(x0, from(z0))) → c72(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c72(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c72(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndspos(x0, pi(z0))) → c72(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndspos(x0, plus(z0, z1))) → c72(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndspos(x0, times(z0, z1))) → c72(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndspos(x0, square(z0))) → c72(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndspos(s(z0), x1)) → c72(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndspos(posrecip(z0), x1)) → c72(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndspos(negrecip(z0), x1)) → c72(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndspos(cons(z0, z1), x1)) → c72(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndspos(cons2(z0, z1), x1)) → c72(2NDSPOS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(2ndspos(rcons(z0, z1), x1)) → c72(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndspos(from(z0), x1)) → c72(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c72(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c72(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndspos(pi(z0), x1)) → c72(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndspos(plus(z0, z1), x1)) → c72(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndspos(times(z0, z1), x1)) → c72(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndspos(square(z0), x1)) → c72(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndspos(x0, 0)) → c72(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndspos(x0, nil)) → c72(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndspos(x0, rnil)) → c72(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndspos(0, x1)) → c72(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndspos(nil, x1)) → c72(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndspos(rnil, x1)) → c72(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(x0, s(z0))) → c73(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndsneg(x0, posrecip(z0))) → c73(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndsneg(x0, negrecip(z0))) → c73(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndsneg(x0, cons(z0, z1))) → c73(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndsneg(x0, cons2(z0, z1))) → c73(2NDSNEG(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(2ndsneg(x0, rcons(z0, z1))) → c73(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndsneg(x0, from(z0))) → c73(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c73(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c73(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndsneg(x0, pi(z0))) → c73(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndsneg(x0, plus(z0, z1))) → c73(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndsneg(x0, times(z0, z1))) → c73(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndsneg(x0, square(z0))) → c73(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndsneg(s(z0), x1)) → c73(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndsneg(posrecip(z0), x1)) → c73(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndsneg(negrecip(z0), x1)) → c73(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndsneg(cons(z0, z1), x1)) → c73(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(cons2(z0, z1), x1)) → c73(2NDSNEG(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(2ndsneg(rcons(z0, z1), x1)) → c73(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(from(z0), x1)) → c73(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c73(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c73(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndsneg(pi(z0), x1)) → c73(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndsneg(plus(z0, z1), x1)) → c73(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndsneg(times(z0, z1), x1)) → c73(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndsneg(square(z0), x1)) → c73(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndsneg(x0, 0)) → c73(2NDSNEG(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndsneg(x0, nil)) → c73(2NDSNEG(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndsneg(x0, rnil)) → c73(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndsneg(0, x1)) → c73(2NDSNEG(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndsneg(nil, x1)) → c73(2NDSNEG(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(rnil, x1)) → c73(2NDSNEG(ok(rnil), proper(x1)), PROPER(x1))
PROPER(pi(s(z0))) → c74(PI(s(proper(z0))), PROPER(s(z0)))
PROPER(pi(posrecip(z0))) → c74(PI(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(pi(negrecip(z0))) → c74(PI(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(pi(cons(z0, z1))) → c74(PI(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(pi(cons2(z0, z1))) → c74(PI(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(pi(rcons(z0, z1))) → c74(PI(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(pi(from(z0))) → c74(PI(from(proper(z0))), PROPER(from(z0)))
PROPER(pi(2ndspos(z0, z1))) → c74(PI(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(pi(2ndsneg(z0, z1))) → c74(PI(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(pi(pi(z0))) → c74(PI(pi(proper(z0))), PROPER(pi(z0)))
PROPER(pi(plus(z0, z1))) → c74(PI(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(pi(times(z0, z1))) → c74(PI(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(pi(square(z0))) → c74(PI(square(proper(z0))), PROPER(square(z0)))
PROPER(pi(0)) → c74(PI(ok(0)))
PROPER(pi(nil)) → c74(PI(ok(nil)))
PROPER(pi(rnil)) → c74(PI(ok(rnil)))
PROPER(plus(x0, s(z0))) → c75(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(plus(x0, posrecip(z0))) → c75(PLUS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(plus(x0, negrecip(z0))) → c75(PLUS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(plus(x0, cons(z0, z1))) → c75(PLUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(plus(x0, cons2(z0, z1))) → c75(PLUS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(plus(x0, rcons(z0, z1))) → c75(PLUS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(plus(x0, from(z0))) → c75(PLUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(plus(x0, 2ndspos(z0, z1))) → c75(PLUS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(plus(x0, 2ndsneg(z0, z1))) → c75(PLUS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(plus(x0, pi(z0))) → c75(PLUS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(plus(x0, plus(z0, z1))) → c75(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(plus(x0, times(z0, z1))) → c75(PLUS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(plus(x0, square(z0))) → c75(PLUS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(plus(s(z0), x1)) → c75(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(plus(posrecip(z0), x1)) → c75(PLUS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(plus(negrecip(z0), x1)) → c75(PLUS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(plus(cons(z0, z1), x1)) → c75(PLUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(plus(cons2(z0, z1), x1)) → c75(PLUS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(plus(rcons(z0, z1), x1)) → c75(PLUS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(plus(from(z0), x1)) → c75(PLUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(plus(2ndspos(z0, z1), x1)) → c75(PLUS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(plus(2ndsneg(z0, z1), x1)) → c75(PLUS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(plus(pi(z0), x1)) → c75(PLUS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(plus(plus(z0, z1), x1)) → c75(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(plus(times(z0, z1), x1)) → c75(PLUS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(plus(square(z0), x1)) → c75(PLUS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(plus(x0, 0)) → c75(PLUS(proper(x0), ok(0)), PROPER(x0))
PROPER(plus(x0, nil)) → c75(PLUS(proper(x0), ok(nil)), PROPER(x0))
PROPER(plus(x0, rnil)) → c75(PLUS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(plus(0, x1)) → c75(PLUS(ok(0), proper(x1)), PROPER(x1))
PROPER(plus(nil, x1)) → c75(PLUS(ok(nil), proper(x1)), PROPER(x1))
PROPER(plus(rnil, x1)) → c75(PLUS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(times(x0, s(z0))) → c76(TIMES(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(times(x0, posrecip(z0))) → c76(TIMES(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(times(x0, negrecip(z0))) → c76(TIMES(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(times(x0, cons(z0, z1))) → c76(TIMES(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(times(x0, cons2(z0, z1))) → c76(TIMES(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(times(x0, rcons(z0, z1))) → c76(TIMES(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(times(x0, from(z0))) → c76(TIMES(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(times(x0, 2ndspos(z0, z1))) → c76(TIMES(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(times(x0, 2ndsneg(z0, z1))) → c76(TIMES(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(times(x0, pi(z0))) → c76(TIMES(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(times(x0, plus(z0, z1))) → c76(TIMES(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(times(x0, times(z0, z1))) → c76(TIMES(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(times(x0, square(z0))) → c76(TIMES(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(times(s(z0), x1)) → c76(TIMES(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(times(posrecip(z0), x1)) → c76(TIMES(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(times(negrecip(z0), x1)) → c76(TIMES(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(times(cons(z0, z1), x1)) → c76(TIMES(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(times(cons2(z0, z1), x1)) → c76(TIMES(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(times(rcons(z0, z1), x1)) → c76(TIMES(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(times(from(z0), x1)) → c76(TIMES(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(times(2ndspos(z0, z1), x1)) → c76(TIMES(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(times(2ndsneg(z0, z1), x1)) → c76(TIMES(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(times(pi(z0), x1)) → c76(TIMES(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(times(plus(z0, z1), x1)) → c76(TIMES(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(times(times(z0, z1), x1)) → c76(TIMES(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(times(square(z0), x1)) → c76(TIMES(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(times(x0, 0)) → c76(TIMES(proper(x0), ok(0)), PROPER(x0))
PROPER(times(x0, nil)) → c76(TIMES(proper(x0), ok(nil)), PROPER(x0))
PROPER(times(x0, rnil)) → c76(TIMES(proper(x0), ok(rnil)), PROPER(x0))
PROPER(times(0, x1)) → c76(TIMES(ok(0), proper(x1)), PROPER(x1))
PROPER(times(nil, x1)) → c76(TIMES(ok(nil), proper(x1)), PROPER(x1))
PROPER(times(rnil, x1)) → c76(TIMES(ok(rnil), proper(x1)), PROPER(x1))
PROPER(square(s(z0))) → c77(SQUARE(s(proper(z0))), PROPER(s(z0)))
PROPER(square(posrecip(z0))) → c77(SQUARE(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(square(negrecip(z0))) → c77(SQUARE(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(square(cons(z0, z1))) → c77(SQUARE(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(square(cons2(z0, z1))) → c77(SQUARE(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(square(rcons(z0, z1))) → c77(SQUARE(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(square(from(z0))) → c77(SQUARE(from(proper(z0))), PROPER(from(z0)))
PROPER(square(2ndspos(z0, z1))) → c77(SQUARE(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(square(2ndsneg(z0, z1))) → c77(SQUARE(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(square(pi(z0))) → c77(SQUARE(pi(proper(z0))), PROPER(pi(z0)))
PROPER(square(plus(z0, z1))) → c77(SQUARE(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(square(times(z0, z1))) → c77(SQUARE(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(square(square(z0))) → c77(SQUARE(square(proper(z0))), PROPER(square(z0)))
PROPER(square(0)) → c77(SQUARE(ok(0)))
PROPER(square(nil)) → c77(SQUARE(ok(nil)))
PROPER(square(rnil)) → c77(SQUARE(ok(rnil)))
S tuples:
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
TOP(mark(z0)) → c78(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c79(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c9(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(2NDSPOS(s(z0), cons2(z1, z2)))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(2NDSNEG(s(z0), cons2(z1, z2)))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c13(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, z2)))) → c13(S(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(s(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, z2)))) → c13(S(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(s(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c13(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c13(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c13(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c13(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c13(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c13(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c13(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c13(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(cons2(z0, z1))) → c13(S(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c13(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c13(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c13(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c14(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c14(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c14(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c14(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c14(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c14(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c14(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c14(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(cons2(z0, z1))) → c14(POSRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c15(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c15(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c15(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c15(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c15(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c15(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c15(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c15(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(cons2(z0, z1))) → c15(NEGRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndspos(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndspos(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndsneg(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndsneg(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c16(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c16(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c16(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c16(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c16(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c16(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c16(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c16(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(cons2(z0, z1), x1)) → c16(CONS(cons2(z0, active(z1)), x1), ACTIVE(cons2(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, 2ndsneg(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(0, z0))) → c17(CONS2(x0, mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(cons2(x0, plus(s(z0), z1))) → c17(CONS2(x0, mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons2(x0, times(0, z0))) → c17(CONS2(x0, mark(0)), ACTIVE(times(0, z0)))
ACTIVE(cons2(x0, times(s(z0), z1))) → c17(CONS2(x0, mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(cons2(x0, s(z0))) → c17(CONS2(x0, s(active(z0))), ACTIVE(s(z0)))
ACTIVE(cons2(x0, posrecip(z0))) → c17(CONS2(x0, posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(cons2(x0, negrecip(z0))) → c17(CONS2(x0, negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(cons2(x0, cons(z0, z1))) → c17(CONS2(x0, cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(cons2(x0, cons2(z0, z1))) → c17(CONS2(x0, cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, from(active(z0))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, square(active(z0))), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c20(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(from(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(from(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c20(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c20(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c20(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c20(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c20(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c20(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c20(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c20(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c20(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c20(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(cons2(z0, z1))) → c20(FROM(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c20(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c20(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c20(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c25(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c25(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c25(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c25(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c25(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c25(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c25(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c25(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c25(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c25(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c25(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(cons2(z0, z1))) → c25(PI(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c25(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c25(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c25(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c30(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(square(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(square(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c30(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c30(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c30(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c30(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c30(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c30(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c30(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c30(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c30(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(cons2(z0, z1))) → c30(SQUARE(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c30(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c30(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c63(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c63(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c63(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c63(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(cons2(z0, z1))) → c63(S(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(s(rcons(z0, z1))) → c63(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c63(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c63(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c63(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c63(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c63(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c63(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c63(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c63(S(ok(0)))
PROPER(s(nil)) → c63(S(ok(nil)))
PROPER(s(rnil)) → c63(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c64(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c64(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c64(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c64(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(cons2(z0, z1))) → c64(POSRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c64(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c64(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c64(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c64(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c64(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c64(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c64(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c64(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c64(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c64(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c64(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c65(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c65(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c65(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c65(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(cons2(z0, z1))) → c65(NEGRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c65(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c65(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c65(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c65(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c65(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c65(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c65(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c65(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c65(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c65(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c65(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c67(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c67(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c67(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c67(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, cons2(z0, z1))) → c67(CONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c67(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c67(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c67(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c67(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c67(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c67(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c67(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c67(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c67(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c67(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c67(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c67(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(cons2(z0, z1), x1)) → c67(CONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c67(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c67(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c67(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c67(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c67(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c67(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c67(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c67(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c67(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c67(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c67(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c67(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c67(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c67(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(cons2(x0, s(z0))) → c68(CONS2(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons2(x0, posrecip(z0))) → c68(CONS2(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons2(x0, negrecip(z0))) → c68(CONS2(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons2(x0, cons(z0, z1))) → c68(CONS2(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons2(x0, cons2(z0, z1))) → c68(CONS2(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons2(x0, rcons(z0, z1))) → c68(CONS2(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons2(x0, from(z0))) → c68(CONS2(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons2(x0, 2ndspos(z0, z1))) → c68(CONS2(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons2(x0, 2ndsneg(z0, z1))) → c68(CONS2(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons2(x0, pi(z0))) → c68(CONS2(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons2(x0, plus(z0, z1))) → c68(CONS2(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons2(x0, times(z0, z1))) → c68(CONS2(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons2(x0, square(z0))) → c68(CONS2(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons2(s(z0), x1)) → c68(CONS2(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons2(posrecip(z0), x1)) → c68(CONS2(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons2(negrecip(z0), x1)) → c68(CONS2(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons2(cons(z0, z1), x1)) → c68(CONS2(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons2(cons2(z0, z1), x1)) → c68(CONS2(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons2(rcons(z0, z1), x1)) → c68(CONS2(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons2(from(z0), x1)) → c68(CONS2(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons2(2ndspos(z0, z1), x1)) → c68(CONS2(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons2(2ndsneg(z0, z1), x1)) → c68(CONS2(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons2(pi(z0), x1)) → c68(CONS2(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons2(plus(z0, z1), x1)) → c68(CONS2(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons2(times(z0, z1), x1)) → c68(CONS2(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons2(square(z0), x1)) → c68(CONS2(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons2(x0, 0)) → c68(CONS2(proper(x0), ok(0)), PROPER(x0))
PROPER(cons2(x0, nil)) → c68(CONS2(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons2(x0, rnil)) → c68(CONS2(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons2(0, x1)) → c68(CONS2(ok(0), proper(x1)), PROPER(x1))
PROPER(cons2(nil, x1)) → c68(CONS2(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons2(rnil, x1)) → c68(CONS2(ok(rnil), proper(x1)), PROPER(x1))
PROPER(rcons(x0, s(z0))) → c70(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c70(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c70(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, cons(z0, z1))) → c70(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, cons2(z0, z1))) → c70(RCONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(rcons(x0, rcons(z0, z1))) → c70(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c70(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c70(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c70(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c70(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c70(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c70(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c70(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(s(z0), x1)) → c70(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c70(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c70(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c70(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(cons2(z0, z1), x1)) → c70(RCONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c70(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c70(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c70(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c70(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c70(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c70(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c70(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c70(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(rcons(x0, 0)) → c70(RCONS(proper(x0), ok(0)), PROPER(x0))
PROPER(rcons(x0, nil)) → c70(RCONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(rcons(x0, rnil)) → c70(RCONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(rcons(0, x1)) → c70(RCONS(ok(0), proper(x1)), PROPER(x1))
PROPER(rcons(nil, x1)) → c70(RCONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c70(RCONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(from(s(z0))) → c71(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(posrecip(z0))) → c71(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(from(negrecip(z0))) → c71(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(from(cons(z0, z1))) → c71(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(cons2(z0, z1))) → c71(FROM(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(from(rcons(z0, z1))) → c71(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(from(from(z0))) → c71(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(2ndspos(z0, z1))) → c71(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(from(2ndsneg(z0, z1))) → c71(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(from(pi(z0))) → c71(FROM(pi(proper(z0))), PROPER(pi(z0)))
PROPER(from(plus(z0, z1))) → c71(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(from(times(z0, z1))) → c71(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(from(square(z0))) → c71(FROM(square(proper(z0))), PROPER(square(z0)))
PROPER(from(0)) → c71(FROM(ok(0)))
PROPER(from(nil)) → c71(FROM(ok(nil)))
PROPER(from(rnil)) → c71(FROM(ok(rnil)))
PROPER(2ndspos(x0, s(z0))) → c72(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndspos(x0, posrecip(z0))) → c72(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndspos(x0, negrecip(z0))) → c72(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndspos(x0, cons(z0, z1))) → c72(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndspos(x0, cons2(z0, z1))) → c72(2NDSPOS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(2ndspos(x0, rcons(z0, z1))) → c72(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndspos(x0, from(z0))) → c72(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c72(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c72(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndspos(x0, pi(z0))) → c72(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndspos(x0, plus(z0, z1))) → c72(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndspos(x0, times(z0, z1))) → c72(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndspos(x0, square(z0))) → c72(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndspos(s(z0), x1)) → c72(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndspos(posrecip(z0), x1)) → c72(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndspos(negrecip(z0), x1)) → c72(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndspos(cons(z0, z1), x1)) → c72(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndspos(cons2(z0, z1), x1)) → c72(2NDSPOS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(2ndspos(rcons(z0, z1), x1)) → c72(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndspos(from(z0), x1)) → c72(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c72(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c72(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndspos(pi(z0), x1)) → c72(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndspos(plus(z0, z1), x1)) → c72(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndspos(times(z0, z1), x1)) → c72(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndspos(square(z0), x1)) → c72(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndspos(x0, 0)) → c72(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndspos(x0, nil)) → c72(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndspos(x0, rnil)) → c72(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndspos(0, x1)) → c72(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndspos(nil, x1)) → c72(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndspos(rnil, x1)) → c72(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(x0, s(z0))) → c73(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndsneg(x0, posrecip(z0))) → c73(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndsneg(x0, negrecip(z0))) → c73(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndsneg(x0, cons(z0, z1))) → c73(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndsneg(x0, cons2(z0, z1))) → c73(2NDSNEG(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(2ndsneg(x0, rcons(z0, z1))) → c73(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndsneg(x0, from(z0))) → c73(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c73(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c73(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndsneg(x0, pi(z0))) → c73(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndsneg(x0, plus(z0, z1))) → c73(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndsneg(x0, times(z0, z1))) → c73(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndsneg(x0, square(z0))) → c73(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndsneg(s(z0), x1)) → c73(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndsneg(posrecip(z0), x1)) → c73(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndsneg(negrecip(z0), x1)) → c73(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndsneg(cons(z0, z1), x1)) → c73(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(cons2(z0, z1), x1)) → c73(2NDSNEG(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(2ndsneg(rcons(z0, z1), x1)) → c73(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(from(z0), x1)) → c73(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c73(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c73(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndsneg(pi(z0), x1)) → c73(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndsneg(plus(z0, z1), x1)) → c73(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndsneg(times(z0, z1), x1)) → c73(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndsneg(square(z0), x1)) → c73(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndsneg(x0, 0)) → c73(2NDSNEG(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndsneg(x0, nil)) → c73(2NDSNEG(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndsneg(x0, rnil)) → c73(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndsneg(0, x1)) → c73(2NDSNEG(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndsneg(nil, x1)) → c73(2NDSNEG(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(rnil, x1)) → c73(2NDSNEG(ok(rnil), proper(x1)), PROPER(x1))
PROPER(pi(s(z0))) → c74(PI(s(proper(z0))), PROPER(s(z0)))
PROPER(pi(posrecip(z0))) → c74(PI(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(pi(negrecip(z0))) → c74(PI(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(pi(cons(z0, z1))) → c74(PI(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(pi(cons2(z0, z1))) → c74(PI(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(pi(rcons(z0, z1))) → c74(PI(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(pi(from(z0))) → c74(PI(from(proper(z0))), PROPER(from(z0)))
PROPER(pi(2ndspos(z0, z1))) → c74(PI(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(pi(2ndsneg(z0, z1))) → c74(PI(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(pi(pi(z0))) → c74(PI(pi(proper(z0))), PROPER(pi(z0)))
PROPER(pi(plus(z0, z1))) → c74(PI(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(pi(times(z0, z1))) → c74(PI(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(pi(square(z0))) → c74(PI(square(proper(z0))), PROPER(square(z0)))
PROPER(pi(0)) → c74(PI(ok(0)))
PROPER(pi(nil)) → c74(PI(ok(nil)))
PROPER(pi(rnil)) → c74(PI(ok(rnil)))
PROPER(plus(x0, s(z0))) → c75(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(plus(x0, posrecip(z0))) → c75(PLUS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(plus(x0, negrecip(z0))) → c75(PLUS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(plus(x0, cons(z0, z1))) → c75(PLUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(plus(x0, cons2(z0, z1))) → c75(PLUS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(plus(x0, rcons(z0, z1))) → c75(PLUS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(plus(x0, from(z0))) → c75(PLUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(plus(x0, 2ndspos(z0, z1))) → c75(PLUS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(plus(x0, 2ndsneg(z0, z1))) → c75(PLUS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(plus(x0, pi(z0))) → c75(PLUS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(plus(x0, plus(z0, z1))) → c75(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(plus(x0, times(z0, z1))) → c75(PLUS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(plus(x0, square(z0))) → c75(PLUS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(plus(s(z0), x1)) → c75(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(plus(posrecip(z0), x1)) → c75(PLUS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(plus(negrecip(z0), x1)) → c75(PLUS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(plus(cons(z0, z1), x1)) → c75(PLUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(plus(cons2(z0, z1), x1)) → c75(PLUS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(plus(rcons(z0, z1), x1)) → c75(PLUS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(plus(from(z0), x1)) → c75(PLUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(plus(2ndspos(z0, z1), x1)) → c75(PLUS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(plus(2ndsneg(z0, z1), x1)) → c75(PLUS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(plus(pi(z0), x1)) → c75(PLUS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(plus(plus(z0, z1), x1)) → c75(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(plus(times(z0, z1), x1)) → c75(PLUS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(plus(square(z0), x1)) → c75(PLUS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(plus(x0, 0)) → c75(PLUS(proper(x0), ok(0)), PROPER(x0))
PROPER(plus(x0, nil)) → c75(PLUS(proper(x0), ok(nil)), PROPER(x0))
PROPER(plus(x0, rnil)) → c75(PLUS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(plus(0, x1)) → c75(PLUS(ok(0), proper(x1)), PROPER(x1))
PROPER(plus(nil, x1)) → c75(PLUS(ok(nil), proper(x1)), PROPER(x1))
PROPER(plus(rnil, x1)) → c75(PLUS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(times(x0, s(z0))) → c76(TIMES(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(times(x0, posrecip(z0))) → c76(TIMES(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(times(x0, negrecip(z0))) → c76(TIMES(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(times(x0, cons(z0, z1))) → c76(TIMES(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(times(x0, cons2(z0, z1))) → c76(TIMES(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(times(x0, rcons(z0, z1))) → c76(TIMES(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(times(x0, from(z0))) → c76(TIMES(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(times(x0, 2ndspos(z0, z1))) → c76(TIMES(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(times(x0, 2ndsneg(z0, z1))) → c76(TIMES(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(times(x0, pi(z0))) → c76(TIMES(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(times(x0, plus(z0, z1))) → c76(TIMES(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(times(x0, times(z0, z1))) → c76(TIMES(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(times(x0, square(z0))) → c76(TIMES(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(times(s(z0), x1)) → c76(TIMES(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(times(posrecip(z0), x1)) → c76(TIMES(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(times(negrecip(z0), x1)) → c76(TIMES(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(times(cons(z0, z1), x1)) → c76(TIMES(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(times(cons2(z0, z1), x1)) → c76(TIMES(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(times(rcons(z0, z1), x1)) → c76(TIMES(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(times(from(z0), x1)) → c76(TIMES(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(times(2ndspos(z0, z1), x1)) → c76(TIMES(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(times(2ndsneg(z0, z1), x1)) → c76(TIMES(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(times(pi(z0), x1)) → c76(TIMES(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(times(plus(z0, z1), x1)) → c76(TIMES(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(times(times(z0, z1), x1)) → c76(TIMES(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(times(square(z0), x1)) → c76(TIMES(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(times(x0, 0)) → c76(TIMES(proper(x0), ok(0)), PROPER(x0))
PROPER(times(x0, nil)) → c76(TIMES(proper(x0), ok(nil)), PROPER(x0))
PROPER(times(x0, rnil)) → c76(TIMES(proper(x0), ok(rnil)), PROPER(x0))
PROPER(times(0, x1)) → c76(TIMES(ok(0), proper(x1)), PROPER(x1))
PROPER(times(nil, x1)) → c76(TIMES(ok(nil), proper(x1)), PROPER(x1))
PROPER(times(rnil, x1)) → c76(TIMES(ok(rnil), proper(x1)), PROPER(x1))
PROPER(square(s(z0))) → c77(SQUARE(s(proper(z0))), PROPER(s(z0)))
PROPER(square(posrecip(z0))) → c77(SQUARE(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(square(negrecip(z0))) → c77(SQUARE(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(square(cons(z0, z1))) → c77(SQUARE(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(square(cons2(z0, z1))) → c77(SQUARE(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(square(rcons(z0, z1))) → c77(SQUARE(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(square(from(z0))) → c77(SQUARE(from(proper(z0))), PROPER(from(z0)))
PROPER(square(2ndspos(z0, z1))) → c77(SQUARE(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(square(2ndsneg(z0, z1))) → c77(SQUARE(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(square(pi(z0))) → c77(SQUARE(pi(proper(z0))), PROPER(pi(z0)))
PROPER(square(plus(z0, z1))) → c77(SQUARE(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(square(times(z0, z1))) → c77(SQUARE(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(square(square(z0))) → c77(SQUARE(square(proper(z0))), PROPER(square(z0)))
PROPER(square(0)) → c77(SQUARE(ok(0)))
PROPER(square(nil)) → c77(SQUARE(ok(nil)))
PROPER(square(rnil)) → c77(SQUARE(ok(rnil)))
K tuples:none
Defined Rule Symbols:
active, 2ndspos, cons2, rcons, posrecip, 2ndsneg, negrecip, s, cons, from, pi, plus, times, square, proper
Defined Pair Symbols:
ACTIVE, S, POSRECIP, NEGRECIP, CONS, CONS2, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, TOP, PROPER
Compound Symbols:
c12, c18, c19, c21, c22, c23, c24, c26, c27, c28, c29, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c78, c79, c, c7, c9, c11, c1, c13, c14, c15, c16, c17, c20, c25, c30, c63, c63, c64, c64, c65, c65, c67, c67, c68, c68, c70, c70, c71, c71, c72, c72, c73, c73, c74, c74, c75, c75, c76, c76, c77, c77
(79) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
TOP(
mark(
z0)) →
c78(
TOP(
proper(
z0)),
PROPER(
z0)) by
TOP(mark(0)) → c78(TOP(ok(0)), PROPER(0))
TOP(mark(s(z0))) → c78(TOP(s(proper(z0))), PROPER(s(z0)))
TOP(mark(posrecip(z0))) → c78(TOP(posrecip(proper(z0))), PROPER(posrecip(z0)))
TOP(mark(negrecip(z0))) → c78(TOP(negrecip(proper(z0))), PROPER(negrecip(z0)))
TOP(mark(nil)) → c78(TOP(ok(nil)), PROPER(nil))
TOP(mark(cons(z0, z1))) → c78(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
TOP(mark(cons2(z0, z1))) → c78(TOP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
TOP(mark(rnil)) → c78(TOP(ok(rnil)), PROPER(rnil))
TOP(mark(rcons(z0, z1))) → c78(TOP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
TOP(mark(from(z0))) → c78(TOP(from(proper(z0))), PROPER(from(z0)))
TOP(mark(2ndspos(z0, z1))) → c78(TOP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
TOP(mark(2ndsneg(z0, z1))) → c78(TOP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
TOP(mark(pi(z0))) → c78(TOP(pi(proper(z0))), PROPER(pi(z0)))
TOP(mark(plus(z0, z1))) → c78(TOP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
TOP(mark(times(z0, z1))) → c78(TOP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
TOP(mark(square(z0))) → c78(TOP(square(proper(z0))), PROPER(square(z0)))
(80) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(2ndspos(0, z0)) → mark(rnil)
active(2ndspos(s(z0), cons(z1, z2))) → mark(2ndspos(s(z0), cons2(z1, z2)))
active(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(z1, z2))) → mark(2ndsneg(s(z0), cons2(z1, z2)))
active(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
active(pi(z0)) → mark(2ndspos(z0, from(0)))
active(plus(0, z0)) → mark(z0)
active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
active(times(0, z0)) → mark(0)
active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
active(square(z0)) → mark(times(z0, z0))
active(s(z0)) → s(active(z0))
active(posrecip(z0)) → posrecip(active(z0))
active(negrecip(z0)) → negrecip(active(z0))
active(cons(z0, z1)) → cons(active(z0), z1)
active(cons2(z0, z1)) → cons2(z0, active(z1))
active(rcons(z0, z1)) → rcons(active(z0), z1)
active(rcons(z0, z1)) → rcons(z0, active(z1))
active(from(z0)) → from(active(z0))
active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
active(pi(z0)) → pi(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(times(z0, z1)) → times(active(z0), z1)
active(times(z0, z1)) → times(z0, active(z1))
active(square(z0)) → square(active(z0))
2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
cons2(z0, mark(z1)) → mark(cons2(z0, z1))
cons2(ok(z0), ok(z1)) → ok(cons2(z0, z1))
rcons(mark(z0), z1) → mark(rcons(z0, z1))
rcons(z0, mark(z1)) → mark(rcons(z0, z1))
rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
posrecip(ok(z0)) → ok(posrecip(z0))
posrecip(mark(z0)) → mark(posrecip(z0))
2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
negrecip(ok(z0)) → ok(negrecip(z0))
negrecip(mark(z0)) → mark(negrecip(z0))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
cons(mark(z0), z1) → mark(cons(z0, z1))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
from(mark(z0)) → mark(from(z0))
from(ok(z0)) → ok(from(z0))
pi(mark(z0)) → mark(pi(z0))
pi(ok(z0)) → ok(pi(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
times(mark(z0), z1) → mark(times(z0, z1))
times(ok(z0), ok(z1)) → ok(times(z0, z1))
times(z0, mark(z1)) → mark(times(z0, z1))
square(mark(z0)) → mark(square(z0))
square(ok(z0)) → ok(square(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(posrecip(z0)) → posrecip(proper(z0))
proper(negrecip(z0)) → negrecip(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(cons2(z0, z1)) → cons2(proper(z0), proper(z1))
proper(rnil) → ok(rnil)
proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
proper(pi(z0)) → pi(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(times(z0, z1)) → times(proper(z0), proper(z1))
proper(square(z0)) → square(proper(z0))
Tuples:
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
TOP(ok(z0)) → c79(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c9(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(2NDSPOS(s(z0), cons2(z1, z2)))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(2NDSNEG(s(z0), cons2(z1, z2)))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c13(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, z2)))) → c13(S(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(s(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, z2)))) → c13(S(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(s(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c13(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c13(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c13(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c13(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c13(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c13(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c13(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c13(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(cons2(z0, z1))) → c13(S(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c13(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c13(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c13(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c14(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c14(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c14(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c14(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c14(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c14(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c14(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c14(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(cons2(z0, z1))) → c14(POSRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c15(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c15(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c15(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c15(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c15(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c15(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c15(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c15(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(cons2(z0, z1))) → c15(NEGRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndspos(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndspos(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndsneg(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndsneg(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c16(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c16(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c16(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c16(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c16(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c16(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c16(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c16(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(cons2(z0, z1), x1)) → c16(CONS(cons2(z0, active(z1)), x1), ACTIVE(cons2(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, 2ndsneg(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(0, z0))) → c17(CONS2(x0, mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(cons2(x0, plus(s(z0), z1))) → c17(CONS2(x0, mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons2(x0, times(0, z0))) → c17(CONS2(x0, mark(0)), ACTIVE(times(0, z0)))
ACTIVE(cons2(x0, times(s(z0), z1))) → c17(CONS2(x0, mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(cons2(x0, s(z0))) → c17(CONS2(x0, s(active(z0))), ACTIVE(s(z0)))
ACTIVE(cons2(x0, posrecip(z0))) → c17(CONS2(x0, posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(cons2(x0, negrecip(z0))) → c17(CONS2(x0, negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(cons2(x0, cons(z0, z1))) → c17(CONS2(x0, cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(cons2(x0, cons2(z0, z1))) → c17(CONS2(x0, cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, from(active(z0))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, square(active(z0))), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c20(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(from(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(from(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c20(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c20(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c20(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c20(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c20(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c20(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c20(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c20(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c20(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c20(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(cons2(z0, z1))) → c20(FROM(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c20(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c20(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c20(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c25(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c25(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c25(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c25(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c25(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c25(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c25(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c25(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c25(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c25(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c25(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(cons2(z0, z1))) → c25(PI(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c25(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c25(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c25(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c30(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(square(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(square(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c30(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c30(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c30(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c30(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c30(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c30(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c30(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c30(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c30(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(cons2(z0, z1))) → c30(SQUARE(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c30(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c30(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c63(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c63(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c63(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c63(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(cons2(z0, z1))) → c63(S(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(s(rcons(z0, z1))) → c63(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c63(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c63(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c63(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c63(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c63(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c63(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c63(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c63(S(ok(0)))
PROPER(s(nil)) → c63(S(ok(nil)))
PROPER(s(rnil)) → c63(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c64(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c64(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c64(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c64(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(cons2(z0, z1))) → c64(POSRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c64(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c64(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c64(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c64(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c64(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c64(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c64(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c64(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c64(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c64(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c64(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c65(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c65(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c65(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c65(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(cons2(z0, z1))) → c65(NEGRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c65(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c65(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c65(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c65(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c65(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c65(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c65(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c65(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c65(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c65(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c65(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c67(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c67(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c67(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c67(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, cons2(z0, z1))) → c67(CONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c67(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c67(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c67(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c67(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c67(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c67(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c67(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c67(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c67(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c67(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c67(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c67(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(cons2(z0, z1), x1)) → c67(CONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c67(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c67(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c67(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c67(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c67(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c67(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c67(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c67(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c67(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c67(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c67(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c67(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c67(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c67(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(cons2(x0, s(z0))) → c68(CONS2(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons2(x0, posrecip(z0))) → c68(CONS2(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons2(x0, negrecip(z0))) → c68(CONS2(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons2(x0, cons(z0, z1))) → c68(CONS2(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons2(x0, cons2(z0, z1))) → c68(CONS2(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons2(x0, rcons(z0, z1))) → c68(CONS2(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons2(x0, from(z0))) → c68(CONS2(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons2(x0, 2ndspos(z0, z1))) → c68(CONS2(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons2(x0, 2ndsneg(z0, z1))) → c68(CONS2(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons2(x0, pi(z0))) → c68(CONS2(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons2(x0, plus(z0, z1))) → c68(CONS2(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons2(x0, times(z0, z1))) → c68(CONS2(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons2(x0, square(z0))) → c68(CONS2(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons2(s(z0), x1)) → c68(CONS2(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons2(posrecip(z0), x1)) → c68(CONS2(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons2(negrecip(z0), x1)) → c68(CONS2(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons2(cons(z0, z1), x1)) → c68(CONS2(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons2(cons2(z0, z1), x1)) → c68(CONS2(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons2(rcons(z0, z1), x1)) → c68(CONS2(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons2(from(z0), x1)) → c68(CONS2(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons2(2ndspos(z0, z1), x1)) → c68(CONS2(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons2(2ndsneg(z0, z1), x1)) → c68(CONS2(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons2(pi(z0), x1)) → c68(CONS2(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons2(plus(z0, z1), x1)) → c68(CONS2(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons2(times(z0, z1), x1)) → c68(CONS2(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons2(square(z0), x1)) → c68(CONS2(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons2(x0, 0)) → c68(CONS2(proper(x0), ok(0)), PROPER(x0))
PROPER(cons2(x0, nil)) → c68(CONS2(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons2(x0, rnil)) → c68(CONS2(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons2(0, x1)) → c68(CONS2(ok(0), proper(x1)), PROPER(x1))
PROPER(cons2(nil, x1)) → c68(CONS2(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons2(rnil, x1)) → c68(CONS2(ok(rnil), proper(x1)), PROPER(x1))
PROPER(rcons(x0, s(z0))) → c70(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c70(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c70(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, cons(z0, z1))) → c70(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, cons2(z0, z1))) → c70(RCONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(rcons(x0, rcons(z0, z1))) → c70(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c70(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c70(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c70(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c70(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c70(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c70(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c70(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(s(z0), x1)) → c70(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c70(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c70(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c70(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(cons2(z0, z1), x1)) → c70(RCONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c70(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c70(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c70(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c70(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c70(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c70(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c70(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c70(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(rcons(x0, 0)) → c70(RCONS(proper(x0), ok(0)), PROPER(x0))
PROPER(rcons(x0, nil)) → c70(RCONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(rcons(x0, rnil)) → c70(RCONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(rcons(0, x1)) → c70(RCONS(ok(0), proper(x1)), PROPER(x1))
PROPER(rcons(nil, x1)) → c70(RCONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c70(RCONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(from(s(z0))) → c71(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(posrecip(z0))) → c71(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(from(negrecip(z0))) → c71(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(from(cons(z0, z1))) → c71(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(cons2(z0, z1))) → c71(FROM(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(from(rcons(z0, z1))) → c71(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(from(from(z0))) → c71(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(2ndspos(z0, z1))) → c71(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(from(2ndsneg(z0, z1))) → c71(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(from(pi(z0))) → c71(FROM(pi(proper(z0))), PROPER(pi(z0)))
PROPER(from(plus(z0, z1))) → c71(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(from(times(z0, z1))) → c71(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(from(square(z0))) → c71(FROM(square(proper(z0))), PROPER(square(z0)))
PROPER(from(0)) → c71(FROM(ok(0)))
PROPER(from(nil)) → c71(FROM(ok(nil)))
PROPER(from(rnil)) → c71(FROM(ok(rnil)))
PROPER(2ndspos(x0, s(z0))) → c72(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndspos(x0, posrecip(z0))) → c72(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndspos(x0, negrecip(z0))) → c72(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndspos(x0, cons(z0, z1))) → c72(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndspos(x0, cons2(z0, z1))) → c72(2NDSPOS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(2ndspos(x0, rcons(z0, z1))) → c72(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndspos(x0, from(z0))) → c72(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c72(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c72(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndspos(x0, pi(z0))) → c72(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndspos(x0, plus(z0, z1))) → c72(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndspos(x0, times(z0, z1))) → c72(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndspos(x0, square(z0))) → c72(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndspos(s(z0), x1)) → c72(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndspos(posrecip(z0), x1)) → c72(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndspos(negrecip(z0), x1)) → c72(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndspos(cons(z0, z1), x1)) → c72(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndspos(cons2(z0, z1), x1)) → c72(2NDSPOS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(2ndspos(rcons(z0, z1), x1)) → c72(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndspos(from(z0), x1)) → c72(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c72(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c72(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndspos(pi(z0), x1)) → c72(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndspos(plus(z0, z1), x1)) → c72(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndspos(times(z0, z1), x1)) → c72(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndspos(square(z0), x1)) → c72(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndspos(x0, 0)) → c72(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndspos(x0, nil)) → c72(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndspos(x0, rnil)) → c72(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndspos(0, x1)) → c72(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndspos(nil, x1)) → c72(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndspos(rnil, x1)) → c72(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(x0, s(z0))) → c73(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndsneg(x0, posrecip(z0))) → c73(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndsneg(x0, negrecip(z0))) → c73(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndsneg(x0, cons(z0, z1))) → c73(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndsneg(x0, cons2(z0, z1))) → c73(2NDSNEG(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(2ndsneg(x0, rcons(z0, z1))) → c73(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndsneg(x0, from(z0))) → c73(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c73(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c73(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndsneg(x0, pi(z0))) → c73(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndsneg(x0, plus(z0, z1))) → c73(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndsneg(x0, times(z0, z1))) → c73(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndsneg(x0, square(z0))) → c73(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndsneg(s(z0), x1)) → c73(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndsneg(posrecip(z0), x1)) → c73(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndsneg(negrecip(z0), x1)) → c73(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndsneg(cons(z0, z1), x1)) → c73(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(cons2(z0, z1), x1)) → c73(2NDSNEG(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(2ndsneg(rcons(z0, z1), x1)) → c73(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(from(z0), x1)) → c73(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c73(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c73(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndsneg(pi(z0), x1)) → c73(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndsneg(plus(z0, z1), x1)) → c73(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndsneg(times(z0, z1), x1)) → c73(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndsneg(square(z0), x1)) → c73(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndsneg(x0, 0)) → c73(2NDSNEG(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndsneg(x0, nil)) → c73(2NDSNEG(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndsneg(x0, rnil)) → c73(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndsneg(0, x1)) → c73(2NDSNEG(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndsneg(nil, x1)) → c73(2NDSNEG(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(rnil, x1)) → c73(2NDSNEG(ok(rnil), proper(x1)), PROPER(x1))
PROPER(pi(s(z0))) → c74(PI(s(proper(z0))), PROPER(s(z0)))
PROPER(pi(posrecip(z0))) → c74(PI(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(pi(negrecip(z0))) → c74(PI(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(pi(cons(z0, z1))) → c74(PI(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(pi(cons2(z0, z1))) → c74(PI(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(pi(rcons(z0, z1))) → c74(PI(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(pi(from(z0))) → c74(PI(from(proper(z0))), PROPER(from(z0)))
PROPER(pi(2ndspos(z0, z1))) → c74(PI(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(pi(2ndsneg(z0, z1))) → c74(PI(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(pi(pi(z0))) → c74(PI(pi(proper(z0))), PROPER(pi(z0)))
PROPER(pi(plus(z0, z1))) → c74(PI(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(pi(times(z0, z1))) → c74(PI(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(pi(square(z0))) → c74(PI(square(proper(z0))), PROPER(square(z0)))
PROPER(pi(0)) → c74(PI(ok(0)))
PROPER(pi(nil)) → c74(PI(ok(nil)))
PROPER(pi(rnil)) → c74(PI(ok(rnil)))
PROPER(plus(x0, s(z0))) → c75(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(plus(x0, posrecip(z0))) → c75(PLUS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(plus(x0, negrecip(z0))) → c75(PLUS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(plus(x0, cons(z0, z1))) → c75(PLUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(plus(x0, cons2(z0, z1))) → c75(PLUS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(plus(x0, rcons(z0, z1))) → c75(PLUS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(plus(x0, from(z0))) → c75(PLUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(plus(x0, 2ndspos(z0, z1))) → c75(PLUS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(plus(x0, 2ndsneg(z0, z1))) → c75(PLUS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(plus(x0, pi(z0))) → c75(PLUS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(plus(x0, plus(z0, z1))) → c75(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(plus(x0, times(z0, z1))) → c75(PLUS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(plus(x0, square(z0))) → c75(PLUS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(plus(s(z0), x1)) → c75(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(plus(posrecip(z0), x1)) → c75(PLUS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(plus(negrecip(z0), x1)) → c75(PLUS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(plus(cons(z0, z1), x1)) → c75(PLUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(plus(cons2(z0, z1), x1)) → c75(PLUS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(plus(rcons(z0, z1), x1)) → c75(PLUS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(plus(from(z0), x1)) → c75(PLUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(plus(2ndspos(z0, z1), x1)) → c75(PLUS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(plus(2ndsneg(z0, z1), x1)) → c75(PLUS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(plus(pi(z0), x1)) → c75(PLUS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(plus(plus(z0, z1), x1)) → c75(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(plus(times(z0, z1), x1)) → c75(PLUS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(plus(square(z0), x1)) → c75(PLUS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(plus(x0, 0)) → c75(PLUS(proper(x0), ok(0)), PROPER(x0))
PROPER(plus(x0, nil)) → c75(PLUS(proper(x0), ok(nil)), PROPER(x0))
PROPER(plus(x0, rnil)) → c75(PLUS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(plus(0, x1)) → c75(PLUS(ok(0), proper(x1)), PROPER(x1))
PROPER(plus(nil, x1)) → c75(PLUS(ok(nil), proper(x1)), PROPER(x1))
PROPER(plus(rnil, x1)) → c75(PLUS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(times(x0, s(z0))) → c76(TIMES(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(times(x0, posrecip(z0))) → c76(TIMES(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(times(x0, negrecip(z0))) → c76(TIMES(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(times(x0, cons(z0, z1))) → c76(TIMES(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(times(x0, cons2(z0, z1))) → c76(TIMES(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(times(x0, rcons(z0, z1))) → c76(TIMES(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(times(x0, from(z0))) → c76(TIMES(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(times(x0, 2ndspos(z0, z1))) → c76(TIMES(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(times(x0, 2ndsneg(z0, z1))) → c76(TIMES(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(times(x0, pi(z0))) → c76(TIMES(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(times(x0, plus(z0, z1))) → c76(TIMES(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(times(x0, times(z0, z1))) → c76(TIMES(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(times(x0, square(z0))) → c76(TIMES(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(times(s(z0), x1)) → c76(TIMES(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(times(posrecip(z0), x1)) → c76(TIMES(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(times(negrecip(z0), x1)) → c76(TIMES(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(times(cons(z0, z1), x1)) → c76(TIMES(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(times(cons2(z0, z1), x1)) → c76(TIMES(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(times(rcons(z0, z1), x1)) → c76(TIMES(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(times(from(z0), x1)) → c76(TIMES(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(times(2ndspos(z0, z1), x1)) → c76(TIMES(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(times(2ndsneg(z0, z1), x1)) → c76(TIMES(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(times(pi(z0), x1)) → c76(TIMES(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(times(plus(z0, z1), x1)) → c76(TIMES(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(times(times(z0, z1), x1)) → c76(TIMES(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(times(square(z0), x1)) → c76(TIMES(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(times(x0, 0)) → c76(TIMES(proper(x0), ok(0)), PROPER(x0))
PROPER(times(x0, nil)) → c76(TIMES(proper(x0), ok(nil)), PROPER(x0))
PROPER(times(x0, rnil)) → c76(TIMES(proper(x0), ok(rnil)), PROPER(x0))
PROPER(times(0, x1)) → c76(TIMES(ok(0), proper(x1)), PROPER(x1))
PROPER(times(nil, x1)) → c76(TIMES(ok(nil), proper(x1)), PROPER(x1))
PROPER(times(rnil, x1)) → c76(TIMES(ok(rnil), proper(x1)), PROPER(x1))
PROPER(square(s(z0))) → c77(SQUARE(s(proper(z0))), PROPER(s(z0)))
PROPER(square(posrecip(z0))) → c77(SQUARE(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(square(negrecip(z0))) → c77(SQUARE(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(square(cons(z0, z1))) → c77(SQUARE(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(square(cons2(z0, z1))) → c77(SQUARE(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(square(rcons(z0, z1))) → c77(SQUARE(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(square(from(z0))) → c77(SQUARE(from(proper(z0))), PROPER(from(z0)))
PROPER(square(2ndspos(z0, z1))) → c77(SQUARE(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(square(2ndsneg(z0, z1))) → c77(SQUARE(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(square(pi(z0))) → c77(SQUARE(pi(proper(z0))), PROPER(pi(z0)))
PROPER(square(plus(z0, z1))) → c77(SQUARE(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(square(times(z0, z1))) → c77(SQUARE(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(square(square(z0))) → c77(SQUARE(square(proper(z0))), PROPER(square(z0)))
PROPER(square(0)) → c77(SQUARE(ok(0)))
PROPER(square(nil)) → c77(SQUARE(ok(nil)))
PROPER(square(rnil)) → c77(SQUARE(ok(rnil)))
TOP(mark(0)) → c78(TOP(ok(0)), PROPER(0))
TOP(mark(s(z0))) → c78(TOP(s(proper(z0))), PROPER(s(z0)))
TOP(mark(posrecip(z0))) → c78(TOP(posrecip(proper(z0))), PROPER(posrecip(z0)))
TOP(mark(negrecip(z0))) → c78(TOP(negrecip(proper(z0))), PROPER(negrecip(z0)))
TOP(mark(nil)) → c78(TOP(ok(nil)), PROPER(nil))
TOP(mark(cons(z0, z1))) → c78(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
TOP(mark(cons2(z0, z1))) → c78(TOP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
TOP(mark(rnil)) → c78(TOP(ok(rnil)), PROPER(rnil))
TOP(mark(rcons(z0, z1))) → c78(TOP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
TOP(mark(from(z0))) → c78(TOP(from(proper(z0))), PROPER(from(z0)))
TOP(mark(2ndspos(z0, z1))) → c78(TOP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
TOP(mark(2ndsneg(z0, z1))) → c78(TOP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
TOP(mark(pi(z0))) → c78(TOP(pi(proper(z0))), PROPER(pi(z0)))
TOP(mark(plus(z0, z1))) → c78(TOP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
TOP(mark(times(z0, z1))) → c78(TOP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
TOP(mark(square(z0))) → c78(TOP(square(proper(z0))), PROPER(square(z0)))
S tuples:
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
TOP(ok(z0)) → c79(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c9(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(2NDSPOS(s(z0), cons2(z1, z2)))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(2NDSNEG(s(z0), cons2(z1, z2)))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c13(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, z2)))) → c13(S(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(s(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, z2)))) → c13(S(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(s(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c13(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c13(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c13(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c13(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c13(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c13(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c13(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c13(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(cons2(z0, z1))) → c13(S(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c13(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c13(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c13(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c14(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c14(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c14(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c14(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c14(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c14(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c14(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c14(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(cons2(z0, z1))) → c14(POSRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c15(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c15(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c15(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c15(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c15(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c15(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c15(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c15(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(cons2(z0, z1))) → c15(NEGRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndspos(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndspos(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndsneg(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndsneg(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c16(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c16(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c16(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c16(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c16(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c16(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c16(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c16(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(cons2(z0, z1), x1)) → c16(CONS(cons2(z0, active(z1)), x1), ACTIVE(cons2(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, 2ndsneg(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(0, z0))) → c17(CONS2(x0, mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(cons2(x0, plus(s(z0), z1))) → c17(CONS2(x0, mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons2(x0, times(0, z0))) → c17(CONS2(x0, mark(0)), ACTIVE(times(0, z0)))
ACTIVE(cons2(x0, times(s(z0), z1))) → c17(CONS2(x0, mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(cons2(x0, s(z0))) → c17(CONS2(x0, s(active(z0))), ACTIVE(s(z0)))
ACTIVE(cons2(x0, posrecip(z0))) → c17(CONS2(x0, posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(cons2(x0, negrecip(z0))) → c17(CONS2(x0, negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(cons2(x0, cons(z0, z1))) → c17(CONS2(x0, cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(cons2(x0, cons2(z0, z1))) → c17(CONS2(x0, cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, from(active(z0))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, square(active(z0))), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c20(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(from(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(from(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c20(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c20(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c20(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c20(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c20(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c20(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c20(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c20(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c20(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c20(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(cons2(z0, z1))) → c20(FROM(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c20(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c20(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c20(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c25(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c25(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c25(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c25(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c25(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c25(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c25(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c25(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c25(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c25(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c25(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(cons2(z0, z1))) → c25(PI(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c25(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c25(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c25(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c30(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(square(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(square(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c30(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c30(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c30(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c30(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c30(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c30(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c30(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c30(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c30(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(cons2(z0, z1))) → c30(SQUARE(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c30(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c30(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c63(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c63(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c63(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c63(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(cons2(z0, z1))) → c63(S(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(s(rcons(z0, z1))) → c63(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c63(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c63(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c63(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c63(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c63(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c63(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c63(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c63(S(ok(0)))
PROPER(s(nil)) → c63(S(ok(nil)))
PROPER(s(rnil)) → c63(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c64(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c64(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c64(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c64(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(cons2(z0, z1))) → c64(POSRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c64(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c64(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c64(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c64(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c64(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c64(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c64(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c64(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c64(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c64(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c64(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c65(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c65(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c65(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c65(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(cons2(z0, z1))) → c65(NEGRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c65(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c65(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c65(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c65(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c65(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c65(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c65(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c65(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c65(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c65(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c65(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c67(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c67(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c67(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c67(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, cons2(z0, z1))) → c67(CONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c67(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c67(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c67(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c67(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c67(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c67(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c67(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c67(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c67(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c67(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c67(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c67(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(cons2(z0, z1), x1)) → c67(CONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c67(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c67(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c67(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c67(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c67(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c67(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c67(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c67(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c67(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c67(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c67(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c67(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c67(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c67(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(cons2(x0, s(z0))) → c68(CONS2(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons2(x0, posrecip(z0))) → c68(CONS2(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons2(x0, negrecip(z0))) → c68(CONS2(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons2(x0, cons(z0, z1))) → c68(CONS2(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons2(x0, cons2(z0, z1))) → c68(CONS2(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons2(x0, rcons(z0, z1))) → c68(CONS2(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons2(x0, from(z0))) → c68(CONS2(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons2(x0, 2ndspos(z0, z1))) → c68(CONS2(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons2(x0, 2ndsneg(z0, z1))) → c68(CONS2(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons2(x0, pi(z0))) → c68(CONS2(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons2(x0, plus(z0, z1))) → c68(CONS2(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons2(x0, times(z0, z1))) → c68(CONS2(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons2(x0, square(z0))) → c68(CONS2(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons2(s(z0), x1)) → c68(CONS2(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons2(posrecip(z0), x1)) → c68(CONS2(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons2(negrecip(z0), x1)) → c68(CONS2(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons2(cons(z0, z1), x1)) → c68(CONS2(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons2(cons2(z0, z1), x1)) → c68(CONS2(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons2(rcons(z0, z1), x1)) → c68(CONS2(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons2(from(z0), x1)) → c68(CONS2(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons2(2ndspos(z0, z1), x1)) → c68(CONS2(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons2(2ndsneg(z0, z1), x1)) → c68(CONS2(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons2(pi(z0), x1)) → c68(CONS2(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons2(plus(z0, z1), x1)) → c68(CONS2(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons2(times(z0, z1), x1)) → c68(CONS2(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons2(square(z0), x1)) → c68(CONS2(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons2(x0, 0)) → c68(CONS2(proper(x0), ok(0)), PROPER(x0))
PROPER(cons2(x0, nil)) → c68(CONS2(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons2(x0, rnil)) → c68(CONS2(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons2(0, x1)) → c68(CONS2(ok(0), proper(x1)), PROPER(x1))
PROPER(cons2(nil, x1)) → c68(CONS2(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons2(rnil, x1)) → c68(CONS2(ok(rnil), proper(x1)), PROPER(x1))
PROPER(rcons(x0, s(z0))) → c70(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c70(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c70(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, cons(z0, z1))) → c70(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, cons2(z0, z1))) → c70(RCONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(rcons(x0, rcons(z0, z1))) → c70(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c70(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c70(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c70(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c70(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c70(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c70(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c70(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(s(z0), x1)) → c70(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c70(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c70(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c70(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(cons2(z0, z1), x1)) → c70(RCONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c70(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c70(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c70(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c70(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c70(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c70(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c70(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c70(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(rcons(x0, 0)) → c70(RCONS(proper(x0), ok(0)), PROPER(x0))
PROPER(rcons(x0, nil)) → c70(RCONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(rcons(x0, rnil)) → c70(RCONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(rcons(0, x1)) → c70(RCONS(ok(0), proper(x1)), PROPER(x1))
PROPER(rcons(nil, x1)) → c70(RCONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c70(RCONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(from(s(z0))) → c71(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(posrecip(z0))) → c71(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(from(negrecip(z0))) → c71(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(from(cons(z0, z1))) → c71(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(cons2(z0, z1))) → c71(FROM(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(from(rcons(z0, z1))) → c71(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(from(from(z0))) → c71(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(2ndspos(z0, z1))) → c71(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(from(2ndsneg(z0, z1))) → c71(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(from(pi(z0))) → c71(FROM(pi(proper(z0))), PROPER(pi(z0)))
PROPER(from(plus(z0, z1))) → c71(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(from(times(z0, z1))) → c71(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(from(square(z0))) → c71(FROM(square(proper(z0))), PROPER(square(z0)))
PROPER(from(0)) → c71(FROM(ok(0)))
PROPER(from(nil)) → c71(FROM(ok(nil)))
PROPER(from(rnil)) → c71(FROM(ok(rnil)))
PROPER(2ndspos(x0, s(z0))) → c72(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndspos(x0, posrecip(z0))) → c72(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndspos(x0, negrecip(z0))) → c72(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndspos(x0, cons(z0, z1))) → c72(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndspos(x0, cons2(z0, z1))) → c72(2NDSPOS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(2ndspos(x0, rcons(z0, z1))) → c72(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndspos(x0, from(z0))) → c72(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c72(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c72(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndspos(x0, pi(z0))) → c72(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndspos(x0, plus(z0, z1))) → c72(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndspos(x0, times(z0, z1))) → c72(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndspos(x0, square(z0))) → c72(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndspos(s(z0), x1)) → c72(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndspos(posrecip(z0), x1)) → c72(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndspos(negrecip(z0), x1)) → c72(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndspos(cons(z0, z1), x1)) → c72(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndspos(cons2(z0, z1), x1)) → c72(2NDSPOS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(2ndspos(rcons(z0, z1), x1)) → c72(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndspos(from(z0), x1)) → c72(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c72(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c72(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndspos(pi(z0), x1)) → c72(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndspos(plus(z0, z1), x1)) → c72(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndspos(times(z0, z1), x1)) → c72(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndspos(square(z0), x1)) → c72(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndspos(x0, 0)) → c72(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndspos(x0, nil)) → c72(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndspos(x0, rnil)) → c72(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndspos(0, x1)) → c72(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndspos(nil, x1)) → c72(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndspos(rnil, x1)) → c72(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(x0, s(z0))) → c73(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndsneg(x0, posrecip(z0))) → c73(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndsneg(x0, negrecip(z0))) → c73(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndsneg(x0, cons(z0, z1))) → c73(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndsneg(x0, cons2(z0, z1))) → c73(2NDSNEG(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(2ndsneg(x0, rcons(z0, z1))) → c73(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndsneg(x0, from(z0))) → c73(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c73(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c73(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndsneg(x0, pi(z0))) → c73(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndsneg(x0, plus(z0, z1))) → c73(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndsneg(x0, times(z0, z1))) → c73(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndsneg(x0, square(z0))) → c73(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndsneg(s(z0), x1)) → c73(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndsneg(posrecip(z0), x1)) → c73(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndsneg(negrecip(z0), x1)) → c73(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndsneg(cons(z0, z1), x1)) → c73(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(cons2(z0, z1), x1)) → c73(2NDSNEG(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(2ndsneg(rcons(z0, z1), x1)) → c73(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(from(z0), x1)) → c73(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c73(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c73(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndsneg(pi(z0), x1)) → c73(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndsneg(plus(z0, z1), x1)) → c73(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndsneg(times(z0, z1), x1)) → c73(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndsneg(square(z0), x1)) → c73(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndsneg(x0, 0)) → c73(2NDSNEG(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndsneg(x0, nil)) → c73(2NDSNEG(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndsneg(x0, rnil)) → c73(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndsneg(0, x1)) → c73(2NDSNEG(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndsneg(nil, x1)) → c73(2NDSNEG(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(rnil, x1)) → c73(2NDSNEG(ok(rnil), proper(x1)), PROPER(x1))
PROPER(pi(s(z0))) → c74(PI(s(proper(z0))), PROPER(s(z0)))
PROPER(pi(posrecip(z0))) → c74(PI(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(pi(negrecip(z0))) → c74(PI(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(pi(cons(z0, z1))) → c74(PI(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(pi(cons2(z0, z1))) → c74(PI(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(pi(rcons(z0, z1))) → c74(PI(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(pi(from(z0))) → c74(PI(from(proper(z0))), PROPER(from(z0)))
PROPER(pi(2ndspos(z0, z1))) → c74(PI(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(pi(2ndsneg(z0, z1))) → c74(PI(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(pi(pi(z0))) → c74(PI(pi(proper(z0))), PROPER(pi(z0)))
PROPER(pi(plus(z0, z1))) → c74(PI(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(pi(times(z0, z1))) → c74(PI(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(pi(square(z0))) → c74(PI(square(proper(z0))), PROPER(square(z0)))
PROPER(pi(0)) → c74(PI(ok(0)))
PROPER(pi(nil)) → c74(PI(ok(nil)))
PROPER(pi(rnil)) → c74(PI(ok(rnil)))
PROPER(plus(x0, s(z0))) → c75(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(plus(x0, posrecip(z0))) → c75(PLUS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(plus(x0, negrecip(z0))) → c75(PLUS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(plus(x0, cons(z0, z1))) → c75(PLUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(plus(x0, cons2(z0, z1))) → c75(PLUS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(plus(x0, rcons(z0, z1))) → c75(PLUS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(plus(x0, from(z0))) → c75(PLUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(plus(x0, 2ndspos(z0, z1))) → c75(PLUS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(plus(x0, 2ndsneg(z0, z1))) → c75(PLUS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(plus(x0, pi(z0))) → c75(PLUS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(plus(x0, plus(z0, z1))) → c75(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(plus(x0, times(z0, z1))) → c75(PLUS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(plus(x0, square(z0))) → c75(PLUS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(plus(s(z0), x1)) → c75(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(plus(posrecip(z0), x1)) → c75(PLUS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(plus(negrecip(z0), x1)) → c75(PLUS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(plus(cons(z0, z1), x1)) → c75(PLUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(plus(cons2(z0, z1), x1)) → c75(PLUS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(plus(rcons(z0, z1), x1)) → c75(PLUS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(plus(from(z0), x1)) → c75(PLUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(plus(2ndspos(z0, z1), x1)) → c75(PLUS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(plus(2ndsneg(z0, z1), x1)) → c75(PLUS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(plus(pi(z0), x1)) → c75(PLUS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(plus(plus(z0, z1), x1)) → c75(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(plus(times(z0, z1), x1)) → c75(PLUS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(plus(square(z0), x1)) → c75(PLUS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(plus(x0, 0)) → c75(PLUS(proper(x0), ok(0)), PROPER(x0))
PROPER(plus(x0, nil)) → c75(PLUS(proper(x0), ok(nil)), PROPER(x0))
PROPER(plus(x0, rnil)) → c75(PLUS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(plus(0, x1)) → c75(PLUS(ok(0), proper(x1)), PROPER(x1))
PROPER(plus(nil, x1)) → c75(PLUS(ok(nil), proper(x1)), PROPER(x1))
PROPER(plus(rnil, x1)) → c75(PLUS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(times(x0, s(z0))) → c76(TIMES(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(times(x0, posrecip(z0))) → c76(TIMES(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(times(x0, negrecip(z0))) → c76(TIMES(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(times(x0, cons(z0, z1))) → c76(TIMES(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(times(x0, cons2(z0, z1))) → c76(TIMES(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(times(x0, rcons(z0, z1))) → c76(TIMES(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(times(x0, from(z0))) → c76(TIMES(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(times(x0, 2ndspos(z0, z1))) → c76(TIMES(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(times(x0, 2ndsneg(z0, z1))) → c76(TIMES(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(times(x0, pi(z0))) → c76(TIMES(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(times(x0, plus(z0, z1))) → c76(TIMES(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(times(x0, times(z0, z1))) → c76(TIMES(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(times(x0, square(z0))) → c76(TIMES(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(times(s(z0), x1)) → c76(TIMES(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(times(posrecip(z0), x1)) → c76(TIMES(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(times(negrecip(z0), x1)) → c76(TIMES(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(times(cons(z0, z1), x1)) → c76(TIMES(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(times(cons2(z0, z1), x1)) → c76(TIMES(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(times(rcons(z0, z1), x1)) → c76(TIMES(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(times(from(z0), x1)) → c76(TIMES(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(times(2ndspos(z0, z1), x1)) → c76(TIMES(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(times(2ndsneg(z0, z1), x1)) → c76(TIMES(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(times(pi(z0), x1)) → c76(TIMES(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(times(plus(z0, z1), x1)) → c76(TIMES(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(times(times(z0, z1), x1)) → c76(TIMES(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(times(square(z0), x1)) → c76(TIMES(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(times(x0, 0)) → c76(TIMES(proper(x0), ok(0)), PROPER(x0))
PROPER(times(x0, nil)) → c76(TIMES(proper(x0), ok(nil)), PROPER(x0))
PROPER(times(x0, rnil)) → c76(TIMES(proper(x0), ok(rnil)), PROPER(x0))
PROPER(times(0, x1)) → c76(TIMES(ok(0), proper(x1)), PROPER(x1))
PROPER(times(nil, x1)) → c76(TIMES(ok(nil), proper(x1)), PROPER(x1))
PROPER(times(rnil, x1)) → c76(TIMES(ok(rnil), proper(x1)), PROPER(x1))
PROPER(square(s(z0))) → c77(SQUARE(s(proper(z0))), PROPER(s(z0)))
PROPER(square(posrecip(z0))) → c77(SQUARE(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(square(negrecip(z0))) → c77(SQUARE(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(square(cons(z0, z1))) → c77(SQUARE(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(square(cons2(z0, z1))) → c77(SQUARE(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(square(rcons(z0, z1))) → c77(SQUARE(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(square(from(z0))) → c77(SQUARE(from(proper(z0))), PROPER(from(z0)))
PROPER(square(2ndspos(z0, z1))) → c77(SQUARE(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(square(2ndsneg(z0, z1))) → c77(SQUARE(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(square(pi(z0))) → c77(SQUARE(pi(proper(z0))), PROPER(pi(z0)))
PROPER(square(plus(z0, z1))) → c77(SQUARE(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(square(times(z0, z1))) → c77(SQUARE(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(square(square(z0))) → c77(SQUARE(square(proper(z0))), PROPER(square(z0)))
PROPER(square(0)) → c77(SQUARE(ok(0)))
PROPER(square(nil)) → c77(SQUARE(ok(nil)))
PROPER(square(rnil)) → c77(SQUARE(ok(rnil)))
TOP(mark(0)) → c78(TOP(ok(0)), PROPER(0))
TOP(mark(s(z0))) → c78(TOP(s(proper(z0))), PROPER(s(z0)))
TOP(mark(posrecip(z0))) → c78(TOP(posrecip(proper(z0))), PROPER(posrecip(z0)))
TOP(mark(negrecip(z0))) → c78(TOP(negrecip(proper(z0))), PROPER(negrecip(z0)))
TOP(mark(nil)) → c78(TOP(ok(nil)), PROPER(nil))
TOP(mark(cons(z0, z1))) → c78(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
TOP(mark(cons2(z0, z1))) → c78(TOP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
TOP(mark(rnil)) → c78(TOP(ok(rnil)), PROPER(rnil))
TOP(mark(rcons(z0, z1))) → c78(TOP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
TOP(mark(from(z0))) → c78(TOP(from(proper(z0))), PROPER(from(z0)))
TOP(mark(2ndspos(z0, z1))) → c78(TOP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
TOP(mark(2ndsneg(z0, z1))) → c78(TOP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
TOP(mark(pi(z0))) → c78(TOP(pi(proper(z0))), PROPER(pi(z0)))
TOP(mark(plus(z0, z1))) → c78(TOP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
TOP(mark(times(z0, z1))) → c78(TOP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
TOP(mark(square(z0))) → c78(TOP(square(proper(z0))), PROPER(square(z0)))
K tuples:none
Defined Rule Symbols:
active, 2ndspos, cons2, rcons, posrecip, 2ndsneg, negrecip, s, cons, from, pi, plus, times, square, proper
Defined Pair Symbols:
ACTIVE, S, POSRECIP, NEGRECIP, CONS, CONS2, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, TOP, PROPER
Compound Symbols:
c12, c18, c19, c21, c22, c23, c24, c26, c27, c28, c29, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c79, c, c7, c9, c11, c1, c13, c14, c15, c16, c17, c20, c25, c30, c63, c63, c64, c64, c65, c65, c67, c67, c68, c68, c70, c70, c71, c71, c72, c72, c73, c73, c74, c74, c75, c75, c76, c76, c77, c77, c78
(81) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 3 trailing tuple parts
(82) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(2ndspos(0, z0)) → mark(rnil)
active(2ndspos(s(z0), cons(z1, z2))) → mark(2ndspos(s(z0), cons2(z1, z2)))
active(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(z1, z2))) → mark(2ndsneg(s(z0), cons2(z1, z2)))
active(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
active(pi(z0)) → mark(2ndspos(z0, from(0)))
active(plus(0, z0)) → mark(z0)
active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
active(times(0, z0)) → mark(0)
active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
active(square(z0)) → mark(times(z0, z0))
active(s(z0)) → s(active(z0))
active(posrecip(z0)) → posrecip(active(z0))
active(negrecip(z0)) → negrecip(active(z0))
active(cons(z0, z1)) → cons(active(z0), z1)
active(cons2(z0, z1)) → cons2(z0, active(z1))
active(rcons(z0, z1)) → rcons(active(z0), z1)
active(rcons(z0, z1)) → rcons(z0, active(z1))
active(from(z0)) → from(active(z0))
active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
active(pi(z0)) → pi(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(times(z0, z1)) → times(active(z0), z1)
active(times(z0, z1)) → times(z0, active(z1))
active(square(z0)) → square(active(z0))
2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
cons2(z0, mark(z1)) → mark(cons2(z0, z1))
cons2(ok(z0), ok(z1)) → ok(cons2(z0, z1))
rcons(mark(z0), z1) → mark(rcons(z0, z1))
rcons(z0, mark(z1)) → mark(rcons(z0, z1))
rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
posrecip(ok(z0)) → ok(posrecip(z0))
posrecip(mark(z0)) → mark(posrecip(z0))
2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
negrecip(ok(z0)) → ok(negrecip(z0))
negrecip(mark(z0)) → mark(negrecip(z0))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
cons(mark(z0), z1) → mark(cons(z0, z1))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
from(mark(z0)) → mark(from(z0))
from(ok(z0)) → ok(from(z0))
pi(mark(z0)) → mark(pi(z0))
pi(ok(z0)) → ok(pi(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
times(mark(z0), z1) → mark(times(z0, z1))
times(ok(z0), ok(z1)) → ok(times(z0, z1))
times(z0, mark(z1)) → mark(times(z0, z1))
square(mark(z0)) → mark(square(z0))
square(ok(z0)) → ok(square(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(posrecip(z0)) → posrecip(proper(z0))
proper(negrecip(z0)) → negrecip(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(cons2(z0, z1)) → cons2(proper(z0), proper(z1))
proper(rnil) → ok(rnil)
proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
proper(pi(z0)) → pi(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(times(z0, z1)) → times(proper(z0), proper(z1))
proper(square(z0)) → square(proper(z0))
Tuples:
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
TOP(ok(z0)) → c79(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c9(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(2NDSPOS(s(z0), cons2(z1, z2)))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(2NDSNEG(s(z0), cons2(z1, z2)))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c13(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, z2)))) → c13(S(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(s(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, z2)))) → c13(S(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(s(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c13(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c13(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c13(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c13(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c13(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c13(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c13(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c13(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(cons2(z0, z1))) → c13(S(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c13(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c13(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c13(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c14(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c14(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c14(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c14(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c14(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c14(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c14(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c14(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(cons2(z0, z1))) → c14(POSRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c15(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c15(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c15(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c15(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c15(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c15(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c15(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c15(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(cons2(z0, z1))) → c15(NEGRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndspos(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndspos(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndsneg(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndsneg(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c16(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c16(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c16(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c16(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c16(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c16(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c16(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c16(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(cons2(z0, z1), x1)) → c16(CONS(cons2(z0, active(z1)), x1), ACTIVE(cons2(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, 2ndsneg(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(0, z0))) → c17(CONS2(x0, mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(cons2(x0, plus(s(z0), z1))) → c17(CONS2(x0, mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons2(x0, times(0, z0))) → c17(CONS2(x0, mark(0)), ACTIVE(times(0, z0)))
ACTIVE(cons2(x0, times(s(z0), z1))) → c17(CONS2(x0, mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(cons2(x0, s(z0))) → c17(CONS2(x0, s(active(z0))), ACTIVE(s(z0)))
ACTIVE(cons2(x0, posrecip(z0))) → c17(CONS2(x0, posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(cons2(x0, negrecip(z0))) → c17(CONS2(x0, negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(cons2(x0, cons(z0, z1))) → c17(CONS2(x0, cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(cons2(x0, cons2(z0, z1))) → c17(CONS2(x0, cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, from(active(z0))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, square(active(z0))), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c20(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(from(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(from(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c20(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c20(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c20(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c20(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c20(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c20(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c20(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c20(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c20(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c20(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(cons2(z0, z1))) → c20(FROM(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c20(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c20(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c20(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c25(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c25(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c25(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c25(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c25(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c25(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c25(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c25(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c25(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c25(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c25(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(cons2(z0, z1))) → c25(PI(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c25(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c25(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c25(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c30(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(square(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(square(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c30(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c30(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c30(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c30(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c30(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c30(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c30(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c30(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c30(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(cons2(z0, z1))) → c30(SQUARE(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c30(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c30(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c63(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c63(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c63(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c63(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(cons2(z0, z1))) → c63(S(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(s(rcons(z0, z1))) → c63(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c63(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c63(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c63(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c63(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c63(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c63(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c63(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c63(S(ok(0)))
PROPER(s(nil)) → c63(S(ok(nil)))
PROPER(s(rnil)) → c63(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c64(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c64(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c64(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c64(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(cons2(z0, z1))) → c64(POSRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c64(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c64(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c64(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c64(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c64(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c64(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c64(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c64(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c64(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c64(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c64(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c65(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c65(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c65(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c65(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(cons2(z0, z1))) → c65(NEGRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c65(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c65(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c65(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c65(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c65(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c65(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c65(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c65(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c65(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c65(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c65(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c67(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c67(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c67(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c67(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, cons2(z0, z1))) → c67(CONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c67(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c67(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c67(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c67(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c67(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c67(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c67(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c67(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c67(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c67(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c67(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c67(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(cons2(z0, z1), x1)) → c67(CONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c67(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c67(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c67(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c67(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c67(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c67(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c67(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c67(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c67(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c67(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c67(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c67(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c67(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c67(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(cons2(x0, s(z0))) → c68(CONS2(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons2(x0, posrecip(z0))) → c68(CONS2(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons2(x0, negrecip(z0))) → c68(CONS2(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons2(x0, cons(z0, z1))) → c68(CONS2(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons2(x0, cons2(z0, z1))) → c68(CONS2(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons2(x0, rcons(z0, z1))) → c68(CONS2(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons2(x0, from(z0))) → c68(CONS2(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons2(x0, 2ndspos(z0, z1))) → c68(CONS2(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons2(x0, 2ndsneg(z0, z1))) → c68(CONS2(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons2(x0, pi(z0))) → c68(CONS2(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons2(x0, plus(z0, z1))) → c68(CONS2(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons2(x0, times(z0, z1))) → c68(CONS2(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons2(x0, square(z0))) → c68(CONS2(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons2(s(z0), x1)) → c68(CONS2(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons2(posrecip(z0), x1)) → c68(CONS2(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons2(negrecip(z0), x1)) → c68(CONS2(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons2(cons(z0, z1), x1)) → c68(CONS2(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons2(cons2(z0, z1), x1)) → c68(CONS2(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons2(rcons(z0, z1), x1)) → c68(CONS2(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons2(from(z0), x1)) → c68(CONS2(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons2(2ndspos(z0, z1), x1)) → c68(CONS2(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons2(2ndsneg(z0, z1), x1)) → c68(CONS2(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons2(pi(z0), x1)) → c68(CONS2(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons2(plus(z0, z1), x1)) → c68(CONS2(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons2(times(z0, z1), x1)) → c68(CONS2(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons2(square(z0), x1)) → c68(CONS2(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons2(x0, 0)) → c68(CONS2(proper(x0), ok(0)), PROPER(x0))
PROPER(cons2(x0, nil)) → c68(CONS2(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons2(x0, rnil)) → c68(CONS2(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons2(0, x1)) → c68(CONS2(ok(0), proper(x1)), PROPER(x1))
PROPER(cons2(nil, x1)) → c68(CONS2(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons2(rnil, x1)) → c68(CONS2(ok(rnil), proper(x1)), PROPER(x1))
PROPER(rcons(x0, s(z0))) → c70(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c70(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c70(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, cons(z0, z1))) → c70(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, cons2(z0, z1))) → c70(RCONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(rcons(x0, rcons(z0, z1))) → c70(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c70(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c70(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c70(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c70(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c70(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c70(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c70(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(s(z0), x1)) → c70(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c70(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c70(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c70(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(cons2(z0, z1), x1)) → c70(RCONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c70(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c70(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c70(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c70(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c70(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c70(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c70(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c70(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(rcons(x0, 0)) → c70(RCONS(proper(x0), ok(0)), PROPER(x0))
PROPER(rcons(x0, nil)) → c70(RCONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(rcons(x0, rnil)) → c70(RCONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(rcons(0, x1)) → c70(RCONS(ok(0), proper(x1)), PROPER(x1))
PROPER(rcons(nil, x1)) → c70(RCONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c70(RCONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(from(s(z0))) → c71(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(posrecip(z0))) → c71(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(from(negrecip(z0))) → c71(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(from(cons(z0, z1))) → c71(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(cons2(z0, z1))) → c71(FROM(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(from(rcons(z0, z1))) → c71(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(from(from(z0))) → c71(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(2ndspos(z0, z1))) → c71(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(from(2ndsneg(z0, z1))) → c71(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(from(pi(z0))) → c71(FROM(pi(proper(z0))), PROPER(pi(z0)))
PROPER(from(plus(z0, z1))) → c71(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(from(times(z0, z1))) → c71(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(from(square(z0))) → c71(FROM(square(proper(z0))), PROPER(square(z0)))
PROPER(from(0)) → c71(FROM(ok(0)))
PROPER(from(nil)) → c71(FROM(ok(nil)))
PROPER(from(rnil)) → c71(FROM(ok(rnil)))
PROPER(2ndspos(x0, s(z0))) → c72(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndspos(x0, posrecip(z0))) → c72(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndspos(x0, negrecip(z0))) → c72(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndspos(x0, cons(z0, z1))) → c72(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndspos(x0, cons2(z0, z1))) → c72(2NDSPOS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(2ndspos(x0, rcons(z0, z1))) → c72(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndspos(x0, from(z0))) → c72(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c72(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c72(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndspos(x0, pi(z0))) → c72(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndspos(x0, plus(z0, z1))) → c72(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndspos(x0, times(z0, z1))) → c72(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndspos(x0, square(z0))) → c72(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndspos(s(z0), x1)) → c72(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndspos(posrecip(z0), x1)) → c72(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndspos(negrecip(z0), x1)) → c72(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndspos(cons(z0, z1), x1)) → c72(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndspos(cons2(z0, z1), x1)) → c72(2NDSPOS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(2ndspos(rcons(z0, z1), x1)) → c72(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndspos(from(z0), x1)) → c72(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c72(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c72(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndspos(pi(z0), x1)) → c72(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndspos(plus(z0, z1), x1)) → c72(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndspos(times(z0, z1), x1)) → c72(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndspos(square(z0), x1)) → c72(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndspos(x0, 0)) → c72(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndspos(x0, nil)) → c72(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndspos(x0, rnil)) → c72(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndspos(0, x1)) → c72(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndspos(nil, x1)) → c72(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndspos(rnil, x1)) → c72(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(x0, s(z0))) → c73(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndsneg(x0, posrecip(z0))) → c73(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndsneg(x0, negrecip(z0))) → c73(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndsneg(x0, cons(z0, z1))) → c73(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndsneg(x0, cons2(z0, z1))) → c73(2NDSNEG(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(2ndsneg(x0, rcons(z0, z1))) → c73(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndsneg(x0, from(z0))) → c73(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c73(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c73(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndsneg(x0, pi(z0))) → c73(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndsneg(x0, plus(z0, z1))) → c73(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndsneg(x0, times(z0, z1))) → c73(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndsneg(x0, square(z0))) → c73(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndsneg(s(z0), x1)) → c73(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndsneg(posrecip(z0), x1)) → c73(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndsneg(negrecip(z0), x1)) → c73(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndsneg(cons(z0, z1), x1)) → c73(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(cons2(z0, z1), x1)) → c73(2NDSNEG(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(2ndsneg(rcons(z0, z1), x1)) → c73(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(from(z0), x1)) → c73(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c73(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c73(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndsneg(pi(z0), x1)) → c73(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndsneg(plus(z0, z1), x1)) → c73(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndsneg(times(z0, z1), x1)) → c73(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndsneg(square(z0), x1)) → c73(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndsneg(x0, 0)) → c73(2NDSNEG(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndsneg(x0, nil)) → c73(2NDSNEG(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndsneg(x0, rnil)) → c73(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndsneg(0, x1)) → c73(2NDSNEG(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndsneg(nil, x1)) → c73(2NDSNEG(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(rnil, x1)) → c73(2NDSNEG(ok(rnil), proper(x1)), PROPER(x1))
PROPER(pi(s(z0))) → c74(PI(s(proper(z0))), PROPER(s(z0)))
PROPER(pi(posrecip(z0))) → c74(PI(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(pi(negrecip(z0))) → c74(PI(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(pi(cons(z0, z1))) → c74(PI(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(pi(cons2(z0, z1))) → c74(PI(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(pi(rcons(z0, z1))) → c74(PI(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(pi(from(z0))) → c74(PI(from(proper(z0))), PROPER(from(z0)))
PROPER(pi(2ndspos(z0, z1))) → c74(PI(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(pi(2ndsneg(z0, z1))) → c74(PI(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(pi(pi(z0))) → c74(PI(pi(proper(z0))), PROPER(pi(z0)))
PROPER(pi(plus(z0, z1))) → c74(PI(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(pi(times(z0, z1))) → c74(PI(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(pi(square(z0))) → c74(PI(square(proper(z0))), PROPER(square(z0)))
PROPER(pi(0)) → c74(PI(ok(0)))
PROPER(pi(nil)) → c74(PI(ok(nil)))
PROPER(pi(rnil)) → c74(PI(ok(rnil)))
PROPER(plus(x0, s(z0))) → c75(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(plus(x0, posrecip(z0))) → c75(PLUS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(plus(x0, negrecip(z0))) → c75(PLUS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(plus(x0, cons(z0, z1))) → c75(PLUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(plus(x0, cons2(z0, z1))) → c75(PLUS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(plus(x0, rcons(z0, z1))) → c75(PLUS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(plus(x0, from(z0))) → c75(PLUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(plus(x0, 2ndspos(z0, z1))) → c75(PLUS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(plus(x0, 2ndsneg(z0, z1))) → c75(PLUS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(plus(x0, pi(z0))) → c75(PLUS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(plus(x0, plus(z0, z1))) → c75(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(plus(x0, times(z0, z1))) → c75(PLUS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(plus(x0, square(z0))) → c75(PLUS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(plus(s(z0), x1)) → c75(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(plus(posrecip(z0), x1)) → c75(PLUS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(plus(negrecip(z0), x1)) → c75(PLUS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(plus(cons(z0, z1), x1)) → c75(PLUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(plus(cons2(z0, z1), x1)) → c75(PLUS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(plus(rcons(z0, z1), x1)) → c75(PLUS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(plus(from(z0), x1)) → c75(PLUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(plus(2ndspos(z0, z1), x1)) → c75(PLUS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(plus(2ndsneg(z0, z1), x1)) → c75(PLUS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(plus(pi(z0), x1)) → c75(PLUS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(plus(plus(z0, z1), x1)) → c75(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(plus(times(z0, z1), x1)) → c75(PLUS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(plus(square(z0), x1)) → c75(PLUS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(plus(x0, 0)) → c75(PLUS(proper(x0), ok(0)), PROPER(x0))
PROPER(plus(x0, nil)) → c75(PLUS(proper(x0), ok(nil)), PROPER(x0))
PROPER(plus(x0, rnil)) → c75(PLUS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(plus(0, x1)) → c75(PLUS(ok(0), proper(x1)), PROPER(x1))
PROPER(plus(nil, x1)) → c75(PLUS(ok(nil), proper(x1)), PROPER(x1))
PROPER(plus(rnil, x1)) → c75(PLUS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(times(x0, s(z0))) → c76(TIMES(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(times(x0, posrecip(z0))) → c76(TIMES(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(times(x0, negrecip(z0))) → c76(TIMES(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(times(x0, cons(z0, z1))) → c76(TIMES(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(times(x0, cons2(z0, z1))) → c76(TIMES(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(times(x0, rcons(z0, z1))) → c76(TIMES(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(times(x0, from(z0))) → c76(TIMES(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(times(x0, 2ndspos(z0, z1))) → c76(TIMES(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(times(x0, 2ndsneg(z0, z1))) → c76(TIMES(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(times(x0, pi(z0))) → c76(TIMES(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(times(x0, plus(z0, z1))) → c76(TIMES(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(times(x0, times(z0, z1))) → c76(TIMES(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(times(x0, square(z0))) → c76(TIMES(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(times(s(z0), x1)) → c76(TIMES(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(times(posrecip(z0), x1)) → c76(TIMES(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(times(negrecip(z0), x1)) → c76(TIMES(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(times(cons(z0, z1), x1)) → c76(TIMES(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(times(cons2(z0, z1), x1)) → c76(TIMES(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(times(rcons(z0, z1), x1)) → c76(TIMES(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(times(from(z0), x1)) → c76(TIMES(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(times(2ndspos(z0, z1), x1)) → c76(TIMES(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(times(2ndsneg(z0, z1), x1)) → c76(TIMES(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(times(pi(z0), x1)) → c76(TIMES(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(times(plus(z0, z1), x1)) → c76(TIMES(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(times(times(z0, z1), x1)) → c76(TIMES(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(times(square(z0), x1)) → c76(TIMES(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(times(x0, 0)) → c76(TIMES(proper(x0), ok(0)), PROPER(x0))
PROPER(times(x0, nil)) → c76(TIMES(proper(x0), ok(nil)), PROPER(x0))
PROPER(times(x0, rnil)) → c76(TIMES(proper(x0), ok(rnil)), PROPER(x0))
PROPER(times(0, x1)) → c76(TIMES(ok(0), proper(x1)), PROPER(x1))
PROPER(times(nil, x1)) → c76(TIMES(ok(nil), proper(x1)), PROPER(x1))
PROPER(times(rnil, x1)) → c76(TIMES(ok(rnil), proper(x1)), PROPER(x1))
PROPER(square(s(z0))) → c77(SQUARE(s(proper(z0))), PROPER(s(z0)))
PROPER(square(posrecip(z0))) → c77(SQUARE(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(square(negrecip(z0))) → c77(SQUARE(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(square(cons(z0, z1))) → c77(SQUARE(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(square(cons2(z0, z1))) → c77(SQUARE(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(square(rcons(z0, z1))) → c77(SQUARE(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(square(from(z0))) → c77(SQUARE(from(proper(z0))), PROPER(from(z0)))
PROPER(square(2ndspos(z0, z1))) → c77(SQUARE(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(square(2ndsneg(z0, z1))) → c77(SQUARE(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(square(pi(z0))) → c77(SQUARE(pi(proper(z0))), PROPER(pi(z0)))
PROPER(square(plus(z0, z1))) → c77(SQUARE(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(square(times(z0, z1))) → c77(SQUARE(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(square(square(z0))) → c77(SQUARE(square(proper(z0))), PROPER(square(z0)))
PROPER(square(0)) → c77(SQUARE(ok(0)))
PROPER(square(nil)) → c77(SQUARE(ok(nil)))
PROPER(square(rnil)) → c77(SQUARE(ok(rnil)))
TOP(mark(s(z0))) → c78(TOP(s(proper(z0))), PROPER(s(z0)))
TOP(mark(posrecip(z0))) → c78(TOP(posrecip(proper(z0))), PROPER(posrecip(z0)))
TOP(mark(negrecip(z0))) → c78(TOP(negrecip(proper(z0))), PROPER(negrecip(z0)))
TOP(mark(cons(z0, z1))) → c78(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
TOP(mark(cons2(z0, z1))) → c78(TOP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
TOP(mark(rcons(z0, z1))) → c78(TOP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
TOP(mark(from(z0))) → c78(TOP(from(proper(z0))), PROPER(from(z0)))
TOP(mark(2ndspos(z0, z1))) → c78(TOP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
TOP(mark(2ndsneg(z0, z1))) → c78(TOP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
TOP(mark(pi(z0))) → c78(TOP(pi(proper(z0))), PROPER(pi(z0)))
TOP(mark(plus(z0, z1))) → c78(TOP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
TOP(mark(times(z0, z1))) → c78(TOP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
TOP(mark(square(z0))) → c78(TOP(square(proper(z0))), PROPER(square(z0)))
TOP(mark(0)) → c78(TOP(ok(0)))
TOP(mark(nil)) → c78(TOP(ok(nil)))
TOP(mark(rnil)) → c78(TOP(ok(rnil)))
S tuples:
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
TOP(ok(z0)) → c79(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c9(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(2NDSPOS(s(z0), cons2(z1, z2)))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(2NDSNEG(s(z0), cons2(z1, z2)))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c13(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, z2)))) → c13(S(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(s(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, z2)))) → c13(S(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(s(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c13(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c13(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c13(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c13(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c13(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c13(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c13(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c13(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(cons2(z0, z1))) → c13(S(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c13(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c13(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c13(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c14(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c14(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c14(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c14(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c14(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c14(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c14(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c14(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(cons2(z0, z1))) → c14(POSRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c15(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c15(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c15(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c15(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c15(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c15(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c15(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c15(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(cons2(z0, z1))) → c15(NEGRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndspos(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndspos(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndsneg(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndsneg(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c16(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c16(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c16(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c16(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c16(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c16(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c16(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c16(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(cons2(z0, z1), x1)) → c16(CONS(cons2(z0, active(z1)), x1), ACTIVE(cons2(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, 2ndsneg(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(0, z0))) → c17(CONS2(x0, mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(cons2(x0, plus(s(z0), z1))) → c17(CONS2(x0, mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons2(x0, times(0, z0))) → c17(CONS2(x0, mark(0)), ACTIVE(times(0, z0)))
ACTIVE(cons2(x0, times(s(z0), z1))) → c17(CONS2(x0, mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(cons2(x0, s(z0))) → c17(CONS2(x0, s(active(z0))), ACTIVE(s(z0)))
ACTIVE(cons2(x0, posrecip(z0))) → c17(CONS2(x0, posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(cons2(x0, negrecip(z0))) → c17(CONS2(x0, negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(cons2(x0, cons(z0, z1))) → c17(CONS2(x0, cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(cons2(x0, cons2(z0, z1))) → c17(CONS2(x0, cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, from(active(z0))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, square(active(z0))), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c20(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(from(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(from(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c20(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c20(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c20(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c20(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c20(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c20(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c20(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c20(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c20(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c20(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(cons2(z0, z1))) → c20(FROM(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c20(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c20(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c20(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c25(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c25(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c25(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c25(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c25(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c25(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c25(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c25(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c25(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c25(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c25(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(cons2(z0, z1))) → c25(PI(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c25(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c25(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c25(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c30(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(square(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(square(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c30(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c30(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c30(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c30(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c30(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c30(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c30(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c30(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c30(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(cons2(z0, z1))) → c30(SQUARE(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c30(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c30(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c63(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c63(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c63(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c63(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(cons2(z0, z1))) → c63(S(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(s(rcons(z0, z1))) → c63(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c63(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c63(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c63(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c63(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c63(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c63(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c63(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c63(S(ok(0)))
PROPER(s(nil)) → c63(S(ok(nil)))
PROPER(s(rnil)) → c63(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c64(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c64(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c64(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c64(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(cons2(z0, z1))) → c64(POSRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c64(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c64(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c64(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c64(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c64(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c64(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c64(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c64(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c64(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c64(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c64(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c65(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c65(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c65(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c65(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(cons2(z0, z1))) → c65(NEGRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c65(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c65(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c65(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c65(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c65(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c65(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c65(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c65(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c65(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c65(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c65(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c67(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c67(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c67(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c67(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, cons2(z0, z1))) → c67(CONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c67(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c67(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c67(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c67(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c67(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c67(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c67(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c67(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c67(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c67(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c67(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c67(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(cons2(z0, z1), x1)) → c67(CONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c67(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c67(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c67(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c67(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c67(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c67(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c67(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c67(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c67(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c67(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c67(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c67(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c67(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c67(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(cons2(x0, s(z0))) → c68(CONS2(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons2(x0, posrecip(z0))) → c68(CONS2(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons2(x0, negrecip(z0))) → c68(CONS2(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons2(x0, cons(z0, z1))) → c68(CONS2(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons2(x0, cons2(z0, z1))) → c68(CONS2(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons2(x0, rcons(z0, z1))) → c68(CONS2(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons2(x0, from(z0))) → c68(CONS2(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons2(x0, 2ndspos(z0, z1))) → c68(CONS2(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons2(x0, 2ndsneg(z0, z1))) → c68(CONS2(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons2(x0, pi(z0))) → c68(CONS2(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons2(x0, plus(z0, z1))) → c68(CONS2(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons2(x0, times(z0, z1))) → c68(CONS2(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons2(x0, square(z0))) → c68(CONS2(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons2(s(z0), x1)) → c68(CONS2(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons2(posrecip(z0), x1)) → c68(CONS2(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons2(negrecip(z0), x1)) → c68(CONS2(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons2(cons(z0, z1), x1)) → c68(CONS2(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons2(cons2(z0, z1), x1)) → c68(CONS2(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons2(rcons(z0, z1), x1)) → c68(CONS2(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons2(from(z0), x1)) → c68(CONS2(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons2(2ndspos(z0, z1), x1)) → c68(CONS2(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons2(2ndsneg(z0, z1), x1)) → c68(CONS2(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons2(pi(z0), x1)) → c68(CONS2(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons2(plus(z0, z1), x1)) → c68(CONS2(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons2(times(z0, z1), x1)) → c68(CONS2(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons2(square(z0), x1)) → c68(CONS2(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons2(x0, 0)) → c68(CONS2(proper(x0), ok(0)), PROPER(x0))
PROPER(cons2(x0, nil)) → c68(CONS2(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons2(x0, rnil)) → c68(CONS2(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons2(0, x1)) → c68(CONS2(ok(0), proper(x1)), PROPER(x1))
PROPER(cons2(nil, x1)) → c68(CONS2(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons2(rnil, x1)) → c68(CONS2(ok(rnil), proper(x1)), PROPER(x1))
PROPER(rcons(x0, s(z0))) → c70(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c70(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c70(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, cons(z0, z1))) → c70(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, cons2(z0, z1))) → c70(RCONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(rcons(x0, rcons(z0, z1))) → c70(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c70(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c70(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c70(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c70(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c70(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c70(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c70(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(s(z0), x1)) → c70(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c70(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c70(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c70(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(cons2(z0, z1), x1)) → c70(RCONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c70(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c70(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c70(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c70(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c70(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c70(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c70(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c70(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(rcons(x0, 0)) → c70(RCONS(proper(x0), ok(0)), PROPER(x0))
PROPER(rcons(x0, nil)) → c70(RCONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(rcons(x0, rnil)) → c70(RCONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(rcons(0, x1)) → c70(RCONS(ok(0), proper(x1)), PROPER(x1))
PROPER(rcons(nil, x1)) → c70(RCONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c70(RCONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(from(s(z0))) → c71(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(posrecip(z0))) → c71(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(from(negrecip(z0))) → c71(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(from(cons(z0, z1))) → c71(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(cons2(z0, z1))) → c71(FROM(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(from(rcons(z0, z1))) → c71(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(from(from(z0))) → c71(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(2ndspos(z0, z1))) → c71(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(from(2ndsneg(z0, z1))) → c71(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(from(pi(z0))) → c71(FROM(pi(proper(z0))), PROPER(pi(z0)))
PROPER(from(plus(z0, z1))) → c71(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(from(times(z0, z1))) → c71(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(from(square(z0))) → c71(FROM(square(proper(z0))), PROPER(square(z0)))
PROPER(from(0)) → c71(FROM(ok(0)))
PROPER(from(nil)) → c71(FROM(ok(nil)))
PROPER(from(rnil)) → c71(FROM(ok(rnil)))
PROPER(2ndspos(x0, s(z0))) → c72(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndspos(x0, posrecip(z0))) → c72(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndspos(x0, negrecip(z0))) → c72(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndspos(x0, cons(z0, z1))) → c72(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndspos(x0, cons2(z0, z1))) → c72(2NDSPOS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(2ndspos(x0, rcons(z0, z1))) → c72(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndspos(x0, from(z0))) → c72(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c72(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c72(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndspos(x0, pi(z0))) → c72(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndspos(x0, plus(z0, z1))) → c72(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndspos(x0, times(z0, z1))) → c72(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndspos(x0, square(z0))) → c72(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndspos(s(z0), x1)) → c72(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndspos(posrecip(z0), x1)) → c72(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndspos(negrecip(z0), x1)) → c72(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndspos(cons(z0, z1), x1)) → c72(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndspos(cons2(z0, z1), x1)) → c72(2NDSPOS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(2ndspos(rcons(z0, z1), x1)) → c72(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndspos(from(z0), x1)) → c72(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c72(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c72(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndspos(pi(z0), x1)) → c72(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndspos(plus(z0, z1), x1)) → c72(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndspos(times(z0, z1), x1)) → c72(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndspos(square(z0), x1)) → c72(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndspos(x0, 0)) → c72(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndspos(x0, nil)) → c72(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndspos(x0, rnil)) → c72(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndspos(0, x1)) → c72(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndspos(nil, x1)) → c72(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndspos(rnil, x1)) → c72(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(x0, s(z0))) → c73(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndsneg(x0, posrecip(z0))) → c73(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndsneg(x0, negrecip(z0))) → c73(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndsneg(x0, cons(z0, z1))) → c73(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndsneg(x0, cons2(z0, z1))) → c73(2NDSNEG(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(2ndsneg(x0, rcons(z0, z1))) → c73(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndsneg(x0, from(z0))) → c73(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c73(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c73(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndsneg(x0, pi(z0))) → c73(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndsneg(x0, plus(z0, z1))) → c73(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndsneg(x0, times(z0, z1))) → c73(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndsneg(x0, square(z0))) → c73(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndsneg(s(z0), x1)) → c73(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndsneg(posrecip(z0), x1)) → c73(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndsneg(negrecip(z0), x1)) → c73(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndsneg(cons(z0, z1), x1)) → c73(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(cons2(z0, z1), x1)) → c73(2NDSNEG(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(2ndsneg(rcons(z0, z1), x1)) → c73(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(from(z0), x1)) → c73(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c73(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c73(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndsneg(pi(z0), x1)) → c73(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndsneg(plus(z0, z1), x1)) → c73(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndsneg(times(z0, z1), x1)) → c73(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndsneg(square(z0), x1)) → c73(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndsneg(x0, 0)) → c73(2NDSNEG(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndsneg(x0, nil)) → c73(2NDSNEG(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndsneg(x0, rnil)) → c73(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndsneg(0, x1)) → c73(2NDSNEG(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndsneg(nil, x1)) → c73(2NDSNEG(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(rnil, x1)) → c73(2NDSNEG(ok(rnil), proper(x1)), PROPER(x1))
PROPER(pi(s(z0))) → c74(PI(s(proper(z0))), PROPER(s(z0)))
PROPER(pi(posrecip(z0))) → c74(PI(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(pi(negrecip(z0))) → c74(PI(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(pi(cons(z0, z1))) → c74(PI(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(pi(cons2(z0, z1))) → c74(PI(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(pi(rcons(z0, z1))) → c74(PI(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(pi(from(z0))) → c74(PI(from(proper(z0))), PROPER(from(z0)))
PROPER(pi(2ndspos(z0, z1))) → c74(PI(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(pi(2ndsneg(z0, z1))) → c74(PI(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(pi(pi(z0))) → c74(PI(pi(proper(z0))), PROPER(pi(z0)))
PROPER(pi(plus(z0, z1))) → c74(PI(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(pi(times(z0, z1))) → c74(PI(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(pi(square(z0))) → c74(PI(square(proper(z0))), PROPER(square(z0)))
PROPER(pi(0)) → c74(PI(ok(0)))
PROPER(pi(nil)) → c74(PI(ok(nil)))
PROPER(pi(rnil)) → c74(PI(ok(rnil)))
PROPER(plus(x0, s(z0))) → c75(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(plus(x0, posrecip(z0))) → c75(PLUS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(plus(x0, negrecip(z0))) → c75(PLUS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(plus(x0, cons(z0, z1))) → c75(PLUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(plus(x0, cons2(z0, z1))) → c75(PLUS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(plus(x0, rcons(z0, z1))) → c75(PLUS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(plus(x0, from(z0))) → c75(PLUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(plus(x0, 2ndspos(z0, z1))) → c75(PLUS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(plus(x0, 2ndsneg(z0, z1))) → c75(PLUS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(plus(x0, pi(z0))) → c75(PLUS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(plus(x0, plus(z0, z1))) → c75(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(plus(x0, times(z0, z1))) → c75(PLUS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(plus(x0, square(z0))) → c75(PLUS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(plus(s(z0), x1)) → c75(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(plus(posrecip(z0), x1)) → c75(PLUS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(plus(negrecip(z0), x1)) → c75(PLUS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(plus(cons(z0, z1), x1)) → c75(PLUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(plus(cons2(z0, z1), x1)) → c75(PLUS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(plus(rcons(z0, z1), x1)) → c75(PLUS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(plus(from(z0), x1)) → c75(PLUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(plus(2ndspos(z0, z1), x1)) → c75(PLUS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(plus(2ndsneg(z0, z1), x1)) → c75(PLUS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(plus(pi(z0), x1)) → c75(PLUS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(plus(plus(z0, z1), x1)) → c75(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(plus(times(z0, z1), x1)) → c75(PLUS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(plus(square(z0), x1)) → c75(PLUS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(plus(x0, 0)) → c75(PLUS(proper(x0), ok(0)), PROPER(x0))
PROPER(plus(x0, nil)) → c75(PLUS(proper(x0), ok(nil)), PROPER(x0))
PROPER(plus(x0, rnil)) → c75(PLUS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(plus(0, x1)) → c75(PLUS(ok(0), proper(x1)), PROPER(x1))
PROPER(plus(nil, x1)) → c75(PLUS(ok(nil), proper(x1)), PROPER(x1))
PROPER(plus(rnil, x1)) → c75(PLUS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(times(x0, s(z0))) → c76(TIMES(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(times(x0, posrecip(z0))) → c76(TIMES(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(times(x0, negrecip(z0))) → c76(TIMES(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(times(x0, cons(z0, z1))) → c76(TIMES(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(times(x0, cons2(z0, z1))) → c76(TIMES(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(times(x0, rcons(z0, z1))) → c76(TIMES(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(times(x0, from(z0))) → c76(TIMES(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(times(x0, 2ndspos(z0, z1))) → c76(TIMES(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(times(x0, 2ndsneg(z0, z1))) → c76(TIMES(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(times(x0, pi(z0))) → c76(TIMES(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(times(x0, plus(z0, z1))) → c76(TIMES(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(times(x0, times(z0, z1))) → c76(TIMES(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(times(x0, square(z0))) → c76(TIMES(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(times(s(z0), x1)) → c76(TIMES(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(times(posrecip(z0), x1)) → c76(TIMES(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(times(negrecip(z0), x1)) → c76(TIMES(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(times(cons(z0, z1), x1)) → c76(TIMES(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(times(cons2(z0, z1), x1)) → c76(TIMES(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(times(rcons(z0, z1), x1)) → c76(TIMES(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(times(from(z0), x1)) → c76(TIMES(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(times(2ndspos(z0, z1), x1)) → c76(TIMES(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(times(2ndsneg(z0, z1), x1)) → c76(TIMES(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(times(pi(z0), x1)) → c76(TIMES(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(times(plus(z0, z1), x1)) → c76(TIMES(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(times(times(z0, z1), x1)) → c76(TIMES(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(times(square(z0), x1)) → c76(TIMES(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(times(x0, 0)) → c76(TIMES(proper(x0), ok(0)), PROPER(x0))
PROPER(times(x0, nil)) → c76(TIMES(proper(x0), ok(nil)), PROPER(x0))
PROPER(times(x0, rnil)) → c76(TIMES(proper(x0), ok(rnil)), PROPER(x0))
PROPER(times(0, x1)) → c76(TIMES(ok(0), proper(x1)), PROPER(x1))
PROPER(times(nil, x1)) → c76(TIMES(ok(nil), proper(x1)), PROPER(x1))
PROPER(times(rnil, x1)) → c76(TIMES(ok(rnil), proper(x1)), PROPER(x1))
PROPER(square(s(z0))) → c77(SQUARE(s(proper(z0))), PROPER(s(z0)))
PROPER(square(posrecip(z0))) → c77(SQUARE(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(square(negrecip(z0))) → c77(SQUARE(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(square(cons(z0, z1))) → c77(SQUARE(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(square(cons2(z0, z1))) → c77(SQUARE(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(square(rcons(z0, z1))) → c77(SQUARE(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(square(from(z0))) → c77(SQUARE(from(proper(z0))), PROPER(from(z0)))
PROPER(square(2ndspos(z0, z1))) → c77(SQUARE(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(square(2ndsneg(z0, z1))) → c77(SQUARE(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(square(pi(z0))) → c77(SQUARE(pi(proper(z0))), PROPER(pi(z0)))
PROPER(square(plus(z0, z1))) → c77(SQUARE(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(square(times(z0, z1))) → c77(SQUARE(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(square(square(z0))) → c77(SQUARE(square(proper(z0))), PROPER(square(z0)))
PROPER(square(0)) → c77(SQUARE(ok(0)))
PROPER(square(nil)) → c77(SQUARE(ok(nil)))
PROPER(square(rnil)) → c77(SQUARE(ok(rnil)))
TOP(mark(s(z0))) → c78(TOP(s(proper(z0))), PROPER(s(z0)))
TOP(mark(posrecip(z0))) → c78(TOP(posrecip(proper(z0))), PROPER(posrecip(z0)))
TOP(mark(negrecip(z0))) → c78(TOP(negrecip(proper(z0))), PROPER(negrecip(z0)))
TOP(mark(cons(z0, z1))) → c78(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
TOP(mark(cons2(z0, z1))) → c78(TOP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
TOP(mark(rcons(z0, z1))) → c78(TOP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
TOP(mark(from(z0))) → c78(TOP(from(proper(z0))), PROPER(from(z0)))
TOP(mark(2ndspos(z0, z1))) → c78(TOP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
TOP(mark(2ndsneg(z0, z1))) → c78(TOP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
TOP(mark(pi(z0))) → c78(TOP(pi(proper(z0))), PROPER(pi(z0)))
TOP(mark(plus(z0, z1))) → c78(TOP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
TOP(mark(times(z0, z1))) → c78(TOP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
TOP(mark(square(z0))) → c78(TOP(square(proper(z0))), PROPER(square(z0)))
TOP(mark(0)) → c78(TOP(ok(0)))
TOP(mark(nil)) → c78(TOP(ok(nil)))
TOP(mark(rnil)) → c78(TOP(ok(rnil)))
K tuples:none
Defined Rule Symbols:
active, 2ndspos, cons2, rcons, posrecip, 2ndsneg, negrecip, s, cons, from, pi, plus, times, square, proper
Defined Pair Symbols:
ACTIVE, S, POSRECIP, NEGRECIP, CONS, CONS2, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, TOP, PROPER
Compound Symbols:
c12, c18, c19, c21, c22, c23, c24, c26, c27, c28, c29, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c79, c, c7, c9, c11, c1, c13, c14, c15, c16, c17, c20, c25, c30, c63, c63, c64, c64, c65, c65, c67, c67, c68, c68, c70, c70, c71, c71, c72, c72, c73, c73, c74, c74, c75, c75, c76, c76, c77, c77, c78, c78
(83) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
TOP(
ok(
z0)) →
c79(
TOP(
active(
z0)),
ACTIVE(
z0)) by
TOP(ok(from(z0))) → c79(TOP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
TOP(ok(2ndspos(0, z0))) → c79(TOP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
TOP(ok(2ndspos(s(z0), cons(z1, z2)))) → c79(TOP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
TOP(ok(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c79(TOP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
TOP(ok(2ndsneg(0, z0))) → c79(TOP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
TOP(ok(2ndsneg(s(z0), cons(z1, z2)))) → c79(TOP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
TOP(ok(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c79(TOP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
TOP(ok(pi(z0))) → c79(TOP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
TOP(ok(plus(0, z0))) → c79(TOP(mark(z0)), ACTIVE(plus(0, z0)))
TOP(ok(plus(s(z0), z1))) → c79(TOP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
TOP(ok(times(0, z0))) → c79(TOP(mark(0)), ACTIVE(times(0, z0)))
TOP(ok(times(s(z0), z1))) → c79(TOP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
TOP(ok(square(z0))) → c79(TOP(mark(times(z0, z0))), ACTIVE(square(z0)))
TOP(ok(s(z0))) → c79(TOP(s(active(z0))), ACTIVE(s(z0)))
TOP(ok(posrecip(z0))) → c79(TOP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
TOP(ok(negrecip(z0))) → c79(TOP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
TOP(ok(cons(z0, z1))) → c79(TOP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
TOP(ok(cons2(z0, z1))) → c79(TOP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
TOP(ok(rcons(z0, z1))) → c79(TOP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
TOP(ok(rcons(z0, z1))) → c79(TOP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
TOP(ok(from(z0))) → c79(TOP(from(active(z0))), ACTIVE(from(z0)))
TOP(ok(2ndspos(z0, z1))) → c79(TOP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
TOP(ok(2ndspos(z0, z1))) → c79(TOP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
TOP(ok(2ndsneg(z0, z1))) → c79(TOP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
TOP(ok(2ndsneg(z0, z1))) → c79(TOP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
TOP(ok(pi(z0))) → c79(TOP(pi(active(z0))), ACTIVE(pi(z0)))
TOP(ok(plus(z0, z1))) → c79(TOP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
TOP(ok(plus(z0, z1))) → c79(TOP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
TOP(ok(times(z0, z1))) → c79(TOP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
TOP(ok(times(z0, z1))) → c79(TOP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
TOP(ok(square(z0))) → c79(TOP(square(active(z0))), ACTIVE(square(z0)))
(84) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(2ndspos(0, z0)) → mark(rnil)
active(2ndspos(s(z0), cons(z1, z2))) → mark(2ndspos(s(z0), cons2(z1, z2)))
active(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(z1, z2))) → mark(2ndsneg(s(z0), cons2(z1, z2)))
active(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
active(pi(z0)) → mark(2ndspos(z0, from(0)))
active(plus(0, z0)) → mark(z0)
active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
active(times(0, z0)) → mark(0)
active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
active(square(z0)) → mark(times(z0, z0))
active(s(z0)) → s(active(z0))
active(posrecip(z0)) → posrecip(active(z0))
active(negrecip(z0)) → negrecip(active(z0))
active(cons(z0, z1)) → cons(active(z0), z1)
active(cons2(z0, z1)) → cons2(z0, active(z1))
active(rcons(z0, z1)) → rcons(active(z0), z1)
active(rcons(z0, z1)) → rcons(z0, active(z1))
active(from(z0)) → from(active(z0))
active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
active(pi(z0)) → pi(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(times(z0, z1)) → times(active(z0), z1)
active(times(z0, z1)) → times(z0, active(z1))
active(square(z0)) → square(active(z0))
2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
cons2(z0, mark(z1)) → mark(cons2(z0, z1))
cons2(ok(z0), ok(z1)) → ok(cons2(z0, z1))
rcons(mark(z0), z1) → mark(rcons(z0, z1))
rcons(z0, mark(z1)) → mark(rcons(z0, z1))
rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
posrecip(ok(z0)) → ok(posrecip(z0))
posrecip(mark(z0)) → mark(posrecip(z0))
2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
negrecip(ok(z0)) → ok(negrecip(z0))
negrecip(mark(z0)) → mark(negrecip(z0))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
cons(mark(z0), z1) → mark(cons(z0, z1))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
from(mark(z0)) → mark(from(z0))
from(ok(z0)) → ok(from(z0))
pi(mark(z0)) → mark(pi(z0))
pi(ok(z0)) → ok(pi(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
times(mark(z0), z1) → mark(times(z0, z1))
times(ok(z0), ok(z1)) → ok(times(z0, z1))
times(z0, mark(z1)) → mark(times(z0, z1))
square(mark(z0)) → mark(square(z0))
square(ok(z0)) → ok(square(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(posrecip(z0)) → posrecip(proper(z0))
proper(negrecip(z0)) → negrecip(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(cons2(z0, z1)) → cons2(proper(z0), proper(z1))
proper(rnil) → ok(rnil)
proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
proper(pi(z0)) → pi(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(times(z0, z1)) → times(proper(z0), proper(z1))
proper(square(z0)) → square(proper(z0))
Tuples:
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c9(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(2NDSPOS(s(z0), cons2(z1, z2)))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(2NDSNEG(s(z0), cons2(z1, z2)))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c13(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, z2)))) → c13(S(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(s(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, z2)))) → c13(S(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(s(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c13(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c13(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c13(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c13(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c13(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c13(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c13(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c13(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(cons2(z0, z1))) → c13(S(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c13(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c13(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c13(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c14(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c14(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c14(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c14(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c14(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c14(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c14(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c14(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(cons2(z0, z1))) → c14(POSRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c15(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c15(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c15(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c15(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c15(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c15(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c15(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c15(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(cons2(z0, z1))) → c15(NEGRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndspos(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndspos(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndsneg(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndsneg(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c16(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c16(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c16(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c16(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c16(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c16(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c16(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c16(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(cons2(z0, z1), x1)) → c16(CONS(cons2(z0, active(z1)), x1), ACTIVE(cons2(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, 2ndsneg(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(0, z0))) → c17(CONS2(x0, mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(cons2(x0, plus(s(z0), z1))) → c17(CONS2(x0, mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons2(x0, times(0, z0))) → c17(CONS2(x0, mark(0)), ACTIVE(times(0, z0)))
ACTIVE(cons2(x0, times(s(z0), z1))) → c17(CONS2(x0, mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(cons2(x0, s(z0))) → c17(CONS2(x0, s(active(z0))), ACTIVE(s(z0)))
ACTIVE(cons2(x0, posrecip(z0))) → c17(CONS2(x0, posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(cons2(x0, negrecip(z0))) → c17(CONS2(x0, negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(cons2(x0, cons(z0, z1))) → c17(CONS2(x0, cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(cons2(x0, cons2(z0, z1))) → c17(CONS2(x0, cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, from(active(z0))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, square(active(z0))), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c20(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(from(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(from(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c20(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c20(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c20(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c20(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c20(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c20(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c20(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c20(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c20(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c20(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(cons2(z0, z1))) → c20(FROM(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c20(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c20(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c20(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c25(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c25(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c25(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c25(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c25(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c25(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c25(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c25(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c25(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c25(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c25(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(cons2(z0, z1))) → c25(PI(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c25(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c25(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c25(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c30(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(square(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(square(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c30(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c30(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c30(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c30(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c30(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c30(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c30(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c30(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c30(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(cons2(z0, z1))) → c30(SQUARE(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c30(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c30(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c63(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c63(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c63(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c63(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(cons2(z0, z1))) → c63(S(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(s(rcons(z0, z1))) → c63(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c63(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c63(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c63(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c63(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c63(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c63(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c63(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c63(S(ok(0)))
PROPER(s(nil)) → c63(S(ok(nil)))
PROPER(s(rnil)) → c63(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c64(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c64(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c64(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c64(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(cons2(z0, z1))) → c64(POSRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c64(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c64(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c64(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c64(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c64(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c64(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c64(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c64(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c64(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c64(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c64(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c65(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c65(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c65(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c65(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(cons2(z0, z1))) → c65(NEGRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c65(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c65(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c65(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c65(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c65(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c65(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c65(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c65(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c65(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c65(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c65(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c67(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c67(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c67(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c67(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, cons2(z0, z1))) → c67(CONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c67(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c67(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c67(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c67(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c67(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c67(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c67(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c67(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c67(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c67(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c67(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c67(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(cons2(z0, z1), x1)) → c67(CONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c67(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c67(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c67(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c67(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c67(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c67(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c67(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c67(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c67(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c67(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c67(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c67(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c67(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c67(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(cons2(x0, s(z0))) → c68(CONS2(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons2(x0, posrecip(z0))) → c68(CONS2(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons2(x0, negrecip(z0))) → c68(CONS2(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons2(x0, cons(z0, z1))) → c68(CONS2(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons2(x0, cons2(z0, z1))) → c68(CONS2(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons2(x0, rcons(z0, z1))) → c68(CONS2(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons2(x0, from(z0))) → c68(CONS2(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons2(x0, 2ndspos(z0, z1))) → c68(CONS2(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons2(x0, 2ndsneg(z0, z1))) → c68(CONS2(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons2(x0, pi(z0))) → c68(CONS2(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons2(x0, plus(z0, z1))) → c68(CONS2(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons2(x0, times(z0, z1))) → c68(CONS2(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons2(x0, square(z0))) → c68(CONS2(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons2(s(z0), x1)) → c68(CONS2(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons2(posrecip(z0), x1)) → c68(CONS2(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons2(negrecip(z0), x1)) → c68(CONS2(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons2(cons(z0, z1), x1)) → c68(CONS2(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons2(cons2(z0, z1), x1)) → c68(CONS2(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons2(rcons(z0, z1), x1)) → c68(CONS2(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons2(from(z0), x1)) → c68(CONS2(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons2(2ndspos(z0, z1), x1)) → c68(CONS2(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons2(2ndsneg(z0, z1), x1)) → c68(CONS2(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons2(pi(z0), x1)) → c68(CONS2(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons2(plus(z0, z1), x1)) → c68(CONS2(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons2(times(z0, z1), x1)) → c68(CONS2(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons2(square(z0), x1)) → c68(CONS2(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons2(x0, 0)) → c68(CONS2(proper(x0), ok(0)), PROPER(x0))
PROPER(cons2(x0, nil)) → c68(CONS2(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons2(x0, rnil)) → c68(CONS2(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons2(0, x1)) → c68(CONS2(ok(0), proper(x1)), PROPER(x1))
PROPER(cons2(nil, x1)) → c68(CONS2(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons2(rnil, x1)) → c68(CONS2(ok(rnil), proper(x1)), PROPER(x1))
PROPER(rcons(x0, s(z0))) → c70(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c70(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c70(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, cons(z0, z1))) → c70(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, cons2(z0, z1))) → c70(RCONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(rcons(x0, rcons(z0, z1))) → c70(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c70(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c70(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c70(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c70(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c70(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c70(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c70(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(s(z0), x1)) → c70(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c70(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c70(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c70(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(cons2(z0, z1), x1)) → c70(RCONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c70(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c70(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c70(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c70(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c70(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c70(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c70(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c70(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(rcons(x0, 0)) → c70(RCONS(proper(x0), ok(0)), PROPER(x0))
PROPER(rcons(x0, nil)) → c70(RCONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(rcons(x0, rnil)) → c70(RCONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(rcons(0, x1)) → c70(RCONS(ok(0), proper(x1)), PROPER(x1))
PROPER(rcons(nil, x1)) → c70(RCONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c70(RCONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(from(s(z0))) → c71(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(posrecip(z0))) → c71(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(from(negrecip(z0))) → c71(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(from(cons(z0, z1))) → c71(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(cons2(z0, z1))) → c71(FROM(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(from(rcons(z0, z1))) → c71(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(from(from(z0))) → c71(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(2ndspos(z0, z1))) → c71(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(from(2ndsneg(z0, z1))) → c71(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(from(pi(z0))) → c71(FROM(pi(proper(z0))), PROPER(pi(z0)))
PROPER(from(plus(z0, z1))) → c71(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(from(times(z0, z1))) → c71(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(from(square(z0))) → c71(FROM(square(proper(z0))), PROPER(square(z0)))
PROPER(from(0)) → c71(FROM(ok(0)))
PROPER(from(nil)) → c71(FROM(ok(nil)))
PROPER(from(rnil)) → c71(FROM(ok(rnil)))
PROPER(2ndspos(x0, s(z0))) → c72(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndspos(x0, posrecip(z0))) → c72(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndspos(x0, negrecip(z0))) → c72(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndspos(x0, cons(z0, z1))) → c72(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndspos(x0, cons2(z0, z1))) → c72(2NDSPOS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(2ndspos(x0, rcons(z0, z1))) → c72(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndspos(x0, from(z0))) → c72(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c72(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c72(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndspos(x0, pi(z0))) → c72(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndspos(x0, plus(z0, z1))) → c72(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndspos(x0, times(z0, z1))) → c72(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndspos(x0, square(z0))) → c72(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndspos(s(z0), x1)) → c72(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndspos(posrecip(z0), x1)) → c72(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndspos(negrecip(z0), x1)) → c72(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndspos(cons(z0, z1), x1)) → c72(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndspos(cons2(z0, z1), x1)) → c72(2NDSPOS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(2ndspos(rcons(z0, z1), x1)) → c72(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndspos(from(z0), x1)) → c72(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c72(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c72(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndspos(pi(z0), x1)) → c72(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndspos(plus(z0, z1), x1)) → c72(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndspos(times(z0, z1), x1)) → c72(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndspos(square(z0), x1)) → c72(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndspos(x0, 0)) → c72(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndspos(x0, nil)) → c72(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndspos(x0, rnil)) → c72(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndspos(0, x1)) → c72(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndspos(nil, x1)) → c72(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndspos(rnil, x1)) → c72(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(x0, s(z0))) → c73(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndsneg(x0, posrecip(z0))) → c73(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndsneg(x0, negrecip(z0))) → c73(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndsneg(x0, cons(z0, z1))) → c73(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndsneg(x0, cons2(z0, z1))) → c73(2NDSNEG(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(2ndsneg(x0, rcons(z0, z1))) → c73(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndsneg(x0, from(z0))) → c73(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c73(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c73(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndsneg(x0, pi(z0))) → c73(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndsneg(x0, plus(z0, z1))) → c73(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndsneg(x0, times(z0, z1))) → c73(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndsneg(x0, square(z0))) → c73(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndsneg(s(z0), x1)) → c73(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndsneg(posrecip(z0), x1)) → c73(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndsneg(negrecip(z0), x1)) → c73(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndsneg(cons(z0, z1), x1)) → c73(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(cons2(z0, z1), x1)) → c73(2NDSNEG(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(2ndsneg(rcons(z0, z1), x1)) → c73(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(from(z0), x1)) → c73(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c73(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c73(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndsneg(pi(z0), x1)) → c73(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndsneg(plus(z0, z1), x1)) → c73(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndsneg(times(z0, z1), x1)) → c73(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndsneg(square(z0), x1)) → c73(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndsneg(x0, 0)) → c73(2NDSNEG(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndsneg(x0, nil)) → c73(2NDSNEG(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndsneg(x0, rnil)) → c73(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndsneg(0, x1)) → c73(2NDSNEG(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndsneg(nil, x1)) → c73(2NDSNEG(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(rnil, x1)) → c73(2NDSNEG(ok(rnil), proper(x1)), PROPER(x1))
PROPER(pi(s(z0))) → c74(PI(s(proper(z0))), PROPER(s(z0)))
PROPER(pi(posrecip(z0))) → c74(PI(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(pi(negrecip(z0))) → c74(PI(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(pi(cons(z0, z1))) → c74(PI(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(pi(cons2(z0, z1))) → c74(PI(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(pi(rcons(z0, z1))) → c74(PI(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(pi(from(z0))) → c74(PI(from(proper(z0))), PROPER(from(z0)))
PROPER(pi(2ndspos(z0, z1))) → c74(PI(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(pi(2ndsneg(z0, z1))) → c74(PI(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(pi(pi(z0))) → c74(PI(pi(proper(z0))), PROPER(pi(z0)))
PROPER(pi(plus(z0, z1))) → c74(PI(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(pi(times(z0, z1))) → c74(PI(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(pi(square(z0))) → c74(PI(square(proper(z0))), PROPER(square(z0)))
PROPER(pi(0)) → c74(PI(ok(0)))
PROPER(pi(nil)) → c74(PI(ok(nil)))
PROPER(pi(rnil)) → c74(PI(ok(rnil)))
PROPER(plus(x0, s(z0))) → c75(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(plus(x0, posrecip(z0))) → c75(PLUS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(plus(x0, negrecip(z0))) → c75(PLUS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(plus(x0, cons(z0, z1))) → c75(PLUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(plus(x0, cons2(z0, z1))) → c75(PLUS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(plus(x0, rcons(z0, z1))) → c75(PLUS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(plus(x0, from(z0))) → c75(PLUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(plus(x0, 2ndspos(z0, z1))) → c75(PLUS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(plus(x0, 2ndsneg(z0, z1))) → c75(PLUS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(plus(x0, pi(z0))) → c75(PLUS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(plus(x0, plus(z0, z1))) → c75(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(plus(x0, times(z0, z1))) → c75(PLUS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(plus(x0, square(z0))) → c75(PLUS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(plus(s(z0), x1)) → c75(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(plus(posrecip(z0), x1)) → c75(PLUS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(plus(negrecip(z0), x1)) → c75(PLUS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(plus(cons(z0, z1), x1)) → c75(PLUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(plus(cons2(z0, z1), x1)) → c75(PLUS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(plus(rcons(z0, z1), x1)) → c75(PLUS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(plus(from(z0), x1)) → c75(PLUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(plus(2ndspos(z0, z1), x1)) → c75(PLUS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(plus(2ndsneg(z0, z1), x1)) → c75(PLUS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(plus(pi(z0), x1)) → c75(PLUS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(plus(plus(z0, z1), x1)) → c75(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(plus(times(z0, z1), x1)) → c75(PLUS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(plus(square(z0), x1)) → c75(PLUS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(plus(x0, 0)) → c75(PLUS(proper(x0), ok(0)), PROPER(x0))
PROPER(plus(x0, nil)) → c75(PLUS(proper(x0), ok(nil)), PROPER(x0))
PROPER(plus(x0, rnil)) → c75(PLUS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(plus(0, x1)) → c75(PLUS(ok(0), proper(x1)), PROPER(x1))
PROPER(plus(nil, x1)) → c75(PLUS(ok(nil), proper(x1)), PROPER(x1))
PROPER(plus(rnil, x1)) → c75(PLUS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(times(x0, s(z0))) → c76(TIMES(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(times(x0, posrecip(z0))) → c76(TIMES(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(times(x0, negrecip(z0))) → c76(TIMES(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(times(x0, cons(z0, z1))) → c76(TIMES(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(times(x0, cons2(z0, z1))) → c76(TIMES(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(times(x0, rcons(z0, z1))) → c76(TIMES(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(times(x0, from(z0))) → c76(TIMES(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(times(x0, 2ndspos(z0, z1))) → c76(TIMES(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(times(x0, 2ndsneg(z0, z1))) → c76(TIMES(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(times(x0, pi(z0))) → c76(TIMES(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(times(x0, plus(z0, z1))) → c76(TIMES(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(times(x0, times(z0, z1))) → c76(TIMES(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(times(x0, square(z0))) → c76(TIMES(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(times(s(z0), x1)) → c76(TIMES(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(times(posrecip(z0), x1)) → c76(TIMES(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(times(negrecip(z0), x1)) → c76(TIMES(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(times(cons(z0, z1), x1)) → c76(TIMES(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(times(cons2(z0, z1), x1)) → c76(TIMES(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(times(rcons(z0, z1), x1)) → c76(TIMES(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(times(from(z0), x1)) → c76(TIMES(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(times(2ndspos(z0, z1), x1)) → c76(TIMES(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(times(2ndsneg(z0, z1), x1)) → c76(TIMES(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(times(pi(z0), x1)) → c76(TIMES(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(times(plus(z0, z1), x1)) → c76(TIMES(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(times(times(z0, z1), x1)) → c76(TIMES(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(times(square(z0), x1)) → c76(TIMES(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(times(x0, 0)) → c76(TIMES(proper(x0), ok(0)), PROPER(x0))
PROPER(times(x0, nil)) → c76(TIMES(proper(x0), ok(nil)), PROPER(x0))
PROPER(times(x0, rnil)) → c76(TIMES(proper(x0), ok(rnil)), PROPER(x0))
PROPER(times(0, x1)) → c76(TIMES(ok(0), proper(x1)), PROPER(x1))
PROPER(times(nil, x1)) → c76(TIMES(ok(nil), proper(x1)), PROPER(x1))
PROPER(times(rnil, x1)) → c76(TIMES(ok(rnil), proper(x1)), PROPER(x1))
PROPER(square(s(z0))) → c77(SQUARE(s(proper(z0))), PROPER(s(z0)))
PROPER(square(posrecip(z0))) → c77(SQUARE(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(square(negrecip(z0))) → c77(SQUARE(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(square(cons(z0, z1))) → c77(SQUARE(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(square(cons2(z0, z1))) → c77(SQUARE(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(square(rcons(z0, z1))) → c77(SQUARE(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(square(from(z0))) → c77(SQUARE(from(proper(z0))), PROPER(from(z0)))
PROPER(square(2ndspos(z0, z1))) → c77(SQUARE(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(square(2ndsneg(z0, z1))) → c77(SQUARE(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(square(pi(z0))) → c77(SQUARE(pi(proper(z0))), PROPER(pi(z0)))
PROPER(square(plus(z0, z1))) → c77(SQUARE(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(square(times(z0, z1))) → c77(SQUARE(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(square(square(z0))) → c77(SQUARE(square(proper(z0))), PROPER(square(z0)))
PROPER(square(0)) → c77(SQUARE(ok(0)))
PROPER(square(nil)) → c77(SQUARE(ok(nil)))
PROPER(square(rnil)) → c77(SQUARE(ok(rnil)))
TOP(mark(s(z0))) → c78(TOP(s(proper(z0))), PROPER(s(z0)))
TOP(mark(posrecip(z0))) → c78(TOP(posrecip(proper(z0))), PROPER(posrecip(z0)))
TOP(mark(negrecip(z0))) → c78(TOP(negrecip(proper(z0))), PROPER(negrecip(z0)))
TOP(mark(cons(z0, z1))) → c78(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
TOP(mark(cons2(z0, z1))) → c78(TOP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
TOP(mark(rcons(z0, z1))) → c78(TOP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
TOP(mark(from(z0))) → c78(TOP(from(proper(z0))), PROPER(from(z0)))
TOP(mark(2ndspos(z0, z1))) → c78(TOP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
TOP(mark(2ndsneg(z0, z1))) → c78(TOP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
TOP(mark(pi(z0))) → c78(TOP(pi(proper(z0))), PROPER(pi(z0)))
TOP(mark(plus(z0, z1))) → c78(TOP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
TOP(mark(times(z0, z1))) → c78(TOP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
TOP(mark(square(z0))) → c78(TOP(square(proper(z0))), PROPER(square(z0)))
TOP(mark(0)) → c78(TOP(ok(0)))
TOP(mark(nil)) → c78(TOP(ok(nil)))
TOP(mark(rnil)) → c78(TOP(ok(rnil)))
TOP(ok(from(z0))) → c79(TOP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
TOP(ok(2ndspos(0, z0))) → c79(TOP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
TOP(ok(2ndspos(s(z0), cons(z1, z2)))) → c79(TOP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
TOP(ok(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c79(TOP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
TOP(ok(2ndsneg(0, z0))) → c79(TOP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
TOP(ok(2ndsneg(s(z0), cons(z1, z2)))) → c79(TOP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
TOP(ok(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c79(TOP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
TOP(ok(pi(z0))) → c79(TOP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
TOP(ok(plus(0, z0))) → c79(TOP(mark(z0)), ACTIVE(plus(0, z0)))
TOP(ok(plus(s(z0), z1))) → c79(TOP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
TOP(ok(times(0, z0))) → c79(TOP(mark(0)), ACTIVE(times(0, z0)))
TOP(ok(times(s(z0), z1))) → c79(TOP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
TOP(ok(square(z0))) → c79(TOP(mark(times(z0, z0))), ACTIVE(square(z0)))
TOP(ok(s(z0))) → c79(TOP(s(active(z0))), ACTIVE(s(z0)))
TOP(ok(posrecip(z0))) → c79(TOP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
TOP(ok(negrecip(z0))) → c79(TOP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
TOP(ok(cons(z0, z1))) → c79(TOP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
TOP(ok(cons2(z0, z1))) → c79(TOP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
TOP(ok(rcons(z0, z1))) → c79(TOP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
TOP(ok(rcons(z0, z1))) → c79(TOP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
TOP(ok(from(z0))) → c79(TOP(from(active(z0))), ACTIVE(from(z0)))
TOP(ok(2ndspos(z0, z1))) → c79(TOP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
TOP(ok(2ndspos(z0, z1))) → c79(TOP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
TOP(ok(2ndsneg(z0, z1))) → c79(TOP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
TOP(ok(2ndsneg(z0, z1))) → c79(TOP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
TOP(ok(pi(z0))) → c79(TOP(pi(active(z0))), ACTIVE(pi(z0)))
TOP(ok(plus(z0, z1))) → c79(TOP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
TOP(ok(plus(z0, z1))) → c79(TOP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
TOP(ok(times(z0, z1))) → c79(TOP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
TOP(ok(times(z0, z1))) → c79(TOP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
TOP(ok(square(z0))) → c79(TOP(square(active(z0))), ACTIVE(square(z0)))
S tuples:
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c9(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(2NDSPOS(s(z0), cons2(z1, z2)))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(2NDSNEG(s(z0), cons2(z1, z2)))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c13(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, z2)))) → c13(S(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(s(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, z2)))) → c13(S(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(s(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c13(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c13(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c13(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c13(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c13(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c13(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c13(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c13(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(cons2(z0, z1))) → c13(S(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c13(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c13(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c13(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c14(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c14(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c14(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c14(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c14(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c14(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c14(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c14(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(cons2(z0, z1))) → c14(POSRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c15(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c15(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c15(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c15(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c15(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c15(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c15(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c15(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(cons2(z0, z1))) → c15(NEGRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndspos(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndspos(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndsneg(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndsneg(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c16(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c16(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c16(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c16(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c16(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c16(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c16(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c16(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(cons2(z0, z1), x1)) → c16(CONS(cons2(z0, active(z1)), x1), ACTIVE(cons2(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, 2ndsneg(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(0, z0))) → c17(CONS2(x0, mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(cons2(x0, plus(s(z0), z1))) → c17(CONS2(x0, mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons2(x0, times(0, z0))) → c17(CONS2(x0, mark(0)), ACTIVE(times(0, z0)))
ACTIVE(cons2(x0, times(s(z0), z1))) → c17(CONS2(x0, mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(cons2(x0, s(z0))) → c17(CONS2(x0, s(active(z0))), ACTIVE(s(z0)))
ACTIVE(cons2(x0, posrecip(z0))) → c17(CONS2(x0, posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(cons2(x0, negrecip(z0))) → c17(CONS2(x0, negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(cons2(x0, cons(z0, z1))) → c17(CONS2(x0, cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(cons2(x0, cons2(z0, z1))) → c17(CONS2(x0, cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, from(active(z0))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, square(active(z0))), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c20(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(from(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(from(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c20(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c20(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c20(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c20(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c20(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c20(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c20(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c20(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c20(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c20(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(cons2(z0, z1))) → c20(FROM(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c20(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c20(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c20(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c25(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c25(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c25(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c25(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c25(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c25(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c25(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c25(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c25(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c25(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c25(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(cons2(z0, z1))) → c25(PI(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c25(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c25(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c25(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c30(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(square(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(square(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c30(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c30(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c30(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c30(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c30(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c30(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c30(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c30(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c30(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(cons2(z0, z1))) → c30(SQUARE(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c30(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c30(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c63(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c63(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c63(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c63(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(cons2(z0, z1))) → c63(S(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(s(rcons(z0, z1))) → c63(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c63(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c63(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c63(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c63(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c63(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c63(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c63(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c63(S(ok(0)))
PROPER(s(nil)) → c63(S(ok(nil)))
PROPER(s(rnil)) → c63(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c64(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c64(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c64(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c64(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(cons2(z0, z1))) → c64(POSRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c64(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c64(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c64(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c64(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c64(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c64(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c64(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c64(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c64(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c64(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c64(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c65(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c65(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c65(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c65(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(cons2(z0, z1))) → c65(NEGRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c65(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c65(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c65(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c65(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c65(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c65(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c65(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c65(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c65(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c65(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c65(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c67(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c67(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c67(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c67(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, cons2(z0, z1))) → c67(CONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c67(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c67(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c67(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c67(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c67(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c67(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c67(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c67(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c67(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c67(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c67(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c67(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(cons2(z0, z1), x1)) → c67(CONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c67(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c67(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c67(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c67(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c67(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c67(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c67(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c67(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c67(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c67(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c67(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c67(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c67(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c67(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(cons2(x0, s(z0))) → c68(CONS2(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons2(x0, posrecip(z0))) → c68(CONS2(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons2(x0, negrecip(z0))) → c68(CONS2(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons2(x0, cons(z0, z1))) → c68(CONS2(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons2(x0, cons2(z0, z1))) → c68(CONS2(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons2(x0, rcons(z0, z1))) → c68(CONS2(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons2(x0, from(z0))) → c68(CONS2(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons2(x0, 2ndspos(z0, z1))) → c68(CONS2(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons2(x0, 2ndsneg(z0, z1))) → c68(CONS2(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons2(x0, pi(z0))) → c68(CONS2(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons2(x0, plus(z0, z1))) → c68(CONS2(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons2(x0, times(z0, z1))) → c68(CONS2(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons2(x0, square(z0))) → c68(CONS2(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons2(s(z0), x1)) → c68(CONS2(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons2(posrecip(z0), x1)) → c68(CONS2(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons2(negrecip(z0), x1)) → c68(CONS2(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons2(cons(z0, z1), x1)) → c68(CONS2(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons2(cons2(z0, z1), x1)) → c68(CONS2(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons2(rcons(z0, z1), x1)) → c68(CONS2(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons2(from(z0), x1)) → c68(CONS2(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons2(2ndspos(z0, z1), x1)) → c68(CONS2(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons2(2ndsneg(z0, z1), x1)) → c68(CONS2(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons2(pi(z0), x1)) → c68(CONS2(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons2(plus(z0, z1), x1)) → c68(CONS2(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons2(times(z0, z1), x1)) → c68(CONS2(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons2(square(z0), x1)) → c68(CONS2(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons2(x0, 0)) → c68(CONS2(proper(x0), ok(0)), PROPER(x0))
PROPER(cons2(x0, nil)) → c68(CONS2(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons2(x0, rnil)) → c68(CONS2(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons2(0, x1)) → c68(CONS2(ok(0), proper(x1)), PROPER(x1))
PROPER(cons2(nil, x1)) → c68(CONS2(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons2(rnil, x1)) → c68(CONS2(ok(rnil), proper(x1)), PROPER(x1))
PROPER(rcons(x0, s(z0))) → c70(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c70(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c70(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, cons(z0, z1))) → c70(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, cons2(z0, z1))) → c70(RCONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(rcons(x0, rcons(z0, z1))) → c70(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c70(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c70(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c70(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c70(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c70(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c70(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c70(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(s(z0), x1)) → c70(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c70(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c70(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c70(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(cons2(z0, z1), x1)) → c70(RCONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c70(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c70(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c70(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c70(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c70(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c70(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c70(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c70(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(rcons(x0, 0)) → c70(RCONS(proper(x0), ok(0)), PROPER(x0))
PROPER(rcons(x0, nil)) → c70(RCONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(rcons(x0, rnil)) → c70(RCONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(rcons(0, x1)) → c70(RCONS(ok(0), proper(x1)), PROPER(x1))
PROPER(rcons(nil, x1)) → c70(RCONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c70(RCONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(from(s(z0))) → c71(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(posrecip(z0))) → c71(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(from(negrecip(z0))) → c71(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(from(cons(z0, z1))) → c71(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(cons2(z0, z1))) → c71(FROM(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(from(rcons(z0, z1))) → c71(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(from(from(z0))) → c71(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(2ndspos(z0, z1))) → c71(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(from(2ndsneg(z0, z1))) → c71(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(from(pi(z0))) → c71(FROM(pi(proper(z0))), PROPER(pi(z0)))
PROPER(from(plus(z0, z1))) → c71(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(from(times(z0, z1))) → c71(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(from(square(z0))) → c71(FROM(square(proper(z0))), PROPER(square(z0)))
PROPER(from(0)) → c71(FROM(ok(0)))
PROPER(from(nil)) → c71(FROM(ok(nil)))
PROPER(from(rnil)) → c71(FROM(ok(rnil)))
PROPER(2ndspos(x0, s(z0))) → c72(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndspos(x0, posrecip(z0))) → c72(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndspos(x0, negrecip(z0))) → c72(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndspos(x0, cons(z0, z1))) → c72(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndspos(x0, cons2(z0, z1))) → c72(2NDSPOS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(2ndspos(x0, rcons(z0, z1))) → c72(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndspos(x0, from(z0))) → c72(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c72(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c72(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndspos(x0, pi(z0))) → c72(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndspos(x0, plus(z0, z1))) → c72(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndspos(x0, times(z0, z1))) → c72(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndspos(x0, square(z0))) → c72(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndspos(s(z0), x1)) → c72(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndspos(posrecip(z0), x1)) → c72(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndspos(negrecip(z0), x1)) → c72(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndspos(cons(z0, z1), x1)) → c72(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndspos(cons2(z0, z1), x1)) → c72(2NDSPOS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(2ndspos(rcons(z0, z1), x1)) → c72(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndspos(from(z0), x1)) → c72(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c72(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c72(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndspos(pi(z0), x1)) → c72(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndspos(plus(z0, z1), x1)) → c72(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndspos(times(z0, z1), x1)) → c72(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndspos(square(z0), x1)) → c72(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndspos(x0, 0)) → c72(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndspos(x0, nil)) → c72(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndspos(x0, rnil)) → c72(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndspos(0, x1)) → c72(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndspos(nil, x1)) → c72(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndspos(rnil, x1)) → c72(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(x0, s(z0))) → c73(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndsneg(x0, posrecip(z0))) → c73(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndsneg(x0, negrecip(z0))) → c73(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndsneg(x0, cons(z0, z1))) → c73(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndsneg(x0, cons2(z0, z1))) → c73(2NDSNEG(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(2ndsneg(x0, rcons(z0, z1))) → c73(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndsneg(x0, from(z0))) → c73(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c73(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c73(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndsneg(x0, pi(z0))) → c73(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndsneg(x0, plus(z0, z1))) → c73(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndsneg(x0, times(z0, z1))) → c73(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndsneg(x0, square(z0))) → c73(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndsneg(s(z0), x1)) → c73(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndsneg(posrecip(z0), x1)) → c73(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndsneg(negrecip(z0), x1)) → c73(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndsneg(cons(z0, z1), x1)) → c73(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(cons2(z0, z1), x1)) → c73(2NDSNEG(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(2ndsneg(rcons(z0, z1), x1)) → c73(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(from(z0), x1)) → c73(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c73(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c73(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndsneg(pi(z0), x1)) → c73(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndsneg(plus(z0, z1), x1)) → c73(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndsneg(times(z0, z1), x1)) → c73(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndsneg(square(z0), x1)) → c73(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndsneg(x0, 0)) → c73(2NDSNEG(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndsneg(x0, nil)) → c73(2NDSNEG(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndsneg(x0, rnil)) → c73(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndsneg(0, x1)) → c73(2NDSNEG(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndsneg(nil, x1)) → c73(2NDSNEG(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(rnil, x1)) → c73(2NDSNEG(ok(rnil), proper(x1)), PROPER(x1))
PROPER(pi(s(z0))) → c74(PI(s(proper(z0))), PROPER(s(z0)))
PROPER(pi(posrecip(z0))) → c74(PI(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(pi(negrecip(z0))) → c74(PI(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(pi(cons(z0, z1))) → c74(PI(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(pi(cons2(z0, z1))) → c74(PI(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(pi(rcons(z0, z1))) → c74(PI(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(pi(from(z0))) → c74(PI(from(proper(z0))), PROPER(from(z0)))
PROPER(pi(2ndspos(z0, z1))) → c74(PI(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(pi(2ndsneg(z0, z1))) → c74(PI(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(pi(pi(z0))) → c74(PI(pi(proper(z0))), PROPER(pi(z0)))
PROPER(pi(plus(z0, z1))) → c74(PI(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(pi(times(z0, z1))) → c74(PI(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(pi(square(z0))) → c74(PI(square(proper(z0))), PROPER(square(z0)))
PROPER(pi(0)) → c74(PI(ok(0)))
PROPER(pi(nil)) → c74(PI(ok(nil)))
PROPER(pi(rnil)) → c74(PI(ok(rnil)))
PROPER(plus(x0, s(z0))) → c75(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(plus(x0, posrecip(z0))) → c75(PLUS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(plus(x0, negrecip(z0))) → c75(PLUS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(plus(x0, cons(z0, z1))) → c75(PLUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(plus(x0, cons2(z0, z1))) → c75(PLUS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(plus(x0, rcons(z0, z1))) → c75(PLUS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(plus(x0, from(z0))) → c75(PLUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(plus(x0, 2ndspos(z0, z1))) → c75(PLUS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(plus(x0, 2ndsneg(z0, z1))) → c75(PLUS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(plus(x0, pi(z0))) → c75(PLUS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(plus(x0, plus(z0, z1))) → c75(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(plus(x0, times(z0, z1))) → c75(PLUS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(plus(x0, square(z0))) → c75(PLUS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(plus(s(z0), x1)) → c75(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(plus(posrecip(z0), x1)) → c75(PLUS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(plus(negrecip(z0), x1)) → c75(PLUS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(plus(cons(z0, z1), x1)) → c75(PLUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(plus(cons2(z0, z1), x1)) → c75(PLUS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(plus(rcons(z0, z1), x1)) → c75(PLUS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(plus(from(z0), x1)) → c75(PLUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(plus(2ndspos(z0, z1), x1)) → c75(PLUS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(plus(2ndsneg(z0, z1), x1)) → c75(PLUS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(plus(pi(z0), x1)) → c75(PLUS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(plus(plus(z0, z1), x1)) → c75(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(plus(times(z0, z1), x1)) → c75(PLUS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(plus(square(z0), x1)) → c75(PLUS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(plus(x0, 0)) → c75(PLUS(proper(x0), ok(0)), PROPER(x0))
PROPER(plus(x0, nil)) → c75(PLUS(proper(x0), ok(nil)), PROPER(x0))
PROPER(plus(x0, rnil)) → c75(PLUS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(plus(0, x1)) → c75(PLUS(ok(0), proper(x1)), PROPER(x1))
PROPER(plus(nil, x1)) → c75(PLUS(ok(nil), proper(x1)), PROPER(x1))
PROPER(plus(rnil, x1)) → c75(PLUS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(times(x0, s(z0))) → c76(TIMES(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(times(x0, posrecip(z0))) → c76(TIMES(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(times(x0, negrecip(z0))) → c76(TIMES(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(times(x0, cons(z0, z1))) → c76(TIMES(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(times(x0, cons2(z0, z1))) → c76(TIMES(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(times(x0, rcons(z0, z1))) → c76(TIMES(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(times(x0, from(z0))) → c76(TIMES(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(times(x0, 2ndspos(z0, z1))) → c76(TIMES(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(times(x0, 2ndsneg(z0, z1))) → c76(TIMES(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(times(x0, pi(z0))) → c76(TIMES(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(times(x0, plus(z0, z1))) → c76(TIMES(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(times(x0, times(z0, z1))) → c76(TIMES(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(times(x0, square(z0))) → c76(TIMES(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(times(s(z0), x1)) → c76(TIMES(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(times(posrecip(z0), x1)) → c76(TIMES(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(times(negrecip(z0), x1)) → c76(TIMES(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(times(cons(z0, z1), x1)) → c76(TIMES(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(times(cons2(z0, z1), x1)) → c76(TIMES(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(times(rcons(z0, z1), x1)) → c76(TIMES(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(times(from(z0), x1)) → c76(TIMES(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(times(2ndspos(z0, z1), x1)) → c76(TIMES(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(times(2ndsneg(z0, z1), x1)) → c76(TIMES(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(times(pi(z0), x1)) → c76(TIMES(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(times(plus(z0, z1), x1)) → c76(TIMES(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(times(times(z0, z1), x1)) → c76(TIMES(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(times(square(z0), x1)) → c76(TIMES(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(times(x0, 0)) → c76(TIMES(proper(x0), ok(0)), PROPER(x0))
PROPER(times(x0, nil)) → c76(TIMES(proper(x0), ok(nil)), PROPER(x0))
PROPER(times(x0, rnil)) → c76(TIMES(proper(x0), ok(rnil)), PROPER(x0))
PROPER(times(0, x1)) → c76(TIMES(ok(0), proper(x1)), PROPER(x1))
PROPER(times(nil, x1)) → c76(TIMES(ok(nil), proper(x1)), PROPER(x1))
PROPER(times(rnil, x1)) → c76(TIMES(ok(rnil), proper(x1)), PROPER(x1))
PROPER(square(s(z0))) → c77(SQUARE(s(proper(z0))), PROPER(s(z0)))
PROPER(square(posrecip(z0))) → c77(SQUARE(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(square(negrecip(z0))) → c77(SQUARE(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(square(cons(z0, z1))) → c77(SQUARE(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(square(cons2(z0, z1))) → c77(SQUARE(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(square(rcons(z0, z1))) → c77(SQUARE(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(square(from(z0))) → c77(SQUARE(from(proper(z0))), PROPER(from(z0)))
PROPER(square(2ndspos(z0, z1))) → c77(SQUARE(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(square(2ndsneg(z0, z1))) → c77(SQUARE(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(square(pi(z0))) → c77(SQUARE(pi(proper(z0))), PROPER(pi(z0)))
PROPER(square(plus(z0, z1))) → c77(SQUARE(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(square(times(z0, z1))) → c77(SQUARE(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(square(square(z0))) → c77(SQUARE(square(proper(z0))), PROPER(square(z0)))
PROPER(square(0)) → c77(SQUARE(ok(0)))
PROPER(square(nil)) → c77(SQUARE(ok(nil)))
PROPER(square(rnil)) → c77(SQUARE(ok(rnil)))
TOP(mark(s(z0))) → c78(TOP(s(proper(z0))), PROPER(s(z0)))
TOP(mark(posrecip(z0))) → c78(TOP(posrecip(proper(z0))), PROPER(posrecip(z0)))
TOP(mark(negrecip(z0))) → c78(TOP(negrecip(proper(z0))), PROPER(negrecip(z0)))
TOP(mark(cons(z0, z1))) → c78(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
TOP(mark(cons2(z0, z1))) → c78(TOP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
TOP(mark(rcons(z0, z1))) → c78(TOP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
TOP(mark(from(z0))) → c78(TOP(from(proper(z0))), PROPER(from(z0)))
TOP(mark(2ndspos(z0, z1))) → c78(TOP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
TOP(mark(2ndsneg(z0, z1))) → c78(TOP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
TOP(mark(pi(z0))) → c78(TOP(pi(proper(z0))), PROPER(pi(z0)))
TOP(mark(plus(z0, z1))) → c78(TOP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
TOP(mark(times(z0, z1))) → c78(TOP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
TOP(mark(square(z0))) → c78(TOP(square(proper(z0))), PROPER(square(z0)))
TOP(mark(0)) → c78(TOP(ok(0)))
TOP(mark(nil)) → c78(TOP(ok(nil)))
TOP(mark(rnil)) → c78(TOP(ok(rnil)))
TOP(ok(from(z0))) → c79(TOP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
TOP(ok(2ndspos(0, z0))) → c79(TOP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
TOP(ok(2ndspos(s(z0), cons(z1, z2)))) → c79(TOP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
TOP(ok(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c79(TOP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
TOP(ok(2ndsneg(0, z0))) → c79(TOP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
TOP(ok(2ndsneg(s(z0), cons(z1, z2)))) → c79(TOP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
TOP(ok(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c79(TOP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
TOP(ok(pi(z0))) → c79(TOP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
TOP(ok(plus(0, z0))) → c79(TOP(mark(z0)), ACTIVE(plus(0, z0)))
TOP(ok(plus(s(z0), z1))) → c79(TOP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
TOP(ok(times(0, z0))) → c79(TOP(mark(0)), ACTIVE(times(0, z0)))
TOP(ok(times(s(z0), z1))) → c79(TOP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
TOP(ok(square(z0))) → c79(TOP(mark(times(z0, z0))), ACTIVE(square(z0)))
TOP(ok(s(z0))) → c79(TOP(s(active(z0))), ACTIVE(s(z0)))
TOP(ok(posrecip(z0))) → c79(TOP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
TOP(ok(negrecip(z0))) → c79(TOP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
TOP(ok(cons(z0, z1))) → c79(TOP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
TOP(ok(cons2(z0, z1))) → c79(TOP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
TOP(ok(rcons(z0, z1))) → c79(TOP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
TOP(ok(rcons(z0, z1))) → c79(TOP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
TOP(ok(from(z0))) → c79(TOP(from(active(z0))), ACTIVE(from(z0)))
TOP(ok(2ndspos(z0, z1))) → c79(TOP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
TOP(ok(2ndspos(z0, z1))) → c79(TOP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
TOP(ok(2ndsneg(z0, z1))) → c79(TOP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
TOP(ok(2ndsneg(z0, z1))) → c79(TOP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
TOP(ok(pi(z0))) → c79(TOP(pi(active(z0))), ACTIVE(pi(z0)))
TOP(ok(plus(z0, z1))) → c79(TOP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
TOP(ok(plus(z0, z1))) → c79(TOP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
TOP(ok(times(z0, z1))) → c79(TOP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
TOP(ok(times(z0, z1))) → c79(TOP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
TOP(ok(square(z0))) → c79(TOP(square(active(z0))), ACTIVE(square(z0)))
K tuples:none
Defined Rule Symbols:
active, 2ndspos, cons2, rcons, posrecip, 2ndsneg, negrecip, s, cons, from, pi, plus, times, square, proper
Defined Pair Symbols:
ACTIVE, S, POSRECIP, NEGRECIP, CONS, CONS2, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP
Compound Symbols:
c12, c18, c19, c21, c22, c23, c24, c26, c27, c28, c29, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c, c7, c9, c11, c1, c13, c14, c15, c16, c17, c20, c25, c30, c63, c63, c64, c64, c65, c65, c67, c67, c68, c68, c70, c70, c71, c71, c72, c72, c73, c73, c74, c74, c75, c75, c76, c76, c77, c77, c78, c78, c79
(85) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID) transformation)
Removed 3 trailing nodes:
TOP(mark(rnil)) → c78(TOP(ok(rnil)))
TOP(mark(0)) → c78(TOP(ok(0)))
TOP(mark(nil)) → c78(TOP(ok(nil)))
(86) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(2ndspos(0, z0)) → mark(rnil)
active(2ndspos(s(z0), cons(z1, z2))) → mark(2ndspos(s(z0), cons2(z1, z2)))
active(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(z1, z2))) → mark(2ndsneg(s(z0), cons2(z1, z2)))
active(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
active(pi(z0)) → mark(2ndspos(z0, from(0)))
active(plus(0, z0)) → mark(z0)
active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
active(times(0, z0)) → mark(0)
active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
active(square(z0)) → mark(times(z0, z0))
active(s(z0)) → s(active(z0))
active(posrecip(z0)) → posrecip(active(z0))
active(negrecip(z0)) → negrecip(active(z0))
active(cons(z0, z1)) → cons(active(z0), z1)
active(cons2(z0, z1)) → cons2(z0, active(z1))
active(rcons(z0, z1)) → rcons(active(z0), z1)
active(rcons(z0, z1)) → rcons(z0, active(z1))
active(from(z0)) → from(active(z0))
active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
active(pi(z0)) → pi(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(times(z0, z1)) → times(active(z0), z1)
active(times(z0, z1)) → times(z0, active(z1))
active(square(z0)) → square(active(z0))
2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
cons2(z0, mark(z1)) → mark(cons2(z0, z1))
cons2(ok(z0), ok(z1)) → ok(cons2(z0, z1))
rcons(mark(z0), z1) → mark(rcons(z0, z1))
rcons(z0, mark(z1)) → mark(rcons(z0, z1))
rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
posrecip(ok(z0)) → ok(posrecip(z0))
posrecip(mark(z0)) → mark(posrecip(z0))
2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
negrecip(ok(z0)) → ok(negrecip(z0))
negrecip(mark(z0)) → mark(negrecip(z0))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
cons(mark(z0), z1) → mark(cons(z0, z1))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
from(mark(z0)) → mark(from(z0))
from(ok(z0)) → ok(from(z0))
pi(mark(z0)) → mark(pi(z0))
pi(ok(z0)) → ok(pi(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
times(mark(z0), z1) → mark(times(z0, z1))
times(ok(z0), ok(z1)) → ok(times(z0, z1))
times(z0, mark(z1)) → mark(times(z0, z1))
square(mark(z0)) → mark(square(z0))
square(ok(z0)) → ok(square(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(posrecip(z0)) → posrecip(proper(z0))
proper(negrecip(z0)) → negrecip(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(cons2(z0, z1)) → cons2(proper(z0), proper(z1))
proper(rnil) → ok(rnil)
proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
proper(pi(z0)) → pi(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(times(z0, z1)) → times(proper(z0), proper(z1))
proper(square(z0)) → square(proper(z0))
Tuples:
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c9(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(2NDSPOS(s(z0), cons2(z1, z2)))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(2NDSNEG(s(z0), cons2(z1, z2)))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c13(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, z2)))) → c13(S(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(s(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, z2)))) → c13(S(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(s(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c13(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c13(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c13(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c13(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c13(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c13(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c13(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c13(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(cons2(z0, z1))) → c13(S(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c13(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c13(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c13(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c14(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c14(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c14(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c14(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c14(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c14(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c14(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c14(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(cons2(z0, z1))) → c14(POSRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c15(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c15(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c15(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c15(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c15(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c15(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c15(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c15(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(cons2(z0, z1))) → c15(NEGRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndspos(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndspos(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndsneg(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndsneg(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c16(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c16(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c16(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c16(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c16(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c16(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c16(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c16(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(cons2(z0, z1), x1)) → c16(CONS(cons2(z0, active(z1)), x1), ACTIVE(cons2(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, 2ndsneg(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(0, z0))) → c17(CONS2(x0, mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(cons2(x0, plus(s(z0), z1))) → c17(CONS2(x0, mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons2(x0, times(0, z0))) → c17(CONS2(x0, mark(0)), ACTIVE(times(0, z0)))
ACTIVE(cons2(x0, times(s(z0), z1))) → c17(CONS2(x0, mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(cons2(x0, s(z0))) → c17(CONS2(x0, s(active(z0))), ACTIVE(s(z0)))
ACTIVE(cons2(x0, posrecip(z0))) → c17(CONS2(x0, posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(cons2(x0, negrecip(z0))) → c17(CONS2(x0, negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(cons2(x0, cons(z0, z1))) → c17(CONS2(x0, cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(cons2(x0, cons2(z0, z1))) → c17(CONS2(x0, cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, from(active(z0))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, square(active(z0))), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c20(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(from(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(from(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c20(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c20(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c20(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c20(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c20(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c20(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c20(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c20(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c20(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c20(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(cons2(z0, z1))) → c20(FROM(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c20(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c20(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c20(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c25(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c25(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c25(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c25(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c25(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c25(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c25(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c25(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c25(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c25(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c25(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(cons2(z0, z1))) → c25(PI(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c25(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c25(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c25(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c30(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(square(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(square(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c30(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c30(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c30(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c30(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c30(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c30(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c30(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c30(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c30(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(cons2(z0, z1))) → c30(SQUARE(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c30(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c30(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c63(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c63(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c63(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c63(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(cons2(z0, z1))) → c63(S(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(s(rcons(z0, z1))) → c63(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c63(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c63(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c63(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c63(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c63(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c63(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c63(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c63(S(ok(0)))
PROPER(s(nil)) → c63(S(ok(nil)))
PROPER(s(rnil)) → c63(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c64(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c64(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c64(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c64(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(cons2(z0, z1))) → c64(POSRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c64(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c64(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c64(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c64(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c64(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c64(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c64(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c64(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c64(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c64(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c64(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c65(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c65(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c65(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c65(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(cons2(z0, z1))) → c65(NEGRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c65(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c65(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c65(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c65(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c65(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c65(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c65(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c65(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c65(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c65(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c65(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c67(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c67(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c67(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c67(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, cons2(z0, z1))) → c67(CONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c67(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c67(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c67(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c67(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c67(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c67(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c67(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c67(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c67(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c67(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c67(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c67(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(cons2(z0, z1), x1)) → c67(CONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c67(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c67(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c67(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c67(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c67(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c67(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c67(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c67(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c67(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c67(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c67(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c67(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c67(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c67(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(cons2(x0, s(z0))) → c68(CONS2(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons2(x0, posrecip(z0))) → c68(CONS2(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons2(x0, negrecip(z0))) → c68(CONS2(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons2(x0, cons(z0, z1))) → c68(CONS2(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons2(x0, cons2(z0, z1))) → c68(CONS2(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons2(x0, rcons(z0, z1))) → c68(CONS2(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons2(x0, from(z0))) → c68(CONS2(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons2(x0, 2ndspos(z0, z1))) → c68(CONS2(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons2(x0, 2ndsneg(z0, z1))) → c68(CONS2(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons2(x0, pi(z0))) → c68(CONS2(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons2(x0, plus(z0, z1))) → c68(CONS2(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons2(x0, times(z0, z1))) → c68(CONS2(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons2(x0, square(z0))) → c68(CONS2(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons2(s(z0), x1)) → c68(CONS2(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons2(posrecip(z0), x1)) → c68(CONS2(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons2(negrecip(z0), x1)) → c68(CONS2(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons2(cons(z0, z1), x1)) → c68(CONS2(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons2(cons2(z0, z1), x1)) → c68(CONS2(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons2(rcons(z0, z1), x1)) → c68(CONS2(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons2(from(z0), x1)) → c68(CONS2(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons2(2ndspos(z0, z1), x1)) → c68(CONS2(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons2(2ndsneg(z0, z1), x1)) → c68(CONS2(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons2(pi(z0), x1)) → c68(CONS2(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons2(plus(z0, z1), x1)) → c68(CONS2(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons2(times(z0, z1), x1)) → c68(CONS2(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons2(square(z0), x1)) → c68(CONS2(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons2(x0, 0)) → c68(CONS2(proper(x0), ok(0)), PROPER(x0))
PROPER(cons2(x0, nil)) → c68(CONS2(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons2(x0, rnil)) → c68(CONS2(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons2(0, x1)) → c68(CONS2(ok(0), proper(x1)), PROPER(x1))
PROPER(cons2(nil, x1)) → c68(CONS2(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons2(rnil, x1)) → c68(CONS2(ok(rnil), proper(x1)), PROPER(x1))
PROPER(rcons(x0, s(z0))) → c70(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c70(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c70(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, cons(z0, z1))) → c70(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, cons2(z0, z1))) → c70(RCONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(rcons(x0, rcons(z0, z1))) → c70(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c70(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c70(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c70(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c70(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c70(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c70(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c70(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(s(z0), x1)) → c70(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c70(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c70(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c70(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(cons2(z0, z1), x1)) → c70(RCONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c70(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c70(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c70(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c70(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c70(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c70(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c70(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c70(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(rcons(x0, 0)) → c70(RCONS(proper(x0), ok(0)), PROPER(x0))
PROPER(rcons(x0, nil)) → c70(RCONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(rcons(x0, rnil)) → c70(RCONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(rcons(0, x1)) → c70(RCONS(ok(0), proper(x1)), PROPER(x1))
PROPER(rcons(nil, x1)) → c70(RCONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c70(RCONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(from(s(z0))) → c71(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(posrecip(z0))) → c71(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(from(negrecip(z0))) → c71(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(from(cons(z0, z1))) → c71(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(cons2(z0, z1))) → c71(FROM(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(from(rcons(z0, z1))) → c71(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(from(from(z0))) → c71(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(2ndspos(z0, z1))) → c71(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(from(2ndsneg(z0, z1))) → c71(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(from(pi(z0))) → c71(FROM(pi(proper(z0))), PROPER(pi(z0)))
PROPER(from(plus(z0, z1))) → c71(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(from(times(z0, z1))) → c71(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(from(square(z0))) → c71(FROM(square(proper(z0))), PROPER(square(z0)))
PROPER(from(0)) → c71(FROM(ok(0)))
PROPER(from(nil)) → c71(FROM(ok(nil)))
PROPER(from(rnil)) → c71(FROM(ok(rnil)))
PROPER(2ndspos(x0, s(z0))) → c72(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndspos(x0, posrecip(z0))) → c72(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndspos(x0, negrecip(z0))) → c72(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndspos(x0, cons(z0, z1))) → c72(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndspos(x0, cons2(z0, z1))) → c72(2NDSPOS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(2ndspos(x0, rcons(z0, z1))) → c72(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndspos(x0, from(z0))) → c72(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c72(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c72(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndspos(x0, pi(z0))) → c72(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndspos(x0, plus(z0, z1))) → c72(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndspos(x0, times(z0, z1))) → c72(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndspos(x0, square(z0))) → c72(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndspos(s(z0), x1)) → c72(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndspos(posrecip(z0), x1)) → c72(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndspos(negrecip(z0), x1)) → c72(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndspos(cons(z0, z1), x1)) → c72(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndspos(cons2(z0, z1), x1)) → c72(2NDSPOS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(2ndspos(rcons(z0, z1), x1)) → c72(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndspos(from(z0), x1)) → c72(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c72(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c72(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndspos(pi(z0), x1)) → c72(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndspos(plus(z0, z1), x1)) → c72(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndspos(times(z0, z1), x1)) → c72(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndspos(square(z0), x1)) → c72(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndspos(x0, 0)) → c72(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndspos(x0, nil)) → c72(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndspos(x0, rnil)) → c72(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndspos(0, x1)) → c72(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndspos(nil, x1)) → c72(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndspos(rnil, x1)) → c72(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(x0, s(z0))) → c73(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndsneg(x0, posrecip(z0))) → c73(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndsneg(x0, negrecip(z0))) → c73(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndsneg(x0, cons(z0, z1))) → c73(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndsneg(x0, cons2(z0, z1))) → c73(2NDSNEG(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(2ndsneg(x0, rcons(z0, z1))) → c73(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndsneg(x0, from(z0))) → c73(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c73(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c73(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndsneg(x0, pi(z0))) → c73(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndsneg(x0, plus(z0, z1))) → c73(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndsneg(x0, times(z0, z1))) → c73(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndsneg(x0, square(z0))) → c73(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndsneg(s(z0), x1)) → c73(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndsneg(posrecip(z0), x1)) → c73(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndsneg(negrecip(z0), x1)) → c73(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndsneg(cons(z0, z1), x1)) → c73(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(cons2(z0, z1), x1)) → c73(2NDSNEG(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(2ndsneg(rcons(z0, z1), x1)) → c73(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(from(z0), x1)) → c73(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c73(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c73(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndsneg(pi(z0), x1)) → c73(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndsneg(plus(z0, z1), x1)) → c73(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndsneg(times(z0, z1), x1)) → c73(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndsneg(square(z0), x1)) → c73(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndsneg(x0, 0)) → c73(2NDSNEG(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndsneg(x0, nil)) → c73(2NDSNEG(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndsneg(x0, rnil)) → c73(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndsneg(0, x1)) → c73(2NDSNEG(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndsneg(nil, x1)) → c73(2NDSNEG(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(rnil, x1)) → c73(2NDSNEG(ok(rnil), proper(x1)), PROPER(x1))
PROPER(pi(s(z0))) → c74(PI(s(proper(z0))), PROPER(s(z0)))
PROPER(pi(posrecip(z0))) → c74(PI(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(pi(negrecip(z0))) → c74(PI(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(pi(cons(z0, z1))) → c74(PI(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(pi(cons2(z0, z1))) → c74(PI(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(pi(rcons(z0, z1))) → c74(PI(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(pi(from(z0))) → c74(PI(from(proper(z0))), PROPER(from(z0)))
PROPER(pi(2ndspos(z0, z1))) → c74(PI(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(pi(2ndsneg(z0, z1))) → c74(PI(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(pi(pi(z0))) → c74(PI(pi(proper(z0))), PROPER(pi(z0)))
PROPER(pi(plus(z0, z1))) → c74(PI(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(pi(times(z0, z1))) → c74(PI(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(pi(square(z0))) → c74(PI(square(proper(z0))), PROPER(square(z0)))
PROPER(pi(0)) → c74(PI(ok(0)))
PROPER(pi(nil)) → c74(PI(ok(nil)))
PROPER(pi(rnil)) → c74(PI(ok(rnil)))
PROPER(plus(x0, s(z0))) → c75(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(plus(x0, posrecip(z0))) → c75(PLUS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(plus(x0, negrecip(z0))) → c75(PLUS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(plus(x0, cons(z0, z1))) → c75(PLUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(plus(x0, cons2(z0, z1))) → c75(PLUS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(plus(x0, rcons(z0, z1))) → c75(PLUS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(plus(x0, from(z0))) → c75(PLUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(plus(x0, 2ndspos(z0, z1))) → c75(PLUS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(plus(x0, 2ndsneg(z0, z1))) → c75(PLUS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(plus(x0, pi(z0))) → c75(PLUS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(plus(x0, plus(z0, z1))) → c75(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(plus(x0, times(z0, z1))) → c75(PLUS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(plus(x0, square(z0))) → c75(PLUS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(plus(s(z0), x1)) → c75(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(plus(posrecip(z0), x1)) → c75(PLUS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(plus(negrecip(z0), x1)) → c75(PLUS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(plus(cons(z0, z1), x1)) → c75(PLUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(plus(cons2(z0, z1), x1)) → c75(PLUS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(plus(rcons(z0, z1), x1)) → c75(PLUS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(plus(from(z0), x1)) → c75(PLUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(plus(2ndspos(z0, z1), x1)) → c75(PLUS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(plus(2ndsneg(z0, z1), x1)) → c75(PLUS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(plus(pi(z0), x1)) → c75(PLUS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(plus(plus(z0, z1), x1)) → c75(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(plus(times(z0, z1), x1)) → c75(PLUS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(plus(square(z0), x1)) → c75(PLUS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(plus(x0, 0)) → c75(PLUS(proper(x0), ok(0)), PROPER(x0))
PROPER(plus(x0, nil)) → c75(PLUS(proper(x0), ok(nil)), PROPER(x0))
PROPER(plus(x0, rnil)) → c75(PLUS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(plus(0, x1)) → c75(PLUS(ok(0), proper(x1)), PROPER(x1))
PROPER(plus(nil, x1)) → c75(PLUS(ok(nil), proper(x1)), PROPER(x1))
PROPER(plus(rnil, x1)) → c75(PLUS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(times(x0, s(z0))) → c76(TIMES(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(times(x0, posrecip(z0))) → c76(TIMES(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(times(x0, negrecip(z0))) → c76(TIMES(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(times(x0, cons(z0, z1))) → c76(TIMES(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(times(x0, cons2(z0, z1))) → c76(TIMES(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(times(x0, rcons(z0, z1))) → c76(TIMES(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(times(x0, from(z0))) → c76(TIMES(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(times(x0, 2ndspos(z0, z1))) → c76(TIMES(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(times(x0, 2ndsneg(z0, z1))) → c76(TIMES(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(times(x0, pi(z0))) → c76(TIMES(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(times(x0, plus(z0, z1))) → c76(TIMES(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(times(x0, times(z0, z1))) → c76(TIMES(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(times(x0, square(z0))) → c76(TIMES(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(times(s(z0), x1)) → c76(TIMES(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(times(posrecip(z0), x1)) → c76(TIMES(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(times(negrecip(z0), x1)) → c76(TIMES(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(times(cons(z0, z1), x1)) → c76(TIMES(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(times(cons2(z0, z1), x1)) → c76(TIMES(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(times(rcons(z0, z1), x1)) → c76(TIMES(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(times(from(z0), x1)) → c76(TIMES(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(times(2ndspos(z0, z1), x1)) → c76(TIMES(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(times(2ndsneg(z0, z1), x1)) → c76(TIMES(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(times(pi(z0), x1)) → c76(TIMES(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(times(plus(z0, z1), x1)) → c76(TIMES(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(times(times(z0, z1), x1)) → c76(TIMES(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(times(square(z0), x1)) → c76(TIMES(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(times(x0, 0)) → c76(TIMES(proper(x0), ok(0)), PROPER(x0))
PROPER(times(x0, nil)) → c76(TIMES(proper(x0), ok(nil)), PROPER(x0))
PROPER(times(x0, rnil)) → c76(TIMES(proper(x0), ok(rnil)), PROPER(x0))
PROPER(times(0, x1)) → c76(TIMES(ok(0), proper(x1)), PROPER(x1))
PROPER(times(nil, x1)) → c76(TIMES(ok(nil), proper(x1)), PROPER(x1))
PROPER(times(rnil, x1)) → c76(TIMES(ok(rnil), proper(x1)), PROPER(x1))
PROPER(square(s(z0))) → c77(SQUARE(s(proper(z0))), PROPER(s(z0)))
PROPER(square(posrecip(z0))) → c77(SQUARE(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(square(negrecip(z0))) → c77(SQUARE(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(square(cons(z0, z1))) → c77(SQUARE(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(square(cons2(z0, z1))) → c77(SQUARE(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(square(rcons(z0, z1))) → c77(SQUARE(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(square(from(z0))) → c77(SQUARE(from(proper(z0))), PROPER(from(z0)))
PROPER(square(2ndspos(z0, z1))) → c77(SQUARE(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(square(2ndsneg(z0, z1))) → c77(SQUARE(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(square(pi(z0))) → c77(SQUARE(pi(proper(z0))), PROPER(pi(z0)))
PROPER(square(plus(z0, z1))) → c77(SQUARE(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(square(times(z0, z1))) → c77(SQUARE(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(square(square(z0))) → c77(SQUARE(square(proper(z0))), PROPER(square(z0)))
PROPER(square(0)) → c77(SQUARE(ok(0)))
PROPER(square(nil)) → c77(SQUARE(ok(nil)))
PROPER(square(rnil)) → c77(SQUARE(ok(rnil)))
TOP(mark(s(z0))) → c78(TOP(s(proper(z0))), PROPER(s(z0)))
TOP(mark(posrecip(z0))) → c78(TOP(posrecip(proper(z0))), PROPER(posrecip(z0)))
TOP(mark(negrecip(z0))) → c78(TOP(negrecip(proper(z0))), PROPER(negrecip(z0)))
TOP(mark(cons(z0, z1))) → c78(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
TOP(mark(cons2(z0, z1))) → c78(TOP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
TOP(mark(rcons(z0, z1))) → c78(TOP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
TOP(mark(from(z0))) → c78(TOP(from(proper(z0))), PROPER(from(z0)))
TOP(mark(2ndspos(z0, z1))) → c78(TOP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
TOP(mark(2ndsneg(z0, z1))) → c78(TOP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
TOP(mark(pi(z0))) → c78(TOP(pi(proper(z0))), PROPER(pi(z0)))
TOP(mark(plus(z0, z1))) → c78(TOP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
TOP(mark(times(z0, z1))) → c78(TOP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
TOP(mark(square(z0))) → c78(TOP(square(proper(z0))), PROPER(square(z0)))
TOP(ok(from(z0))) → c79(TOP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
TOP(ok(2ndspos(0, z0))) → c79(TOP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
TOP(ok(2ndspos(s(z0), cons(z1, z2)))) → c79(TOP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
TOP(ok(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c79(TOP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
TOP(ok(2ndsneg(0, z0))) → c79(TOP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
TOP(ok(2ndsneg(s(z0), cons(z1, z2)))) → c79(TOP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
TOP(ok(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c79(TOP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
TOP(ok(pi(z0))) → c79(TOP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
TOP(ok(plus(0, z0))) → c79(TOP(mark(z0)), ACTIVE(plus(0, z0)))
TOP(ok(plus(s(z0), z1))) → c79(TOP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
TOP(ok(times(0, z0))) → c79(TOP(mark(0)), ACTIVE(times(0, z0)))
TOP(ok(times(s(z0), z1))) → c79(TOP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
TOP(ok(square(z0))) → c79(TOP(mark(times(z0, z0))), ACTIVE(square(z0)))
TOP(ok(s(z0))) → c79(TOP(s(active(z0))), ACTIVE(s(z0)))
TOP(ok(posrecip(z0))) → c79(TOP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
TOP(ok(negrecip(z0))) → c79(TOP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
TOP(ok(cons(z0, z1))) → c79(TOP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
TOP(ok(cons2(z0, z1))) → c79(TOP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
TOP(ok(rcons(z0, z1))) → c79(TOP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
TOP(ok(rcons(z0, z1))) → c79(TOP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
TOP(ok(from(z0))) → c79(TOP(from(active(z0))), ACTIVE(from(z0)))
TOP(ok(2ndspos(z0, z1))) → c79(TOP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
TOP(ok(2ndspos(z0, z1))) → c79(TOP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
TOP(ok(2ndsneg(z0, z1))) → c79(TOP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
TOP(ok(2ndsneg(z0, z1))) → c79(TOP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
TOP(ok(pi(z0))) → c79(TOP(pi(active(z0))), ACTIVE(pi(z0)))
TOP(ok(plus(z0, z1))) → c79(TOP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
TOP(ok(plus(z0, z1))) → c79(TOP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
TOP(ok(times(z0, z1))) → c79(TOP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
TOP(ok(times(z0, z1))) → c79(TOP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
TOP(ok(square(z0))) → c79(TOP(square(active(z0))), ACTIVE(square(z0)))
S tuples:
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c9(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(2NDSPOS(s(z0), cons2(z1, z2)))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(2NDSNEG(s(z0), cons2(z1, z2)))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c13(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, z2)))) → c13(S(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(s(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, z2)))) → c13(S(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(s(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c13(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c13(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c13(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c13(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c13(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c13(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c13(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c13(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(cons2(z0, z1))) → c13(S(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c13(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c13(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c13(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c14(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c14(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c14(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c14(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c14(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c14(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c14(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c14(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(cons2(z0, z1))) → c14(POSRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c15(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c15(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c15(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c15(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c15(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c15(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c15(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c15(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(cons2(z0, z1))) → c15(NEGRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndspos(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndspos(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndsneg(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndsneg(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c16(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c16(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c16(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c16(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c16(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c16(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c16(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c16(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(cons2(z0, z1), x1)) → c16(CONS(cons2(z0, active(z1)), x1), ACTIVE(cons2(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, 2ndsneg(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(0, z0))) → c17(CONS2(x0, mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(cons2(x0, plus(s(z0), z1))) → c17(CONS2(x0, mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons2(x0, times(0, z0))) → c17(CONS2(x0, mark(0)), ACTIVE(times(0, z0)))
ACTIVE(cons2(x0, times(s(z0), z1))) → c17(CONS2(x0, mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(cons2(x0, s(z0))) → c17(CONS2(x0, s(active(z0))), ACTIVE(s(z0)))
ACTIVE(cons2(x0, posrecip(z0))) → c17(CONS2(x0, posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(cons2(x0, negrecip(z0))) → c17(CONS2(x0, negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(cons2(x0, cons(z0, z1))) → c17(CONS2(x0, cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(cons2(x0, cons2(z0, z1))) → c17(CONS2(x0, cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, from(active(z0))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, square(active(z0))), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c20(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(from(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(from(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c20(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c20(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c20(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c20(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c20(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c20(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c20(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c20(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c20(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c20(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(cons2(z0, z1))) → c20(FROM(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c20(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c20(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c20(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c25(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c25(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c25(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c25(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c25(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c25(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c25(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c25(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c25(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c25(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c25(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(cons2(z0, z1))) → c25(PI(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c25(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c25(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c25(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c30(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(square(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(square(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c30(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c30(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c30(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c30(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c30(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c30(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c30(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c30(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c30(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(cons2(z0, z1))) → c30(SQUARE(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c30(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c30(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c63(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c63(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c63(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c63(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(cons2(z0, z1))) → c63(S(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(s(rcons(z0, z1))) → c63(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c63(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c63(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c63(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c63(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c63(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c63(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c63(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c63(S(ok(0)))
PROPER(s(nil)) → c63(S(ok(nil)))
PROPER(s(rnil)) → c63(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c64(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c64(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c64(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c64(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(cons2(z0, z1))) → c64(POSRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c64(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c64(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c64(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c64(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c64(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c64(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c64(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c64(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c64(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c64(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c64(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c65(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c65(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c65(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c65(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(cons2(z0, z1))) → c65(NEGRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c65(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c65(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c65(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c65(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c65(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c65(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c65(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c65(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c65(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c65(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c65(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c67(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c67(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c67(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c67(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, cons2(z0, z1))) → c67(CONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c67(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c67(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c67(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c67(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c67(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c67(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c67(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c67(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c67(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c67(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c67(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c67(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(cons2(z0, z1), x1)) → c67(CONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c67(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c67(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c67(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c67(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c67(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c67(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c67(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c67(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c67(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c67(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c67(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c67(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c67(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c67(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(cons2(x0, s(z0))) → c68(CONS2(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons2(x0, posrecip(z0))) → c68(CONS2(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons2(x0, negrecip(z0))) → c68(CONS2(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons2(x0, cons(z0, z1))) → c68(CONS2(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons2(x0, cons2(z0, z1))) → c68(CONS2(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons2(x0, rcons(z0, z1))) → c68(CONS2(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons2(x0, from(z0))) → c68(CONS2(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons2(x0, 2ndspos(z0, z1))) → c68(CONS2(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons2(x0, 2ndsneg(z0, z1))) → c68(CONS2(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons2(x0, pi(z0))) → c68(CONS2(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons2(x0, plus(z0, z1))) → c68(CONS2(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons2(x0, times(z0, z1))) → c68(CONS2(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons2(x0, square(z0))) → c68(CONS2(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons2(s(z0), x1)) → c68(CONS2(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons2(posrecip(z0), x1)) → c68(CONS2(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons2(negrecip(z0), x1)) → c68(CONS2(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons2(cons(z0, z1), x1)) → c68(CONS2(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons2(cons2(z0, z1), x1)) → c68(CONS2(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons2(rcons(z0, z1), x1)) → c68(CONS2(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons2(from(z0), x1)) → c68(CONS2(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons2(2ndspos(z0, z1), x1)) → c68(CONS2(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons2(2ndsneg(z0, z1), x1)) → c68(CONS2(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons2(pi(z0), x1)) → c68(CONS2(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons2(plus(z0, z1), x1)) → c68(CONS2(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons2(times(z0, z1), x1)) → c68(CONS2(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons2(square(z0), x1)) → c68(CONS2(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons2(x0, 0)) → c68(CONS2(proper(x0), ok(0)), PROPER(x0))
PROPER(cons2(x0, nil)) → c68(CONS2(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons2(x0, rnil)) → c68(CONS2(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons2(0, x1)) → c68(CONS2(ok(0), proper(x1)), PROPER(x1))
PROPER(cons2(nil, x1)) → c68(CONS2(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons2(rnil, x1)) → c68(CONS2(ok(rnil), proper(x1)), PROPER(x1))
PROPER(rcons(x0, s(z0))) → c70(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c70(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c70(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, cons(z0, z1))) → c70(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, cons2(z0, z1))) → c70(RCONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(rcons(x0, rcons(z0, z1))) → c70(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c70(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c70(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c70(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c70(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c70(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c70(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c70(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(s(z0), x1)) → c70(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c70(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c70(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c70(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(cons2(z0, z1), x1)) → c70(RCONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c70(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c70(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c70(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c70(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c70(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c70(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c70(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c70(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(rcons(x0, 0)) → c70(RCONS(proper(x0), ok(0)), PROPER(x0))
PROPER(rcons(x0, nil)) → c70(RCONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(rcons(x0, rnil)) → c70(RCONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(rcons(0, x1)) → c70(RCONS(ok(0), proper(x1)), PROPER(x1))
PROPER(rcons(nil, x1)) → c70(RCONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c70(RCONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(from(s(z0))) → c71(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(posrecip(z0))) → c71(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(from(negrecip(z0))) → c71(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(from(cons(z0, z1))) → c71(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(cons2(z0, z1))) → c71(FROM(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(from(rcons(z0, z1))) → c71(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(from(from(z0))) → c71(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(2ndspos(z0, z1))) → c71(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(from(2ndsneg(z0, z1))) → c71(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(from(pi(z0))) → c71(FROM(pi(proper(z0))), PROPER(pi(z0)))
PROPER(from(plus(z0, z1))) → c71(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(from(times(z0, z1))) → c71(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(from(square(z0))) → c71(FROM(square(proper(z0))), PROPER(square(z0)))
PROPER(from(0)) → c71(FROM(ok(0)))
PROPER(from(nil)) → c71(FROM(ok(nil)))
PROPER(from(rnil)) → c71(FROM(ok(rnil)))
PROPER(2ndspos(x0, s(z0))) → c72(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndspos(x0, posrecip(z0))) → c72(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndspos(x0, negrecip(z0))) → c72(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndspos(x0, cons(z0, z1))) → c72(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndspos(x0, cons2(z0, z1))) → c72(2NDSPOS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(2ndspos(x0, rcons(z0, z1))) → c72(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndspos(x0, from(z0))) → c72(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c72(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c72(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndspos(x0, pi(z0))) → c72(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndspos(x0, plus(z0, z1))) → c72(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndspos(x0, times(z0, z1))) → c72(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndspos(x0, square(z0))) → c72(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndspos(s(z0), x1)) → c72(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndspos(posrecip(z0), x1)) → c72(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndspos(negrecip(z0), x1)) → c72(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndspos(cons(z0, z1), x1)) → c72(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndspos(cons2(z0, z1), x1)) → c72(2NDSPOS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(2ndspos(rcons(z0, z1), x1)) → c72(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndspos(from(z0), x1)) → c72(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c72(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c72(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndspos(pi(z0), x1)) → c72(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndspos(plus(z0, z1), x1)) → c72(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndspos(times(z0, z1), x1)) → c72(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndspos(square(z0), x1)) → c72(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndspos(x0, 0)) → c72(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndspos(x0, nil)) → c72(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndspos(x0, rnil)) → c72(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndspos(0, x1)) → c72(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndspos(nil, x1)) → c72(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndspos(rnil, x1)) → c72(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(x0, s(z0))) → c73(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndsneg(x0, posrecip(z0))) → c73(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndsneg(x0, negrecip(z0))) → c73(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndsneg(x0, cons(z0, z1))) → c73(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndsneg(x0, cons2(z0, z1))) → c73(2NDSNEG(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(2ndsneg(x0, rcons(z0, z1))) → c73(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndsneg(x0, from(z0))) → c73(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c73(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c73(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndsneg(x0, pi(z0))) → c73(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndsneg(x0, plus(z0, z1))) → c73(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndsneg(x0, times(z0, z1))) → c73(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndsneg(x0, square(z0))) → c73(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndsneg(s(z0), x1)) → c73(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndsneg(posrecip(z0), x1)) → c73(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndsneg(negrecip(z0), x1)) → c73(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndsneg(cons(z0, z1), x1)) → c73(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(cons2(z0, z1), x1)) → c73(2NDSNEG(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(2ndsneg(rcons(z0, z1), x1)) → c73(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(from(z0), x1)) → c73(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c73(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c73(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndsneg(pi(z0), x1)) → c73(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndsneg(plus(z0, z1), x1)) → c73(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndsneg(times(z0, z1), x1)) → c73(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndsneg(square(z0), x1)) → c73(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndsneg(x0, 0)) → c73(2NDSNEG(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndsneg(x0, nil)) → c73(2NDSNEG(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndsneg(x0, rnil)) → c73(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndsneg(0, x1)) → c73(2NDSNEG(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndsneg(nil, x1)) → c73(2NDSNEG(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(rnil, x1)) → c73(2NDSNEG(ok(rnil), proper(x1)), PROPER(x1))
PROPER(pi(s(z0))) → c74(PI(s(proper(z0))), PROPER(s(z0)))
PROPER(pi(posrecip(z0))) → c74(PI(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(pi(negrecip(z0))) → c74(PI(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(pi(cons(z0, z1))) → c74(PI(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(pi(cons2(z0, z1))) → c74(PI(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(pi(rcons(z0, z1))) → c74(PI(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(pi(from(z0))) → c74(PI(from(proper(z0))), PROPER(from(z0)))
PROPER(pi(2ndspos(z0, z1))) → c74(PI(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(pi(2ndsneg(z0, z1))) → c74(PI(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(pi(pi(z0))) → c74(PI(pi(proper(z0))), PROPER(pi(z0)))
PROPER(pi(plus(z0, z1))) → c74(PI(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(pi(times(z0, z1))) → c74(PI(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(pi(square(z0))) → c74(PI(square(proper(z0))), PROPER(square(z0)))
PROPER(pi(0)) → c74(PI(ok(0)))
PROPER(pi(nil)) → c74(PI(ok(nil)))
PROPER(pi(rnil)) → c74(PI(ok(rnil)))
PROPER(plus(x0, s(z0))) → c75(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(plus(x0, posrecip(z0))) → c75(PLUS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(plus(x0, negrecip(z0))) → c75(PLUS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(plus(x0, cons(z0, z1))) → c75(PLUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(plus(x0, cons2(z0, z1))) → c75(PLUS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(plus(x0, rcons(z0, z1))) → c75(PLUS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(plus(x0, from(z0))) → c75(PLUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(plus(x0, 2ndspos(z0, z1))) → c75(PLUS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(plus(x0, 2ndsneg(z0, z1))) → c75(PLUS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(plus(x0, pi(z0))) → c75(PLUS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(plus(x0, plus(z0, z1))) → c75(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(plus(x0, times(z0, z1))) → c75(PLUS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(plus(x0, square(z0))) → c75(PLUS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(plus(s(z0), x1)) → c75(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(plus(posrecip(z0), x1)) → c75(PLUS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(plus(negrecip(z0), x1)) → c75(PLUS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(plus(cons(z0, z1), x1)) → c75(PLUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(plus(cons2(z0, z1), x1)) → c75(PLUS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(plus(rcons(z0, z1), x1)) → c75(PLUS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(plus(from(z0), x1)) → c75(PLUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(plus(2ndspos(z0, z1), x1)) → c75(PLUS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(plus(2ndsneg(z0, z1), x1)) → c75(PLUS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(plus(pi(z0), x1)) → c75(PLUS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(plus(plus(z0, z1), x1)) → c75(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(plus(times(z0, z1), x1)) → c75(PLUS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(plus(square(z0), x1)) → c75(PLUS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(plus(x0, 0)) → c75(PLUS(proper(x0), ok(0)), PROPER(x0))
PROPER(plus(x0, nil)) → c75(PLUS(proper(x0), ok(nil)), PROPER(x0))
PROPER(plus(x0, rnil)) → c75(PLUS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(plus(0, x1)) → c75(PLUS(ok(0), proper(x1)), PROPER(x1))
PROPER(plus(nil, x1)) → c75(PLUS(ok(nil), proper(x1)), PROPER(x1))
PROPER(plus(rnil, x1)) → c75(PLUS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(times(x0, s(z0))) → c76(TIMES(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(times(x0, posrecip(z0))) → c76(TIMES(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(times(x0, negrecip(z0))) → c76(TIMES(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(times(x0, cons(z0, z1))) → c76(TIMES(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(times(x0, cons2(z0, z1))) → c76(TIMES(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(times(x0, rcons(z0, z1))) → c76(TIMES(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(times(x0, from(z0))) → c76(TIMES(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(times(x0, 2ndspos(z0, z1))) → c76(TIMES(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(times(x0, 2ndsneg(z0, z1))) → c76(TIMES(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(times(x0, pi(z0))) → c76(TIMES(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(times(x0, plus(z0, z1))) → c76(TIMES(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(times(x0, times(z0, z1))) → c76(TIMES(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(times(x0, square(z0))) → c76(TIMES(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(times(s(z0), x1)) → c76(TIMES(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(times(posrecip(z0), x1)) → c76(TIMES(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(times(negrecip(z0), x1)) → c76(TIMES(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(times(cons(z0, z1), x1)) → c76(TIMES(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(times(cons2(z0, z1), x1)) → c76(TIMES(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(times(rcons(z0, z1), x1)) → c76(TIMES(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(times(from(z0), x1)) → c76(TIMES(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(times(2ndspos(z0, z1), x1)) → c76(TIMES(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(times(2ndsneg(z0, z1), x1)) → c76(TIMES(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(times(pi(z0), x1)) → c76(TIMES(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(times(plus(z0, z1), x1)) → c76(TIMES(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(times(times(z0, z1), x1)) → c76(TIMES(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(times(square(z0), x1)) → c76(TIMES(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(times(x0, 0)) → c76(TIMES(proper(x0), ok(0)), PROPER(x0))
PROPER(times(x0, nil)) → c76(TIMES(proper(x0), ok(nil)), PROPER(x0))
PROPER(times(x0, rnil)) → c76(TIMES(proper(x0), ok(rnil)), PROPER(x0))
PROPER(times(0, x1)) → c76(TIMES(ok(0), proper(x1)), PROPER(x1))
PROPER(times(nil, x1)) → c76(TIMES(ok(nil), proper(x1)), PROPER(x1))
PROPER(times(rnil, x1)) → c76(TIMES(ok(rnil), proper(x1)), PROPER(x1))
PROPER(square(s(z0))) → c77(SQUARE(s(proper(z0))), PROPER(s(z0)))
PROPER(square(posrecip(z0))) → c77(SQUARE(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(square(negrecip(z0))) → c77(SQUARE(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(square(cons(z0, z1))) → c77(SQUARE(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(square(cons2(z0, z1))) → c77(SQUARE(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(square(rcons(z0, z1))) → c77(SQUARE(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(square(from(z0))) → c77(SQUARE(from(proper(z0))), PROPER(from(z0)))
PROPER(square(2ndspos(z0, z1))) → c77(SQUARE(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(square(2ndsneg(z0, z1))) → c77(SQUARE(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(square(pi(z0))) → c77(SQUARE(pi(proper(z0))), PROPER(pi(z0)))
PROPER(square(plus(z0, z1))) → c77(SQUARE(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(square(times(z0, z1))) → c77(SQUARE(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(square(square(z0))) → c77(SQUARE(square(proper(z0))), PROPER(square(z0)))
PROPER(square(0)) → c77(SQUARE(ok(0)))
PROPER(square(nil)) → c77(SQUARE(ok(nil)))
PROPER(square(rnil)) → c77(SQUARE(ok(rnil)))
TOP(mark(s(z0))) → c78(TOP(s(proper(z0))), PROPER(s(z0)))
TOP(mark(posrecip(z0))) → c78(TOP(posrecip(proper(z0))), PROPER(posrecip(z0)))
TOP(mark(negrecip(z0))) → c78(TOP(negrecip(proper(z0))), PROPER(negrecip(z0)))
TOP(mark(cons(z0, z1))) → c78(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
TOP(mark(cons2(z0, z1))) → c78(TOP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
TOP(mark(rcons(z0, z1))) → c78(TOP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
TOP(mark(from(z0))) → c78(TOP(from(proper(z0))), PROPER(from(z0)))
TOP(mark(2ndspos(z0, z1))) → c78(TOP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
TOP(mark(2ndsneg(z0, z1))) → c78(TOP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
TOP(mark(pi(z0))) → c78(TOP(pi(proper(z0))), PROPER(pi(z0)))
TOP(mark(plus(z0, z1))) → c78(TOP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
TOP(mark(times(z0, z1))) → c78(TOP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
TOP(mark(square(z0))) → c78(TOP(square(proper(z0))), PROPER(square(z0)))
TOP(ok(from(z0))) → c79(TOP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
TOP(ok(2ndspos(0, z0))) → c79(TOP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
TOP(ok(2ndspos(s(z0), cons(z1, z2)))) → c79(TOP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
TOP(ok(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c79(TOP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
TOP(ok(2ndsneg(0, z0))) → c79(TOP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
TOP(ok(2ndsneg(s(z0), cons(z1, z2)))) → c79(TOP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
TOP(ok(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c79(TOP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
TOP(ok(pi(z0))) → c79(TOP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
TOP(ok(plus(0, z0))) → c79(TOP(mark(z0)), ACTIVE(plus(0, z0)))
TOP(ok(plus(s(z0), z1))) → c79(TOP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
TOP(ok(times(0, z0))) → c79(TOP(mark(0)), ACTIVE(times(0, z0)))
TOP(ok(times(s(z0), z1))) → c79(TOP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
TOP(ok(square(z0))) → c79(TOP(mark(times(z0, z0))), ACTIVE(square(z0)))
TOP(ok(s(z0))) → c79(TOP(s(active(z0))), ACTIVE(s(z0)))
TOP(ok(posrecip(z0))) → c79(TOP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
TOP(ok(negrecip(z0))) → c79(TOP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
TOP(ok(cons(z0, z1))) → c79(TOP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
TOP(ok(cons2(z0, z1))) → c79(TOP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
TOP(ok(rcons(z0, z1))) → c79(TOP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
TOP(ok(rcons(z0, z1))) → c79(TOP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
TOP(ok(from(z0))) → c79(TOP(from(active(z0))), ACTIVE(from(z0)))
TOP(ok(2ndspos(z0, z1))) → c79(TOP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
TOP(ok(2ndspos(z0, z1))) → c79(TOP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
TOP(ok(2ndsneg(z0, z1))) → c79(TOP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
TOP(ok(2ndsneg(z0, z1))) → c79(TOP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
TOP(ok(pi(z0))) → c79(TOP(pi(active(z0))), ACTIVE(pi(z0)))
TOP(ok(plus(z0, z1))) → c79(TOP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
TOP(ok(plus(z0, z1))) → c79(TOP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
TOP(ok(times(z0, z1))) → c79(TOP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
TOP(ok(times(z0, z1))) → c79(TOP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
TOP(ok(square(z0))) → c79(TOP(square(active(z0))), ACTIVE(square(z0)))
K tuples:none
Defined Rule Symbols:
active, 2ndspos, cons2, rcons, posrecip, 2ndsneg, negrecip, s, cons, from, pi, plus, times, square, proper
Defined Pair Symbols:
ACTIVE, S, POSRECIP, NEGRECIP, CONS, CONS2, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP
Compound Symbols:
c12, c18, c19, c21, c22, c23, c24, c26, c27, c28, c29, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c, c7, c9, c11, c1, c13, c14, c15, c16, c17, c20, c25, c30, c63, c63, c64, c64, c65, c65, c67, c67, c68, c68, c70, c70, c71, c71, c72, c72, c73, c73, c74, c74, c75, c75, c76, c76, c77, c77, c78, c79
(87) CdtUnreachableProof (EQUIVALENT transformation)
The following tuples could be removed as they are not reachable from basic start terms:
ACTIVE(square(z0)) → c12(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c18(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c19(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c21(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c22(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c23(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c24(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c26(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c27(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c28(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c29(TIMES(z0, active(z1)), ACTIVE(z1))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c7(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c9(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c11(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(2NDSPOS(s(z0), cons2(z1, z2)))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndspos(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(2NDSNEG(s(z0), cons2(z1, z2)))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(S(z0))
ACTIVE(2ndsneg(s(z0), cons(z1, z2))) → c1(CONS2(z1, z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c13(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, z2)))) → c13(S(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(s(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c13(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, z2)))) → c13(S(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(s(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c13(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c13(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c13(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c13(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c13(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c13(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c13(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c13(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c13(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(cons2(z0, z1))) → c13(S(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c13(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c13(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c13(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c13(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c13(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c13(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c13(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c13(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c14(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, z2)))) → c14(POSRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(posrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c14(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c14(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c14(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c14(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c14(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c14(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c14(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c14(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c14(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(cons2(z0, z1))) → c14(POSRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c14(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c14(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c14(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c14(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c14(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c14(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c14(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c14(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c15(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, z2)))) → c15(NEGRECIP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(negrecip(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c15(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c15(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c15(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c15(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c15(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c15(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c15(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c15(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c15(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(cons2(z0, z1))) → c15(NEGRECIP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c15(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c15(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c15(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c15(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c15(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c15(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c15(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c15(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndspos(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndspos(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c16(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, z2)), x1)) → c16(CONS(mark(2ndsneg(s(z0), cons2(z1, z2))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons(2ndsneg(s(z0), cons2(z1, cons(z2, z3))), x1)) → c16(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c16(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c16(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c16(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c16(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c16(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c16(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c16(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c16(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(cons2(z0, z1), x1)) → c16(CONS(cons2(z0, active(z1)), x1), ACTIVE(cons2(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c16(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c16(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c16(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c16(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c16(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c16(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c16(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c16(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, 2ndsneg(0, z0))) → c17(CONS2(x0, mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons(z1, z2)))) → c17(CONS2(x0, mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(cons2(x0, 2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c17(CONS2(x0, mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(0, z0))) → c17(CONS2(x0, mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(cons2(x0, plus(s(z0), z1))) → c17(CONS2(x0, mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons2(x0, times(0, z0))) → c17(CONS2(x0, mark(0)), ACTIVE(times(0, z0)))
ACTIVE(cons2(x0, times(s(z0), z1))) → c17(CONS2(x0, mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(cons2(x0, s(z0))) → c17(CONS2(x0, s(active(z0))), ACTIVE(s(z0)))
ACTIVE(cons2(x0, posrecip(z0))) → c17(CONS2(x0, posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(cons2(x0, negrecip(z0))) → c17(CONS2(x0, negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(cons2(x0, cons(z0, z1))) → c17(CONS2(x0, cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(cons2(x0, cons2(z0, z1))) → c17(CONS2(x0, cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, rcons(z0, z1))) → c17(CONS2(x0, rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(cons2(x0, from(z0))) → c17(CONS2(x0, from(active(z0))), ACTIVE(from(z0)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndspos(z0, z1))) → c17(CONS2(x0, 2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, 2ndsneg(z0, z1))) → c17(CONS2(x0, 2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons2(x0, pi(z0))) → c17(CONS2(x0, pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, plus(z0, z1))) → c17(CONS2(x0, plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, times(z0, z1))) → c17(CONS2(x0, times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(cons2(x0, square(z0))) → c17(CONS2(x0, square(active(z0))), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c20(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(from(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c20(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, z2)))) → c20(FROM(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(from(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c20(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c20(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c20(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c20(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c20(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c20(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c20(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c20(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c20(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c20(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c20(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(cons2(z0, z1))) → c20(FROM(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c20(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c20(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c20(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c20(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c20(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c20(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c20(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c20(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c25(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c25(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, z2)))) → c25(PI(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(pi(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c25(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c25(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c25(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c25(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c25(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c25(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c25(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c25(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c25(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c25(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c25(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(cons2(z0, z1))) → c25(PI(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c25(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c25(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c25(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c25(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c25(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c25(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c25(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c25(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c30(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
ACTIVE(square(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c30(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, z2)))) → c30(SQUARE(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
ACTIVE(square(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c30(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c30(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c30(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c30(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c30(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c30(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c30(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c30(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c30(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c30(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(cons2(z0, z1))) → c30(SQUARE(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c30(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c30(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c30(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c30(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c30(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c30(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c30(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c30(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c63(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c63(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c63(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c63(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(cons2(z0, z1))) → c63(S(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(s(rcons(z0, z1))) → c63(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c63(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c63(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c63(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c63(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c63(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c63(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c63(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c63(S(ok(0)))
PROPER(s(nil)) → c63(S(ok(nil)))
PROPER(s(rnil)) → c63(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c64(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c64(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c64(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c64(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(cons2(z0, z1))) → c64(POSRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c64(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c64(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c64(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c64(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c64(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c64(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c64(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c64(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c64(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c64(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c64(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c65(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c65(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c65(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c65(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(cons2(z0, z1))) → c65(NEGRECIP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c65(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c65(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c65(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c65(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c65(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c65(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c65(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c65(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c65(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c65(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c65(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c67(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c67(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c67(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c67(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, cons2(z0, z1))) → c67(CONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c67(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c67(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c67(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c67(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c67(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c67(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c67(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c67(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c67(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c67(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c67(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c67(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(cons2(z0, z1), x1)) → c67(CONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c67(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c67(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c67(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c67(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c67(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c67(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c67(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c67(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c67(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c67(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c67(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c67(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c67(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c67(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(cons2(x0, s(z0))) → c68(CONS2(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons2(x0, posrecip(z0))) → c68(CONS2(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons2(x0, negrecip(z0))) → c68(CONS2(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons2(x0, cons(z0, z1))) → c68(CONS2(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons2(x0, cons2(z0, z1))) → c68(CONS2(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(cons2(x0, rcons(z0, z1))) → c68(CONS2(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons2(x0, from(z0))) → c68(CONS2(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons2(x0, 2ndspos(z0, z1))) → c68(CONS2(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons2(x0, 2ndsneg(z0, z1))) → c68(CONS2(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons2(x0, pi(z0))) → c68(CONS2(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons2(x0, plus(z0, z1))) → c68(CONS2(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons2(x0, times(z0, z1))) → c68(CONS2(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons2(x0, square(z0))) → c68(CONS2(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons2(s(z0), x1)) → c68(CONS2(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons2(posrecip(z0), x1)) → c68(CONS2(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons2(negrecip(z0), x1)) → c68(CONS2(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons2(cons(z0, z1), x1)) → c68(CONS2(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons2(cons2(z0, z1), x1)) → c68(CONS2(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(cons2(rcons(z0, z1), x1)) → c68(CONS2(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons2(from(z0), x1)) → c68(CONS2(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons2(2ndspos(z0, z1), x1)) → c68(CONS2(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons2(2ndsneg(z0, z1), x1)) → c68(CONS2(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons2(pi(z0), x1)) → c68(CONS2(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons2(plus(z0, z1), x1)) → c68(CONS2(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons2(times(z0, z1), x1)) → c68(CONS2(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons2(square(z0), x1)) → c68(CONS2(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons2(x0, 0)) → c68(CONS2(proper(x0), ok(0)), PROPER(x0))
PROPER(cons2(x0, nil)) → c68(CONS2(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons2(x0, rnil)) → c68(CONS2(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons2(0, x1)) → c68(CONS2(ok(0), proper(x1)), PROPER(x1))
PROPER(cons2(nil, x1)) → c68(CONS2(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons2(rnil, x1)) → c68(CONS2(ok(rnil), proper(x1)), PROPER(x1))
PROPER(rcons(x0, s(z0))) → c70(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c70(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c70(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, cons(z0, z1))) → c70(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, cons2(z0, z1))) → c70(RCONS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(rcons(x0, rcons(z0, z1))) → c70(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c70(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c70(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c70(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c70(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c70(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c70(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c70(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(s(z0), x1)) → c70(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c70(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c70(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c70(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(cons2(z0, z1), x1)) → c70(RCONS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c70(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c70(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c70(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c70(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c70(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c70(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c70(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c70(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(rcons(x0, 0)) → c70(RCONS(proper(x0), ok(0)), PROPER(x0))
PROPER(rcons(x0, nil)) → c70(RCONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(rcons(x0, rnil)) → c70(RCONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(rcons(0, x1)) → c70(RCONS(ok(0), proper(x1)), PROPER(x1))
PROPER(rcons(nil, x1)) → c70(RCONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c70(RCONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(from(s(z0))) → c71(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(posrecip(z0))) → c71(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(from(negrecip(z0))) → c71(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(from(cons(z0, z1))) → c71(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(cons2(z0, z1))) → c71(FROM(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(from(rcons(z0, z1))) → c71(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(from(from(z0))) → c71(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(2ndspos(z0, z1))) → c71(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(from(2ndsneg(z0, z1))) → c71(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(from(pi(z0))) → c71(FROM(pi(proper(z0))), PROPER(pi(z0)))
PROPER(from(plus(z0, z1))) → c71(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(from(times(z0, z1))) → c71(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(from(square(z0))) → c71(FROM(square(proper(z0))), PROPER(square(z0)))
PROPER(from(0)) → c71(FROM(ok(0)))
PROPER(from(nil)) → c71(FROM(ok(nil)))
PROPER(from(rnil)) → c71(FROM(ok(rnil)))
PROPER(2ndspos(x0, s(z0))) → c72(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndspos(x0, posrecip(z0))) → c72(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndspos(x0, negrecip(z0))) → c72(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndspos(x0, cons(z0, z1))) → c72(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndspos(x0, cons2(z0, z1))) → c72(2NDSPOS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(2ndspos(x0, rcons(z0, z1))) → c72(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndspos(x0, from(z0))) → c72(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c72(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c72(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndspos(x0, pi(z0))) → c72(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndspos(x0, plus(z0, z1))) → c72(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndspos(x0, times(z0, z1))) → c72(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndspos(x0, square(z0))) → c72(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndspos(s(z0), x1)) → c72(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndspos(posrecip(z0), x1)) → c72(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndspos(negrecip(z0), x1)) → c72(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndspos(cons(z0, z1), x1)) → c72(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndspos(cons2(z0, z1), x1)) → c72(2NDSPOS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(2ndspos(rcons(z0, z1), x1)) → c72(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndspos(from(z0), x1)) → c72(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c72(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c72(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndspos(pi(z0), x1)) → c72(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndspos(plus(z0, z1), x1)) → c72(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndspos(times(z0, z1), x1)) → c72(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndspos(square(z0), x1)) → c72(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndspos(x0, 0)) → c72(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndspos(x0, nil)) → c72(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndspos(x0, rnil)) → c72(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndspos(0, x1)) → c72(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndspos(nil, x1)) → c72(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndspos(rnil, x1)) → c72(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(x0, s(z0))) → c73(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndsneg(x0, posrecip(z0))) → c73(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndsneg(x0, negrecip(z0))) → c73(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndsneg(x0, cons(z0, z1))) → c73(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndsneg(x0, cons2(z0, z1))) → c73(2NDSNEG(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(2ndsneg(x0, rcons(z0, z1))) → c73(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndsneg(x0, from(z0))) → c73(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c73(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c73(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndsneg(x0, pi(z0))) → c73(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndsneg(x0, plus(z0, z1))) → c73(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndsneg(x0, times(z0, z1))) → c73(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndsneg(x0, square(z0))) → c73(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndsneg(s(z0), x1)) → c73(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndsneg(posrecip(z0), x1)) → c73(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndsneg(negrecip(z0), x1)) → c73(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndsneg(cons(z0, z1), x1)) → c73(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(cons2(z0, z1), x1)) → c73(2NDSNEG(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(2ndsneg(rcons(z0, z1), x1)) → c73(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(from(z0), x1)) → c73(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c73(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c73(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndsneg(pi(z0), x1)) → c73(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndsneg(plus(z0, z1), x1)) → c73(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndsneg(times(z0, z1), x1)) → c73(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndsneg(square(z0), x1)) → c73(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndsneg(x0, 0)) → c73(2NDSNEG(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndsneg(x0, nil)) → c73(2NDSNEG(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndsneg(x0, rnil)) → c73(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndsneg(0, x1)) → c73(2NDSNEG(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndsneg(nil, x1)) → c73(2NDSNEG(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(rnil, x1)) → c73(2NDSNEG(ok(rnil), proper(x1)), PROPER(x1))
PROPER(pi(s(z0))) → c74(PI(s(proper(z0))), PROPER(s(z0)))
PROPER(pi(posrecip(z0))) → c74(PI(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(pi(negrecip(z0))) → c74(PI(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(pi(cons(z0, z1))) → c74(PI(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(pi(cons2(z0, z1))) → c74(PI(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(pi(rcons(z0, z1))) → c74(PI(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(pi(from(z0))) → c74(PI(from(proper(z0))), PROPER(from(z0)))
PROPER(pi(2ndspos(z0, z1))) → c74(PI(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(pi(2ndsneg(z0, z1))) → c74(PI(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(pi(pi(z0))) → c74(PI(pi(proper(z0))), PROPER(pi(z0)))
PROPER(pi(plus(z0, z1))) → c74(PI(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(pi(times(z0, z1))) → c74(PI(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(pi(square(z0))) → c74(PI(square(proper(z0))), PROPER(square(z0)))
PROPER(pi(0)) → c74(PI(ok(0)))
PROPER(pi(nil)) → c74(PI(ok(nil)))
PROPER(pi(rnil)) → c74(PI(ok(rnil)))
PROPER(plus(x0, s(z0))) → c75(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(plus(x0, posrecip(z0))) → c75(PLUS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(plus(x0, negrecip(z0))) → c75(PLUS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(plus(x0, cons(z0, z1))) → c75(PLUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(plus(x0, cons2(z0, z1))) → c75(PLUS(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(plus(x0, rcons(z0, z1))) → c75(PLUS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(plus(x0, from(z0))) → c75(PLUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(plus(x0, 2ndspos(z0, z1))) → c75(PLUS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(plus(x0, 2ndsneg(z0, z1))) → c75(PLUS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(plus(x0, pi(z0))) → c75(PLUS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(plus(x0, plus(z0, z1))) → c75(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(plus(x0, times(z0, z1))) → c75(PLUS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(plus(x0, square(z0))) → c75(PLUS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(plus(s(z0), x1)) → c75(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(plus(posrecip(z0), x1)) → c75(PLUS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(plus(negrecip(z0), x1)) → c75(PLUS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(plus(cons(z0, z1), x1)) → c75(PLUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(plus(cons2(z0, z1), x1)) → c75(PLUS(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(plus(rcons(z0, z1), x1)) → c75(PLUS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(plus(from(z0), x1)) → c75(PLUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(plus(2ndspos(z0, z1), x1)) → c75(PLUS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(plus(2ndsneg(z0, z1), x1)) → c75(PLUS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(plus(pi(z0), x1)) → c75(PLUS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(plus(plus(z0, z1), x1)) → c75(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(plus(times(z0, z1), x1)) → c75(PLUS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(plus(square(z0), x1)) → c75(PLUS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(plus(x0, 0)) → c75(PLUS(proper(x0), ok(0)), PROPER(x0))
PROPER(plus(x0, nil)) → c75(PLUS(proper(x0), ok(nil)), PROPER(x0))
PROPER(plus(x0, rnil)) → c75(PLUS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(plus(0, x1)) → c75(PLUS(ok(0), proper(x1)), PROPER(x1))
PROPER(plus(nil, x1)) → c75(PLUS(ok(nil), proper(x1)), PROPER(x1))
PROPER(plus(rnil, x1)) → c75(PLUS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(times(x0, s(z0))) → c76(TIMES(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(times(x0, posrecip(z0))) → c76(TIMES(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(times(x0, negrecip(z0))) → c76(TIMES(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(times(x0, cons(z0, z1))) → c76(TIMES(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(times(x0, cons2(z0, z1))) → c76(TIMES(proper(x0), cons2(proper(z0), proper(z1))), PROPER(x0), PROPER(cons2(z0, z1)))
PROPER(times(x0, rcons(z0, z1))) → c76(TIMES(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(times(x0, from(z0))) → c76(TIMES(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(times(x0, 2ndspos(z0, z1))) → c76(TIMES(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(times(x0, 2ndsneg(z0, z1))) → c76(TIMES(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(times(x0, pi(z0))) → c76(TIMES(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(times(x0, plus(z0, z1))) → c76(TIMES(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(times(x0, times(z0, z1))) → c76(TIMES(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(times(x0, square(z0))) → c76(TIMES(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(times(s(z0), x1)) → c76(TIMES(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(times(posrecip(z0), x1)) → c76(TIMES(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(times(negrecip(z0), x1)) → c76(TIMES(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(times(cons(z0, z1), x1)) → c76(TIMES(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(times(cons2(z0, z1), x1)) → c76(TIMES(cons2(proper(z0), proper(z1)), proper(x1)), PROPER(cons2(z0, z1)), PROPER(x1))
PROPER(times(rcons(z0, z1), x1)) → c76(TIMES(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(times(from(z0), x1)) → c76(TIMES(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(times(2ndspos(z0, z1), x1)) → c76(TIMES(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(times(2ndsneg(z0, z1), x1)) → c76(TIMES(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(times(pi(z0), x1)) → c76(TIMES(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(times(plus(z0, z1), x1)) → c76(TIMES(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(times(times(z0, z1), x1)) → c76(TIMES(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(times(square(z0), x1)) → c76(TIMES(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(times(x0, 0)) → c76(TIMES(proper(x0), ok(0)), PROPER(x0))
PROPER(times(x0, nil)) → c76(TIMES(proper(x0), ok(nil)), PROPER(x0))
PROPER(times(x0, rnil)) → c76(TIMES(proper(x0), ok(rnil)), PROPER(x0))
PROPER(times(0, x1)) → c76(TIMES(ok(0), proper(x1)), PROPER(x1))
PROPER(times(nil, x1)) → c76(TIMES(ok(nil), proper(x1)), PROPER(x1))
PROPER(times(rnil, x1)) → c76(TIMES(ok(rnil), proper(x1)), PROPER(x1))
PROPER(square(s(z0))) → c77(SQUARE(s(proper(z0))), PROPER(s(z0)))
PROPER(square(posrecip(z0))) → c77(SQUARE(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(square(negrecip(z0))) → c77(SQUARE(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(square(cons(z0, z1))) → c77(SQUARE(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(square(cons2(z0, z1))) → c77(SQUARE(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
PROPER(square(rcons(z0, z1))) → c77(SQUARE(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(square(from(z0))) → c77(SQUARE(from(proper(z0))), PROPER(from(z0)))
PROPER(square(2ndspos(z0, z1))) → c77(SQUARE(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(square(2ndsneg(z0, z1))) → c77(SQUARE(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(square(pi(z0))) → c77(SQUARE(pi(proper(z0))), PROPER(pi(z0)))
PROPER(square(plus(z0, z1))) → c77(SQUARE(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(square(times(z0, z1))) → c77(SQUARE(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(square(square(z0))) → c77(SQUARE(square(proper(z0))), PROPER(square(z0)))
PROPER(square(0)) → c77(SQUARE(ok(0)))
PROPER(square(nil)) → c77(SQUARE(ok(nil)))
PROPER(square(rnil)) → c77(SQUARE(ok(rnil)))
TOP(mark(s(z0))) → c78(TOP(s(proper(z0))), PROPER(s(z0)))
TOP(mark(posrecip(z0))) → c78(TOP(posrecip(proper(z0))), PROPER(posrecip(z0)))
TOP(mark(negrecip(z0))) → c78(TOP(negrecip(proper(z0))), PROPER(negrecip(z0)))
TOP(mark(cons(z0, z1))) → c78(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
TOP(mark(cons2(z0, z1))) → c78(TOP(cons2(proper(z0), proper(z1))), PROPER(cons2(z0, z1)))
TOP(mark(rcons(z0, z1))) → c78(TOP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
TOP(mark(from(z0))) → c78(TOP(from(proper(z0))), PROPER(from(z0)))
TOP(mark(2ndspos(z0, z1))) → c78(TOP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
TOP(mark(2ndsneg(z0, z1))) → c78(TOP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
TOP(mark(pi(z0))) → c78(TOP(pi(proper(z0))), PROPER(pi(z0)))
TOP(mark(plus(z0, z1))) → c78(TOP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
TOP(mark(times(z0, z1))) → c78(TOP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
TOP(mark(square(z0))) → c78(TOP(square(proper(z0))), PROPER(square(z0)))
TOP(ok(from(z0))) → c79(TOP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
TOP(ok(2ndspos(0, z0))) → c79(TOP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
TOP(ok(2ndspos(s(z0), cons(z1, z2)))) → c79(TOP(mark(2ndspos(s(z0), cons2(z1, z2)))), ACTIVE(2ndspos(s(z0), cons(z1, z2))))
TOP(ok(2ndspos(s(z0), cons2(z1, cons(z2, z3))))) → c79(TOP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons2(z1, cons(z2, z3)))))
TOP(ok(2ndsneg(0, z0))) → c79(TOP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
TOP(ok(2ndsneg(s(z0), cons(z1, z2)))) → c79(TOP(mark(2ndsneg(s(z0), cons2(z1, z2)))), ACTIVE(2ndsneg(s(z0), cons(z1, z2))))
TOP(ok(2ndsneg(s(z0), cons2(z1, cons(z2, z3))))) → c79(TOP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))))
TOP(ok(pi(z0))) → c79(TOP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
TOP(ok(plus(0, z0))) → c79(TOP(mark(z0)), ACTIVE(plus(0, z0)))
TOP(ok(plus(s(z0), z1))) → c79(TOP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
TOP(ok(times(0, z0))) → c79(TOP(mark(0)), ACTIVE(times(0, z0)))
TOP(ok(times(s(z0), z1))) → c79(TOP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
TOP(ok(square(z0))) → c79(TOP(mark(times(z0, z0))), ACTIVE(square(z0)))
TOP(ok(s(z0))) → c79(TOP(s(active(z0))), ACTIVE(s(z0)))
TOP(ok(posrecip(z0))) → c79(TOP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
TOP(ok(negrecip(z0))) → c79(TOP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
TOP(ok(cons(z0, z1))) → c79(TOP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
TOP(ok(cons2(z0, z1))) → c79(TOP(cons2(z0, active(z1))), ACTIVE(cons2(z0, z1)))
TOP(ok(rcons(z0, z1))) → c79(TOP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
TOP(ok(rcons(z0, z1))) → c79(TOP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
TOP(ok(from(z0))) → c79(TOP(from(active(z0))), ACTIVE(from(z0)))
TOP(ok(2ndspos(z0, z1))) → c79(TOP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
TOP(ok(2ndspos(z0, z1))) → c79(TOP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
TOP(ok(2ndsneg(z0, z1))) → c79(TOP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
TOP(ok(2ndsneg(z0, z1))) → c79(TOP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
TOP(ok(pi(z0))) → c79(TOP(pi(active(z0))), ACTIVE(pi(z0)))
TOP(ok(plus(z0, z1))) → c79(TOP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
TOP(ok(plus(z0, z1))) → c79(TOP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
TOP(ok(times(z0, z1))) → c79(TOP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
TOP(ok(times(z0, z1))) → c79(TOP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
TOP(ok(square(z0))) → c79(TOP(square(active(z0))), ACTIVE(square(z0)))
(88) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(2ndspos(0, z0)) → mark(rnil)
active(2ndspos(s(z0), cons(z1, z2))) → mark(2ndspos(s(z0), cons2(z1, z2)))
active(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(z1, z2))) → mark(2ndsneg(s(z0), cons2(z1, z2)))
active(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
active(pi(z0)) → mark(2ndspos(z0, from(0)))
active(plus(0, z0)) → mark(z0)
active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
active(times(0, z0)) → mark(0)
active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
active(square(z0)) → mark(times(z0, z0))
active(s(z0)) → s(active(z0))
active(posrecip(z0)) → posrecip(active(z0))
active(negrecip(z0)) → negrecip(active(z0))
active(cons(z0, z1)) → cons(active(z0), z1)
active(cons2(z0, z1)) → cons2(z0, active(z1))
active(rcons(z0, z1)) → rcons(active(z0), z1)
active(rcons(z0, z1)) → rcons(z0, active(z1))
active(from(z0)) → from(active(z0))
active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
active(pi(z0)) → pi(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(times(z0, z1)) → times(active(z0), z1)
active(times(z0, z1)) → times(z0, active(z1))
active(square(z0)) → square(active(z0))
2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
cons2(z0, mark(z1)) → mark(cons2(z0, z1))
cons2(ok(z0), ok(z1)) → ok(cons2(z0, z1))
rcons(mark(z0), z1) → mark(rcons(z0, z1))
rcons(z0, mark(z1)) → mark(rcons(z0, z1))
rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
posrecip(ok(z0)) → ok(posrecip(z0))
posrecip(mark(z0)) → mark(posrecip(z0))
2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
negrecip(ok(z0)) → ok(negrecip(z0))
negrecip(mark(z0)) → mark(negrecip(z0))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
cons(mark(z0), z1) → mark(cons(z0, z1))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
from(mark(z0)) → mark(from(z0))
from(ok(z0)) → ok(from(z0))
pi(mark(z0)) → mark(pi(z0))
pi(ok(z0)) → ok(pi(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
times(mark(z0), z1) → mark(times(z0, z1))
times(ok(z0), ok(z1)) → ok(times(z0, z1))
times(z0, mark(z1)) → mark(times(z0, z1))
square(mark(z0)) → mark(square(z0))
square(ok(z0)) → ok(square(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(posrecip(z0)) → posrecip(proper(z0))
proper(negrecip(z0)) → negrecip(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(cons2(z0, z1)) → cons2(proper(z0), proper(z1))
proper(rnil) → ok(rnil)
proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
proper(pi(z0)) → pi(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(times(z0, z1)) → times(proper(z0), proper(z1))
proper(square(z0)) → square(proper(z0))
Tuples:
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
S tuples:
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
K tuples:none
Defined Rule Symbols:
active, 2ndspos, cons2, rcons, posrecip, 2ndsneg, negrecip, s, cons, from, pi, plus, times, square, proper
Defined Pair Symbols:
S, POSRECIP, NEGRECIP, CONS, CONS2, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE
Compound Symbols:
c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61
(89) CdtUsableRulesProof (EQUIVALENT transformation)
The following rules are not usable and were removed:
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(2ndspos(0, z0)) → mark(rnil)
active(2ndspos(s(z0), cons(z1, z2))) → mark(2ndspos(s(z0), cons2(z1, z2)))
active(2ndspos(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(z1, z2))) → mark(2ndsneg(s(z0), cons2(z1, z2)))
active(2ndsneg(s(z0), cons2(z1, cons(z2, z3)))) → mark(rcons(negrecip(z2), 2ndspos(z0, z3)))
active(pi(z0)) → mark(2ndspos(z0, from(0)))
active(plus(0, z0)) → mark(z0)
active(plus(s(z0), z1)) → mark(s(plus(z0, z1)))
active(times(0, z0)) → mark(0)
active(times(s(z0), z1)) → mark(plus(z1, times(z0, z1)))
active(square(z0)) → mark(times(z0, z0))
active(s(z0)) → s(active(z0))
active(posrecip(z0)) → posrecip(active(z0))
active(negrecip(z0)) → negrecip(active(z0))
active(cons(z0, z1)) → cons(active(z0), z1)
active(cons2(z0, z1)) → cons2(z0, active(z1))
active(rcons(z0, z1)) → rcons(active(z0), z1)
active(rcons(z0, z1)) → rcons(z0, active(z1))
active(from(z0)) → from(active(z0))
active(2ndspos(z0, z1)) → 2ndspos(active(z0), z1)
active(2ndspos(z0, z1)) → 2ndspos(z0, active(z1))
active(2ndsneg(z0, z1)) → 2ndsneg(active(z0), z1)
active(2ndsneg(z0, z1)) → 2ndsneg(z0, active(z1))
active(pi(z0)) → pi(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(times(z0, z1)) → times(active(z0), z1)
active(times(z0, z1)) → times(z0, active(z1))
active(square(z0)) → square(active(z0))
2ndspos(z0, mark(z1)) → mark(2ndspos(z0, z1))
2ndspos(mark(z0), z1) → mark(2ndspos(z0, z1))
2ndspos(ok(z0), ok(z1)) → ok(2ndspos(z0, z1))
cons2(z0, mark(z1)) → mark(cons2(z0, z1))
cons2(ok(z0), ok(z1)) → ok(cons2(z0, z1))
rcons(mark(z0), z1) → mark(rcons(z0, z1))
rcons(z0, mark(z1)) → mark(rcons(z0, z1))
rcons(ok(z0), ok(z1)) → ok(rcons(z0, z1))
posrecip(ok(z0)) → ok(posrecip(z0))
posrecip(mark(z0)) → mark(posrecip(z0))
2ndsneg(z0, mark(z1)) → mark(2ndsneg(z0, z1))
2ndsneg(mark(z0), z1) → mark(2ndsneg(z0, z1))
2ndsneg(ok(z0), ok(z1)) → ok(2ndsneg(z0, z1))
negrecip(ok(z0)) → ok(negrecip(z0))
negrecip(mark(z0)) → mark(negrecip(z0))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
cons(mark(z0), z1) → mark(cons(z0, z1))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
from(mark(z0)) → mark(from(z0))
from(ok(z0)) → ok(from(z0))
pi(mark(z0)) → mark(pi(z0))
pi(ok(z0)) → ok(pi(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
times(mark(z0), z1) → mark(times(z0, z1))
times(ok(z0), ok(z1)) → ok(times(z0, z1))
times(z0, mark(z1)) → mark(times(z0, z1))
square(mark(z0)) → mark(square(z0))
square(ok(z0)) → ok(square(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(posrecip(z0)) → posrecip(proper(z0))
proper(negrecip(z0)) → negrecip(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(cons2(z0, z1)) → cons2(proper(z0), proper(z1))
proper(rnil) → ok(rnil)
proper(rcons(z0, z1)) → rcons(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(2ndspos(z0, z1)) → 2ndspos(proper(z0), proper(z1))
proper(2ndsneg(z0, z1)) → 2ndsneg(proper(z0), proper(z1))
proper(pi(z0)) → pi(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(times(z0, z1)) → times(proper(z0), proper(z1))
proper(square(z0)) → square(proper(z0))
(90) Obligation:
Complexity Dependency Tuples Problem
Rules:none
Tuples:
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
S tuples:
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
K tuples:none
Defined Rule Symbols:none
Defined Pair Symbols:
S, POSRECIP, NEGRECIP, CONS, CONS2, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE
Compound Symbols:
c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61
(91) CdtRuleRemovalProof (UPPER BOUND (ADD(O(n^1))) transformation)
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
We considered the (Usable) Rules:none
And the Tuples:
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
The order we found is given by the following interpretation:
Polynomial interpretation :
POL(2NDSNEG(x1, x2)) = 0
POL(2NDSPOS(x1, x2)) = x1
POL(CONS(x1, x2)) = 0
POL(CONS2(x1, x2)) = 0
POL(FROM(x1)) = 0
POL(NEGRECIP(x1)) = 0
POL(PI(x1)) = 0
POL(PLUS(x1, x2)) = [4]x2
POL(POSRECIP(x1)) = 0
POL(RCONS(x1, x2)) = 0
POL(S(x1)) = 0
POL(SQUARE(x1)) = 0
POL(TIMES(x1, x2)) = 0
POL(c31(x1)) = x1
POL(c32(x1)) = x1
POL(c33(x1)) = x1
POL(c34(x1)) = x1
POL(c35(x1)) = x1
POL(c36(x1)) = x1
POL(c37(x1)) = x1
POL(c38(x1)) = x1
POL(c39(x1)) = x1
POL(c40(x1)) = x1
POL(c41(x1)) = x1
POL(c42(x1)) = x1
POL(c43(x1)) = x1
POL(c44(x1)) = x1
POL(c45(x1)) = x1
POL(c46(x1)) = x1
POL(c47(x1)) = x1
POL(c48(x1)) = x1
POL(c49(x1)) = x1
POL(c50(x1)) = x1
POL(c51(x1)) = x1
POL(c52(x1)) = x1
POL(c53(x1)) = x1
POL(c54(x1)) = x1
POL(c55(x1)) = x1
POL(c56(x1)) = x1
POL(c57(x1)) = x1
POL(c58(x1)) = x1
POL(c59(x1)) = x1
POL(c60(x1)) = x1
POL(c61(x1)) = x1
POL(mark(x1)) = [4] + x1
POL(ok(x1)) = x1
(92) Obligation:
Complexity Dependency Tuples Problem
Rules:none
Tuples:
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
S tuples:
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
K tuples:
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
Defined Rule Symbols:none
Defined Pair Symbols:
S, POSRECIP, NEGRECIP, CONS, CONS2, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE
Compound Symbols:
c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61
(93) CdtRuleRemovalProof (UPPER BOUND (ADD(O(n^1))) transformation)
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
We considered the (Usable) Rules:none
And the Tuples:
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
The order we found is given by the following interpretation:
Polynomial interpretation :
POL(2NDSNEG(x1, x2)) = 0
POL(2NDSPOS(x1, x2)) = 0
POL(CONS(x1, x2)) = 0
POL(CONS2(x1, x2)) = [4]x1
POL(FROM(x1)) = 0
POL(NEGRECIP(x1)) = 0
POL(PI(x1)) = 0
POL(PLUS(x1, x2)) = 0
POL(POSRECIP(x1)) = 0
POL(RCONS(x1, x2)) = 0
POL(S(x1)) = 0
POL(SQUARE(x1)) = 0
POL(TIMES(x1, x2)) = 0
POL(c31(x1)) = x1
POL(c32(x1)) = x1
POL(c33(x1)) = x1
POL(c34(x1)) = x1
POL(c35(x1)) = x1
POL(c36(x1)) = x1
POL(c37(x1)) = x1
POL(c38(x1)) = x1
POL(c39(x1)) = x1
POL(c40(x1)) = x1
POL(c41(x1)) = x1
POL(c42(x1)) = x1
POL(c43(x1)) = x1
POL(c44(x1)) = x1
POL(c45(x1)) = x1
POL(c46(x1)) = x1
POL(c47(x1)) = x1
POL(c48(x1)) = x1
POL(c49(x1)) = x1
POL(c50(x1)) = x1
POL(c51(x1)) = x1
POL(c52(x1)) = x1
POL(c53(x1)) = x1
POL(c54(x1)) = x1
POL(c55(x1)) = x1
POL(c56(x1)) = x1
POL(c57(x1)) = x1
POL(c58(x1)) = x1
POL(c59(x1)) = x1
POL(c60(x1)) = x1
POL(c61(x1)) = x1
POL(mark(x1)) = [2]
POL(ok(x1)) = [2] + x1
(94) Obligation:
Complexity Dependency Tuples Problem
Rules:none
Tuples:
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
S tuples:
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
K tuples:
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
Defined Rule Symbols:none
Defined Pair Symbols:
S, POSRECIP, NEGRECIP, CONS, CONS2, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE
Compound Symbols:
c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61
(95) CdtRuleRemovalProof (UPPER BOUND (ADD(O(n^1))) transformation)
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
We considered the (Usable) Rules:none
And the Tuples:
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
The order we found is given by the following interpretation:
Polynomial interpretation :
POL(2NDSNEG(x1, x2)) = [4]x2
POL(2NDSPOS(x1, x2)) = 0
POL(CONS(x1, x2)) = 0
POL(CONS2(x1, x2)) = 0
POL(FROM(x1)) = 0
POL(NEGRECIP(x1)) = [2]x1
POL(PI(x1)) = 0
POL(PLUS(x1, x2)) = 0
POL(POSRECIP(x1)) = 0
POL(RCONS(x1, x2)) = 0
POL(S(x1)) = 0
POL(SQUARE(x1)) = 0
POL(TIMES(x1, x2)) = 0
POL(c31(x1)) = x1
POL(c32(x1)) = x1
POL(c33(x1)) = x1
POL(c34(x1)) = x1
POL(c35(x1)) = x1
POL(c36(x1)) = x1
POL(c37(x1)) = x1
POL(c38(x1)) = x1
POL(c39(x1)) = x1
POL(c40(x1)) = x1
POL(c41(x1)) = x1
POL(c42(x1)) = x1
POL(c43(x1)) = x1
POL(c44(x1)) = x1
POL(c45(x1)) = x1
POL(c46(x1)) = x1
POL(c47(x1)) = x1
POL(c48(x1)) = x1
POL(c49(x1)) = x1
POL(c50(x1)) = x1
POL(c51(x1)) = x1
POL(c52(x1)) = x1
POL(c53(x1)) = x1
POL(c54(x1)) = x1
POL(c55(x1)) = x1
POL(c56(x1)) = x1
POL(c57(x1)) = x1
POL(c58(x1)) = x1
POL(c59(x1)) = x1
POL(c60(x1)) = x1
POL(c61(x1)) = x1
POL(mark(x1)) = [4] + x1
POL(ok(x1)) = x1
(96) Obligation:
Complexity Dependency Tuples Problem
Rules:none
Tuples:
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
S tuples:
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
K tuples:
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
Defined Rule Symbols:none
Defined Pair Symbols:
S, POSRECIP, NEGRECIP, CONS, CONS2, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE
Compound Symbols:
c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61
(97) CdtRuleRemovalProof (UPPER BOUND (ADD(O(n^1))) transformation)
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
We considered the (Usable) Rules:none
And the Tuples:
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
The order we found is given by the following interpretation:
Polynomial interpretation :
POL(2NDSNEG(x1, x2)) = 0
POL(2NDSPOS(x1, x2)) = 0
POL(CONS(x1, x2)) = [2]x1 + [2]x2
POL(CONS2(x1, x2)) = x1
POL(FROM(x1)) = 0
POL(NEGRECIP(x1)) = 0
POL(PI(x1)) = 0
POL(PLUS(x1, x2)) = [4]x2
POL(POSRECIP(x1)) = 0
POL(RCONS(x1, x2)) = 0
POL(S(x1)) = 0
POL(SQUARE(x1)) = 0
POL(TIMES(x1, x2)) = [4]x1
POL(c31(x1)) = x1
POL(c32(x1)) = x1
POL(c33(x1)) = x1
POL(c34(x1)) = x1
POL(c35(x1)) = x1
POL(c36(x1)) = x1
POL(c37(x1)) = x1
POL(c38(x1)) = x1
POL(c39(x1)) = x1
POL(c40(x1)) = x1
POL(c41(x1)) = x1
POL(c42(x1)) = x1
POL(c43(x1)) = x1
POL(c44(x1)) = x1
POL(c45(x1)) = x1
POL(c46(x1)) = x1
POL(c47(x1)) = x1
POL(c48(x1)) = x1
POL(c49(x1)) = x1
POL(c50(x1)) = x1
POL(c51(x1)) = x1
POL(c52(x1)) = x1
POL(c53(x1)) = x1
POL(c54(x1)) = x1
POL(c55(x1)) = x1
POL(c56(x1)) = x1
POL(c57(x1)) = x1
POL(c58(x1)) = x1
POL(c59(x1)) = x1
POL(c60(x1)) = x1
POL(c61(x1)) = x1
POL(mark(x1)) = x1
POL(ok(x1)) = [4] + x1
(98) Obligation:
Complexity Dependency Tuples Problem
Rules:none
Tuples:
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
S tuples:
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
K tuples:
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
Defined Rule Symbols:none
Defined Pair Symbols:
S, POSRECIP, NEGRECIP, CONS, CONS2, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE
Compound Symbols:
c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61
(99) CdtRuleRemovalProof (UPPER BOUND (ADD(O(n^1))) transformation)
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
We considered the (Usable) Rules:none
And the Tuples:
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
The order we found is given by the following interpretation:
Polynomial interpretation :
POL(2NDSNEG(x1, x2)) = 0
POL(2NDSPOS(x1, x2)) = 0
POL(CONS(x1, x2)) = x2
POL(CONS2(x1, x2)) = [5]x1
POL(FROM(x1)) = 0
POL(NEGRECIP(x1)) = 0
POL(PI(x1)) = 0
POL(PLUS(x1, x2)) = 0
POL(POSRECIP(x1)) = 0
POL(RCONS(x1, x2)) = 0
POL(S(x1)) = 0
POL(SQUARE(x1)) = 0
POL(TIMES(x1, x2)) = [5]x2
POL(c31(x1)) = x1
POL(c32(x1)) = x1
POL(c33(x1)) = x1
POL(c34(x1)) = x1
POL(c35(x1)) = x1
POL(c36(x1)) = x1
POL(c37(x1)) = x1
POL(c38(x1)) = x1
POL(c39(x1)) = x1
POL(c40(x1)) = x1
POL(c41(x1)) = x1
POL(c42(x1)) = x1
POL(c43(x1)) = x1
POL(c44(x1)) = x1
POL(c45(x1)) = x1
POL(c46(x1)) = x1
POL(c47(x1)) = x1
POL(c48(x1)) = x1
POL(c49(x1)) = x1
POL(c50(x1)) = x1
POL(c51(x1)) = x1
POL(c52(x1)) = x1
POL(c53(x1)) = x1
POL(c54(x1)) = x1
POL(c55(x1)) = x1
POL(c56(x1)) = x1
POL(c57(x1)) = x1
POL(c58(x1)) = x1
POL(c59(x1)) = x1
POL(c60(x1)) = x1
POL(c61(x1)) = x1
POL(mark(x1)) = [5] + x1
POL(ok(x1)) = x1
(100) Obligation:
Complexity Dependency Tuples Problem
Rules:none
Tuples:
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
S tuples:
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
K tuples:
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
Defined Rule Symbols:none
Defined Pair Symbols:
S, POSRECIP, NEGRECIP, CONS, CONS2, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE
Compound Symbols:
c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61
(101) CdtRuleRemovalProof (UPPER BOUND (ADD(O(n^1))) transformation)
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
We considered the (Usable) Rules:none
And the Tuples:
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
The order we found is given by the following interpretation:
Polynomial interpretation :
POL(2NDSNEG(x1, x2)) = 0
POL(2NDSPOS(x1, x2)) = 0
POL(CONS(x1, x2)) = [2]x2
POL(CONS2(x1, x2)) = [4]x2
POL(FROM(x1)) = 0
POL(NEGRECIP(x1)) = 0
POL(PI(x1)) = 0
POL(PLUS(x1, x2)) = 0
POL(POSRECIP(x1)) = 0
POL(RCONS(x1, x2)) = 0
POL(S(x1)) = 0
POL(SQUARE(x1)) = 0
POL(TIMES(x1, x2)) = 0
POL(c31(x1)) = x1
POL(c32(x1)) = x1
POL(c33(x1)) = x1
POL(c34(x1)) = x1
POL(c35(x1)) = x1
POL(c36(x1)) = x1
POL(c37(x1)) = x1
POL(c38(x1)) = x1
POL(c39(x1)) = x1
POL(c40(x1)) = x1
POL(c41(x1)) = x1
POL(c42(x1)) = x1
POL(c43(x1)) = x1
POL(c44(x1)) = x1
POL(c45(x1)) = x1
POL(c46(x1)) = x1
POL(c47(x1)) = x1
POL(c48(x1)) = x1
POL(c49(x1)) = x1
POL(c50(x1)) = x1
POL(c51(x1)) = x1
POL(c52(x1)) = x1
POL(c53(x1)) = x1
POL(c54(x1)) = x1
POL(c55(x1)) = x1
POL(c56(x1)) = x1
POL(c57(x1)) = x1
POL(c58(x1)) = x1
POL(c59(x1)) = x1
POL(c60(x1)) = x1
POL(c61(x1)) = x1
POL(mark(x1)) = [4] + x1
POL(ok(x1)) = x1
(102) Obligation:
Complexity Dependency Tuples Problem
Rules:none
Tuples:
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
S tuples:
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
K tuples:
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
Defined Rule Symbols:none
Defined Pair Symbols:
S, POSRECIP, NEGRECIP, CONS, CONS2, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE
Compound Symbols:
c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61
(103) CdtRuleRemovalProof (UPPER BOUND (ADD(O(n^1))) transformation)
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
We considered the (Usable) Rules:none
And the Tuples:
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
The order we found is given by the following interpretation:
Polynomial interpretation :
POL(2NDSNEG(x1, x2)) = [4]x1
POL(2NDSPOS(x1, x2)) = 0
POL(CONS(x1, x2)) = x1
POL(CONS2(x1, x2)) = [2]x1 + [2]x2
POL(FROM(x1)) = 0
POL(NEGRECIP(x1)) = 0
POL(PI(x1)) = 0
POL(PLUS(x1, x2)) = 0
POL(POSRECIP(x1)) = x1
POL(RCONS(x1, x2)) = 0
POL(S(x1)) = 0
POL(SQUARE(x1)) = 0
POL(TIMES(x1, x2)) = 0
POL(c31(x1)) = x1
POL(c32(x1)) = x1
POL(c33(x1)) = x1
POL(c34(x1)) = x1
POL(c35(x1)) = x1
POL(c36(x1)) = x1
POL(c37(x1)) = x1
POL(c38(x1)) = x1
POL(c39(x1)) = x1
POL(c40(x1)) = x1
POL(c41(x1)) = x1
POL(c42(x1)) = x1
POL(c43(x1)) = x1
POL(c44(x1)) = x1
POL(c45(x1)) = x1
POL(c46(x1)) = x1
POL(c47(x1)) = x1
POL(c48(x1)) = x1
POL(c49(x1)) = x1
POL(c50(x1)) = x1
POL(c51(x1)) = x1
POL(c52(x1)) = x1
POL(c53(x1)) = x1
POL(c54(x1)) = x1
POL(c55(x1)) = x1
POL(c56(x1)) = x1
POL(c57(x1)) = x1
POL(c58(x1)) = x1
POL(c59(x1)) = x1
POL(c60(x1)) = x1
POL(c61(x1)) = x1
POL(mark(x1)) = [1] + x1
POL(ok(x1)) = x1
(104) Obligation:
Complexity Dependency Tuples Problem
Rules:none
Tuples:
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
S tuples:
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
K tuples:
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
Defined Rule Symbols:none
Defined Pair Symbols:
S, POSRECIP, NEGRECIP, CONS, CONS2, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE
Compound Symbols:
c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61
(105) CdtRuleRemovalProof (UPPER BOUND (ADD(O(n^1))) transformation)
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
We considered the (Usable) Rules:none
And the Tuples:
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
The order we found is given by the following interpretation:
Polynomial interpretation :
POL(2NDSNEG(x1, x2)) = 0
POL(2NDSPOS(x1, x2)) = 0
POL(CONS(x1, x2)) = [3]x2
POL(CONS2(x1, x2)) = [3]x1 + [3]x2
POL(FROM(x1)) = 0
POL(NEGRECIP(x1)) = 0
POL(PI(x1)) = 0
POL(PLUS(x1, x2)) = [4]x2
POL(POSRECIP(x1)) = 0
POL(RCONS(x1, x2)) = [4]x1
POL(S(x1)) = 0
POL(SQUARE(x1)) = [4]x1
POL(TIMES(x1, x2)) = 0
POL(c31(x1)) = x1
POL(c32(x1)) = x1
POL(c33(x1)) = x1
POL(c34(x1)) = x1
POL(c35(x1)) = x1
POL(c36(x1)) = x1
POL(c37(x1)) = x1
POL(c38(x1)) = x1
POL(c39(x1)) = x1
POL(c40(x1)) = x1
POL(c41(x1)) = x1
POL(c42(x1)) = x1
POL(c43(x1)) = x1
POL(c44(x1)) = x1
POL(c45(x1)) = x1
POL(c46(x1)) = x1
POL(c47(x1)) = x1
POL(c48(x1)) = x1
POL(c49(x1)) = x1
POL(c50(x1)) = x1
POL(c51(x1)) = x1
POL(c52(x1)) = x1
POL(c53(x1)) = x1
POL(c54(x1)) = x1
POL(c55(x1)) = x1
POL(c56(x1)) = x1
POL(c57(x1)) = x1
POL(c58(x1)) = x1
POL(c59(x1)) = x1
POL(c60(x1)) = x1
POL(c61(x1)) = x1
POL(mark(x1)) = [4] + x1
POL(ok(x1)) = [4] + x1
(106) Obligation:
Complexity Dependency Tuples Problem
Rules:none
Tuples:
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
S tuples:
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
K tuples:
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
Defined Rule Symbols:none
Defined Pair Symbols:
S, POSRECIP, NEGRECIP, CONS, CONS2, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE
Compound Symbols:
c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61
(107) CdtRuleRemovalProof (UPPER BOUND (ADD(O(n^1))) transformation)
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
We considered the (Usable) Rules:none
And the Tuples:
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
The order we found is given by the following interpretation:
Polynomial interpretation :
POL(2NDSNEG(x1, x2)) = 0
POL(2NDSPOS(x1, x2)) = 0
POL(CONS(x1, x2)) = 0
POL(CONS2(x1, x2)) = [2]x1 + [3]x2
POL(FROM(x1)) = 0
POL(NEGRECIP(x1)) = 0
POL(PI(x1)) = 0
POL(PLUS(x1, x2)) = [2]x2
POL(POSRECIP(x1)) = 0
POL(RCONS(x1, x2)) = [2]x1
POL(S(x1)) = x1
POL(SQUARE(x1)) = [2]x1
POL(TIMES(x1, x2)) = [4]x1 + [3]x2
POL(c31(x1)) = x1
POL(c32(x1)) = x1
POL(c33(x1)) = x1
POL(c34(x1)) = x1
POL(c35(x1)) = x1
POL(c36(x1)) = x1
POL(c37(x1)) = x1
POL(c38(x1)) = x1
POL(c39(x1)) = x1
POL(c40(x1)) = x1
POL(c41(x1)) = x1
POL(c42(x1)) = x1
POL(c43(x1)) = x1
POL(c44(x1)) = x1
POL(c45(x1)) = x1
POL(c46(x1)) = x1
POL(c47(x1)) = x1
POL(c48(x1)) = x1
POL(c49(x1)) = x1
POL(c50(x1)) = x1
POL(c51(x1)) = x1
POL(c52(x1)) = x1
POL(c53(x1)) = x1
POL(c54(x1)) = x1
POL(c55(x1)) = x1
POL(c56(x1)) = x1
POL(c57(x1)) = x1
POL(c58(x1)) = x1
POL(c59(x1)) = x1
POL(c60(x1)) = x1
POL(c61(x1)) = x1
POL(mark(x1)) = [1] + x1
POL(ok(x1)) = [2] + x1
(108) Obligation:
Complexity Dependency Tuples Problem
Rules:none
Tuples:
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
S tuples:
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
K tuples:
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
Defined Rule Symbols:none
Defined Pair Symbols:
S, POSRECIP, NEGRECIP, CONS, CONS2, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE
Compound Symbols:
c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61
(109) CdtRuleRemovalProof (UPPER BOUND (ADD(O(n^1))) transformation)
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
We considered the (Usable) Rules:none
And the Tuples:
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
The order we found is given by the following interpretation:
Polynomial interpretation :
POL(2NDSNEG(x1, x2)) = [4]x2
POL(2NDSPOS(x1, x2)) = 0
POL(CONS(x1, x2)) = 0
POL(CONS2(x1, x2)) = 0
POL(FROM(x1)) = 0
POL(NEGRECIP(x1)) = 0
POL(PI(x1)) = 0
POL(PLUS(x1, x2)) = [2]x2
POL(POSRECIP(x1)) = x1
POL(RCONS(x1, x2)) = 0
POL(S(x1)) = [3]x1
POL(SQUARE(x1)) = 0
POL(TIMES(x1, x2)) = 0
POL(c31(x1)) = x1
POL(c32(x1)) = x1
POL(c33(x1)) = x1
POL(c34(x1)) = x1
POL(c35(x1)) = x1
POL(c36(x1)) = x1
POL(c37(x1)) = x1
POL(c38(x1)) = x1
POL(c39(x1)) = x1
POL(c40(x1)) = x1
POL(c41(x1)) = x1
POL(c42(x1)) = x1
POL(c43(x1)) = x1
POL(c44(x1)) = x1
POL(c45(x1)) = x1
POL(c46(x1)) = x1
POL(c47(x1)) = x1
POL(c48(x1)) = x1
POL(c49(x1)) = x1
POL(c50(x1)) = x1
POL(c51(x1)) = x1
POL(c52(x1)) = x1
POL(c53(x1)) = x1
POL(c54(x1)) = x1
POL(c55(x1)) = x1
POL(c56(x1)) = x1
POL(c57(x1)) = x1
POL(c58(x1)) = x1
POL(c59(x1)) = x1
POL(c60(x1)) = x1
POL(c61(x1)) = x1
POL(mark(x1)) = [5] + x1
POL(ok(x1)) = [2] + x1
(110) Obligation:
Complexity Dependency Tuples Problem
Rules:none
Tuples:
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
S tuples:
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
K tuples:
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
Defined Rule Symbols:none
Defined Pair Symbols:
S, POSRECIP, NEGRECIP, CONS, CONS2, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE
Compound Symbols:
c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61
(111) CdtRuleRemovalProof (UPPER BOUND (ADD(O(n^1))) transformation)
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
We considered the (Usable) Rules:none
And the Tuples:
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
The order we found is given by the following interpretation:
Polynomial interpretation :
POL(2NDSNEG(x1, x2)) = 0
POL(2NDSPOS(x1, x2)) = 0
POL(CONS(x1, x2)) = 0
POL(CONS2(x1, x2)) = [3]x1
POL(FROM(x1)) = 0
POL(NEGRECIP(x1)) = x1
POL(PI(x1)) = 0
POL(PLUS(x1, x2)) = 0
POL(POSRECIP(x1)) = 0
POL(RCONS(x1, x2)) = 0
POL(S(x1)) = 0
POL(SQUARE(x1)) = [2]x1
POL(TIMES(x1, x2)) = [3]x1 + [2]x2
POL(c31(x1)) = x1
POL(c32(x1)) = x1
POL(c33(x1)) = x1
POL(c34(x1)) = x1
POL(c35(x1)) = x1
POL(c36(x1)) = x1
POL(c37(x1)) = x1
POL(c38(x1)) = x1
POL(c39(x1)) = x1
POL(c40(x1)) = x1
POL(c41(x1)) = x1
POL(c42(x1)) = x1
POL(c43(x1)) = x1
POL(c44(x1)) = x1
POL(c45(x1)) = x1
POL(c46(x1)) = x1
POL(c47(x1)) = x1
POL(c48(x1)) = x1
POL(c49(x1)) = x1
POL(c50(x1)) = x1
POL(c51(x1)) = x1
POL(c52(x1)) = x1
POL(c53(x1)) = x1
POL(c54(x1)) = x1
POL(c55(x1)) = x1
POL(c56(x1)) = x1
POL(c57(x1)) = x1
POL(c58(x1)) = x1
POL(c59(x1)) = x1
POL(c60(x1)) = x1
POL(c61(x1)) = x1
POL(mark(x1)) = x1
POL(ok(x1)) = [1] + x1
(112) Obligation:
Complexity Dependency Tuples Problem
Rules:none
Tuples:
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
S tuples:
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
K tuples:
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
Defined Rule Symbols:none
Defined Pair Symbols:
S, POSRECIP, NEGRECIP, CONS, CONS2, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE
Compound Symbols:
c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61
(113) CdtRuleRemovalProof (UPPER BOUND (ADD(O(n^1))) transformation)
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
FROM(ok(z0)) → c45(FROM(z0))
We considered the (Usable) Rules:none
And the Tuples:
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
The order we found is given by the following interpretation:
Polynomial interpretation :
POL(2NDSNEG(x1, x2)) = [2]x1
POL(2NDSPOS(x1, x2)) = 0
POL(CONS(x1, x2)) = 0
POL(CONS2(x1, x2)) = [3]x1 + [3]x2
POL(FROM(x1)) = x1
POL(NEGRECIP(x1)) = 0
POL(PI(x1)) = 0
POL(PLUS(x1, x2)) = 0
POL(POSRECIP(x1)) = 0
POL(RCONS(x1, x2)) = [2]x1
POL(S(x1)) = 0
POL(SQUARE(x1)) = 0
POL(TIMES(x1, x2)) = [2]x2
POL(c31(x1)) = x1
POL(c32(x1)) = x1
POL(c33(x1)) = x1
POL(c34(x1)) = x1
POL(c35(x1)) = x1
POL(c36(x1)) = x1
POL(c37(x1)) = x1
POL(c38(x1)) = x1
POL(c39(x1)) = x1
POL(c40(x1)) = x1
POL(c41(x1)) = x1
POL(c42(x1)) = x1
POL(c43(x1)) = x1
POL(c44(x1)) = x1
POL(c45(x1)) = x1
POL(c46(x1)) = x1
POL(c47(x1)) = x1
POL(c48(x1)) = x1
POL(c49(x1)) = x1
POL(c50(x1)) = x1
POL(c51(x1)) = x1
POL(c52(x1)) = x1
POL(c53(x1)) = x1
POL(c54(x1)) = x1
POL(c55(x1)) = x1
POL(c56(x1)) = x1
POL(c57(x1)) = x1
POL(c58(x1)) = x1
POL(c59(x1)) = x1
POL(c60(x1)) = x1
POL(c61(x1)) = x1
POL(mark(x1)) = x1
POL(ok(x1)) = [1] + x1
(114) Obligation:
Complexity Dependency Tuples Problem
Rules:none
Tuples:
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
S tuples:
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
K tuples:
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
FROM(ok(z0)) → c45(FROM(z0))
Defined Rule Symbols:none
Defined Pair Symbols:
S, POSRECIP, NEGRECIP, CONS, CONS2, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE
Compound Symbols:
c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61
(115) CdtRuleRemovalProof (UPPER BOUND (ADD(O(n^1))) transformation)
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
We considered the (Usable) Rules:none
And the Tuples:
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
The order we found is given by the following interpretation:
Polynomial interpretation :
POL(2NDSNEG(x1, x2)) = [2]x2
POL(2NDSPOS(x1, x2)) = 0
POL(CONS(x1, x2)) = [4]x1
POL(CONS2(x1, x2)) = [3]x1 + [4]x2
POL(FROM(x1)) = 0
POL(NEGRECIP(x1)) = [4]x1
POL(PI(x1)) = 0
POL(PLUS(x1, x2)) = x1
POL(POSRECIP(x1)) = [2]x1
POL(RCONS(x1, x2)) = [4]x1
POL(S(x1)) = 0
POL(SQUARE(x1)) = 0
POL(TIMES(x1, x2)) = [4]x1 + [4]x2
POL(c31(x1)) = x1
POL(c32(x1)) = x1
POL(c33(x1)) = x1
POL(c34(x1)) = x1
POL(c35(x1)) = x1
POL(c36(x1)) = x1
POL(c37(x1)) = x1
POL(c38(x1)) = x1
POL(c39(x1)) = x1
POL(c40(x1)) = x1
POL(c41(x1)) = x1
POL(c42(x1)) = x1
POL(c43(x1)) = x1
POL(c44(x1)) = x1
POL(c45(x1)) = x1
POL(c46(x1)) = x1
POL(c47(x1)) = x1
POL(c48(x1)) = x1
POL(c49(x1)) = x1
POL(c50(x1)) = x1
POL(c51(x1)) = x1
POL(c52(x1)) = x1
POL(c53(x1)) = x1
POL(c54(x1)) = x1
POL(c55(x1)) = x1
POL(c56(x1)) = x1
POL(c57(x1)) = x1
POL(c58(x1)) = x1
POL(c59(x1)) = x1
POL(c60(x1)) = x1
POL(c61(x1)) = x1
POL(mark(x1)) = [1] + x1
POL(ok(x1)) = [2] + x1
(116) Obligation:
Complexity Dependency Tuples Problem
Rules:none
Tuples:
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
S tuples:
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
K tuples:
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
FROM(ok(z0)) → c45(FROM(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
Defined Rule Symbols:none
Defined Pair Symbols:
S, POSRECIP, NEGRECIP, CONS, CONS2, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE
Compound Symbols:
c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61
(117) CdtRuleRemovalProof (UPPER BOUND (ADD(O(n^1))) transformation)
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
We considered the (Usable) Rules:none
And the Tuples:
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
The order we found is given by the following interpretation:
Polynomial interpretation :
POL(2NDSNEG(x1, x2)) = 0
POL(2NDSPOS(x1, x2)) = x1
POL(CONS(x1, x2)) = [4]x1
POL(CONS2(x1, x2)) = [4]x1 + [2]x2
POL(FROM(x1)) = 0
POL(NEGRECIP(x1)) = 0
POL(PI(x1)) = 0
POL(PLUS(x1, x2)) = [4]x1
POL(POSRECIP(x1)) = 0
POL(RCONS(x1, x2)) = [2]x1
POL(S(x1)) = 0
POL(SQUARE(x1)) = 0
POL(TIMES(x1, x2)) = [4]x1
POL(c31(x1)) = x1
POL(c32(x1)) = x1
POL(c33(x1)) = x1
POL(c34(x1)) = x1
POL(c35(x1)) = x1
POL(c36(x1)) = x1
POL(c37(x1)) = x1
POL(c38(x1)) = x1
POL(c39(x1)) = x1
POL(c40(x1)) = x1
POL(c41(x1)) = x1
POL(c42(x1)) = x1
POL(c43(x1)) = x1
POL(c44(x1)) = x1
POL(c45(x1)) = x1
POL(c46(x1)) = x1
POL(c47(x1)) = x1
POL(c48(x1)) = x1
POL(c49(x1)) = x1
POL(c50(x1)) = x1
POL(c51(x1)) = x1
POL(c52(x1)) = x1
POL(c53(x1)) = x1
POL(c54(x1)) = x1
POL(c55(x1)) = x1
POL(c56(x1)) = x1
POL(c57(x1)) = x1
POL(c58(x1)) = x1
POL(c59(x1)) = x1
POL(c60(x1)) = x1
POL(c61(x1)) = x1
POL(mark(x1)) = x1
POL(ok(x1)) = [1] + x1
(118) Obligation:
Complexity Dependency Tuples Problem
Rules:none
Tuples:
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
S tuples:
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
K tuples:
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
FROM(ok(z0)) → c45(FROM(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
Defined Rule Symbols:none
Defined Pair Symbols:
S, POSRECIP, NEGRECIP, CONS, CONS2, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE
Compound Symbols:
c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61
(119) CdtRuleRemovalProof (UPPER BOUND (ADD(O(n^1))) transformation)
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
PI(mark(z0)) → c52(PI(z0))
We considered the (Usable) Rules:none
And the Tuples:
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
The order we found is given by the following interpretation:
Polynomial interpretation :
POL(2NDSNEG(x1, x2)) = [4]x1 + [3]x2
POL(2NDSPOS(x1, x2)) = [2]x1
POL(CONS(x1, x2)) = 0
POL(CONS2(x1, x2)) = 0
POL(FROM(x1)) = 0
POL(NEGRECIP(x1)) = [2]x1
POL(PI(x1)) = x1
POL(PLUS(x1, x2)) = 0
POL(POSRECIP(x1)) = 0
POL(RCONS(x1, x2)) = 0
POL(S(x1)) = 0
POL(SQUARE(x1)) = 0
POL(TIMES(x1, x2)) = [4]x1 + [2]x2
POL(c31(x1)) = x1
POL(c32(x1)) = x1
POL(c33(x1)) = x1
POL(c34(x1)) = x1
POL(c35(x1)) = x1
POL(c36(x1)) = x1
POL(c37(x1)) = x1
POL(c38(x1)) = x1
POL(c39(x1)) = x1
POL(c40(x1)) = x1
POL(c41(x1)) = x1
POL(c42(x1)) = x1
POL(c43(x1)) = x1
POL(c44(x1)) = x1
POL(c45(x1)) = x1
POL(c46(x1)) = x1
POL(c47(x1)) = x1
POL(c48(x1)) = x1
POL(c49(x1)) = x1
POL(c50(x1)) = x1
POL(c51(x1)) = x1
POL(c52(x1)) = x1
POL(c53(x1)) = x1
POL(c54(x1)) = x1
POL(c55(x1)) = x1
POL(c56(x1)) = x1
POL(c57(x1)) = x1
POL(c58(x1)) = x1
POL(c59(x1)) = x1
POL(c60(x1)) = x1
POL(c61(x1)) = x1
POL(mark(x1)) = [1] + x1
POL(ok(x1)) = x1
(120) Obligation:
Complexity Dependency Tuples Problem
Rules:none
Tuples:
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
S tuples:
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
PI(ok(z0)) → c53(PI(z0))
K tuples:
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
FROM(ok(z0)) → c45(FROM(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
PI(mark(z0)) → c52(PI(z0))
Defined Rule Symbols:none
Defined Pair Symbols:
S, POSRECIP, NEGRECIP, CONS, CONS2, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE
Compound Symbols:
c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61
(121) CdtRuleRemovalProof (UPPER BOUND (ADD(O(n^1))) transformation)
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
FROM(mark(z0)) → c44(FROM(z0))
We considered the (Usable) Rules:none
And the Tuples:
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
The order we found is given by the following interpretation:
Polynomial interpretation :
POL(2NDSNEG(x1, x2)) = 0
POL(2NDSPOS(x1, x2)) = [2]x1
POL(CONS(x1, x2)) = [4]x1 + [3]x2
POL(CONS2(x1, x2)) = [2]x1
POL(FROM(x1)) = x1
POL(NEGRECIP(x1)) = 0
POL(PI(x1)) = 0
POL(PLUS(x1, x2)) = 0
POL(POSRECIP(x1)) = 0
POL(RCONS(x1, x2)) = [2]x1
POL(S(x1)) = 0
POL(SQUARE(x1)) = [4]x1
POL(TIMES(x1, x2)) = [4]x2
POL(c31(x1)) = x1
POL(c32(x1)) = x1
POL(c33(x1)) = x1
POL(c34(x1)) = x1
POL(c35(x1)) = x1
POL(c36(x1)) = x1
POL(c37(x1)) = x1
POL(c38(x1)) = x1
POL(c39(x1)) = x1
POL(c40(x1)) = x1
POL(c41(x1)) = x1
POL(c42(x1)) = x1
POL(c43(x1)) = x1
POL(c44(x1)) = x1
POL(c45(x1)) = x1
POL(c46(x1)) = x1
POL(c47(x1)) = x1
POL(c48(x1)) = x1
POL(c49(x1)) = x1
POL(c50(x1)) = x1
POL(c51(x1)) = x1
POL(c52(x1)) = x1
POL(c53(x1)) = x1
POL(c54(x1)) = x1
POL(c55(x1)) = x1
POL(c56(x1)) = x1
POL(c57(x1)) = x1
POL(c58(x1)) = x1
POL(c59(x1)) = x1
POL(c60(x1)) = x1
POL(c61(x1)) = x1
POL(mark(x1)) = [1] + x1
POL(ok(x1)) = [3] + x1
(122) Obligation:
Complexity Dependency Tuples Problem
Rules:none
Tuples:
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
S tuples:
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
PI(ok(z0)) → c53(PI(z0))
K tuples:
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
FROM(ok(z0)) → c45(FROM(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
PI(mark(z0)) → c52(PI(z0))
FROM(mark(z0)) → c44(FROM(z0))
Defined Rule Symbols:none
Defined Pair Symbols:
S, POSRECIP, NEGRECIP, CONS, CONS2, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE
Compound Symbols:
c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61
(123) CdtRuleRemovalProof (UPPER BOUND (ADD(O(n^1))) transformation)
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
We considered the (Usable) Rules:none
And the Tuples:
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
The order we found is given by the following interpretation:
Polynomial interpretation :
POL(2NDSNEG(x1, x2)) = [4]x1 + [2]x2
POL(2NDSPOS(x1, x2)) = 0
POL(CONS(x1, x2)) = 0
POL(CONS2(x1, x2)) = [2]x1
POL(FROM(x1)) = [2]x1
POL(NEGRECIP(x1)) = 0
POL(PI(x1)) = 0
POL(PLUS(x1, x2)) = [3]x1
POL(POSRECIP(x1)) = 0
POL(RCONS(x1, x2)) = [3]x1 + [2]x2
POL(S(x1)) = 0
POL(SQUARE(x1)) = 0
POL(TIMES(x1, x2)) = [4]x1 + [4]x2
POL(c31(x1)) = x1
POL(c32(x1)) = x1
POL(c33(x1)) = x1
POL(c34(x1)) = x1
POL(c35(x1)) = x1
POL(c36(x1)) = x1
POL(c37(x1)) = x1
POL(c38(x1)) = x1
POL(c39(x1)) = x1
POL(c40(x1)) = x1
POL(c41(x1)) = x1
POL(c42(x1)) = x1
POL(c43(x1)) = x1
POL(c44(x1)) = x1
POL(c45(x1)) = x1
POL(c46(x1)) = x1
POL(c47(x1)) = x1
POL(c48(x1)) = x1
POL(c49(x1)) = x1
POL(c50(x1)) = x1
POL(c51(x1)) = x1
POL(c52(x1)) = x1
POL(c53(x1)) = x1
POL(c54(x1)) = x1
POL(c55(x1)) = x1
POL(c56(x1)) = x1
POL(c57(x1)) = x1
POL(c58(x1)) = x1
POL(c59(x1)) = x1
POL(c60(x1)) = x1
POL(c61(x1)) = x1
POL(mark(x1)) = [4] + x1
POL(ok(x1)) = [2] + x1
(124) Obligation:
Complexity Dependency Tuples Problem
Rules:none
Tuples:
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
S tuples:
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
PI(ok(z0)) → c53(PI(z0))
K tuples:
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
FROM(ok(z0)) → c45(FROM(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
PI(mark(z0)) → c52(PI(z0))
FROM(mark(z0)) → c44(FROM(z0))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
Defined Rule Symbols:none
Defined Pair Symbols:
S, POSRECIP, NEGRECIP, CONS, CONS2, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE
Compound Symbols:
c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61
(125) CdtRuleRemovalProof (UPPER BOUND (ADD(O(n^1))) transformation)
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
We considered the (Usable) Rules:none
And the Tuples:
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
The order we found is given by the following interpretation:
Polynomial interpretation :
POL(2NDSNEG(x1, x2)) = 0
POL(2NDSPOS(x1, x2)) = [2]x1 + x2
POL(CONS(x1, x2)) = [4]x1 + [2]x2
POL(CONS2(x1, x2)) = [4]x2
POL(FROM(x1)) = 0
POL(NEGRECIP(x1)) = 0
POL(PI(x1)) = 0
POL(PLUS(x1, x2)) = 0
POL(POSRECIP(x1)) = 0
POL(RCONS(x1, x2)) = [3]x1 + [2]x2
POL(S(x1)) = 0
POL(SQUARE(x1)) = [4]x1
POL(TIMES(x1, x2)) = [2]x1
POL(c31(x1)) = x1
POL(c32(x1)) = x1
POL(c33(x1)) = x1
POL(c34(x1)) = x1
POL(c35(x1)) = x1
POL(c36(x1)) = x1
POL(c37(x1)) = x1
POL(c38(x1)) = x1
POL(c39(x1)) = x1
POL(c40(x1)) = x1
POL(c41(x1)) = x1
POL(c42(x1)) = x1
POL(c43(x1)) = x1
POL(c44(x1)) = x1
POL(c45(x1)) = x1
POL(c46(x1)) = x1
POL(c47(x1)) = x1
POL(c48(x1)) = x1
POL(c49(x1)) = x1
POL(c50(x1)) = x1
POL(c51(x1)) = x1
POL(c52(x1)) = x1
POL(c53(x1)) = x1
POL(c54(x1)) = x1
POL(c55(x1)) = x1
POL(c56(x1)) = x1
POL(c57(x1)) = x1
POL(c58(x1)) = x1
POL(c59(x1)) = x1
POL(c60(x1)) = x1
POL(c61(x1)) = x1
POL(mark(x1)) = [1] + x1
POL(ok(x1)) = [5] + x1
(126) Obligation:
Complexity Dependency Tuples Problem
Rules:none
Tuples:
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
S tuples:
PI(ok(z0)) → c53(PI(z0))
K tuples:
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
FROM(ok(z0)) → c45(FROM(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
PI(mark(z0)) → c52(PI(z0))
FROM(mark(z0)) → c44(FROM(z0))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
Defined Rule Symbols:none
Defined Pair Symbols:
S, POSRECIP, NEGRECIP, CONS, CONS2, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE
Compound Symbols:
c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61
(127) CdtRuleRemovalProof (UPPER BOUND (ADD(O(n^1))) transformation)
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
PI(ok(z0)) → c53(PI(z0))
We considered the (Usable) Rules:none
And the Tuples:
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
The order we found is given by the following interpretation:
Polynomial interpretation :
POL(2NDSNEG(x1, x2)) = [3]x2
POL(2NDSPOS(x1, x2)) = [2]x1 + [4]x2
POL(CONS(x1, x2)) = [4]x2
POL(CONS2(x1, x2)) = [2]x1
POL(FROM(x1)) = [2]x1
POL(NEGRECIP(x1)) = 0
POL(PI(x1)) = x1
POL(PLUS(x1, x2)) = [4]x1
POL(POSRECIP(x1)) = 0
POL(RCONS(x1, x2)) = 0
POL(S(x1)) = 0
POL(SQUARE(x1)) = 0
POL(TIMES(x1, x2)) = [2]x1 + [4]x2
POL(c31(x1)) = x1
POL(c32(x1)) = x1
POL(c33(x1)) = x1
POL(c34(x1)) = x1
POL(c35(x1)) = x1
POL(c36(x1)) = x1
POL(c37(x1)) = x1
POL(c38(x1)) = x1
POL(c39(x1)) = x1
POL(c40(x1)) = x1
POL(c41(x1)) = x1
POL(c42(x1)) = x1
POL(c43(x1)) = x1
POL(c44(x1)) = x1
POL(c45(x1)) = x1
POL(c46(x1)) = x1
POL(c47(x1)) = x1
POL(c48(x1)) = x1
POL(c49(x1)) = x1
POL(c50(x1)) = x1
POL(c51(x1)) = x1
POL(c52(x1)) = x1
POL(c53(x1)) = x1
POL(c54(x1)) = x1
POL(c55(x1)) = x1
POL(c56(x1)) = x1
POL(c57(x1)) = x1
POL(c58(x1)) = x1
POL(c59(x1)) = x1
POL(c60(x1)) = x1
POL(c61(x1)) = x1
POL(mark(x1)) = x1
POL(ok(x1)) = [1] + x1
(128) Obligation:
Complexity Dependency Tuples Problem
Rules:none
Tuples:
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
FROM(mark(z0)) → c44(FROM(z0))
FROM(ok(z0)) → c45(FROM(z0))
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
PI(mark(z0)) → c52(PI(z0))
PI(ok(z0)) → c53(PI(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
S tuples:none
K tuples:
2NDSPOS(mark(z0), z1) → c46(2NDSPOS(z0, z1))
PLUS(z0, mark(z1)) → c55(PLUS(z0, z1))
CONS2(ok(z0), ok(z1)) → c40(CONS2(z0, z1))
NEGRECIP(mark(z0)) → c35(NEGRECIP(z0))
2NDSNEG(z0, mark(z1)) → c50(2NDSNEG(z0, z1))
CONS(ok(z0), ok(z1)) → c38(CONS(z0, z1))
PLUS(ok(z0), ok(z1)) → c56(PLUS(z0, z1))
TIMES(ok(z0), ok(z1)) → c59(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c58(TIMES(z0, z1))
CONS2(z0, mark(z1)) → c39(CONS2(z0, z1))
POSRECIP(mark(z0)) → c33(POSRECIP(z0))
CONS(mark(z0), z1) → c37(CONS(z0, z1))
2NDSNEG(mark(z0), z1) → c49(2NDSNEG(z0, z1))
RCONS(mark(z0), z1) → c41(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c43(RCONS(z0, z1))
SQUARE(mark(z0)) → c60(SQUARE(z0))
SQUARE(ok(z0)) → c61(SQUARE(z0))
S(mark(z0)) → c31(S(z0))
S(ok(z0)) → c32(S(z0))
TIMES(mark(z0), z1) → c57(TIMES(z0, z1))
POSRECIP(ok(z0)) → c34(POSRECIP(z0))
2NDSNEG(ok(z0), ok(z1)) → c51(2NDSNEG(z0, z1))
NEGRECIP(ok(z0)) → c36(NEGRECIP(z0))
FROM(ok(z0)) → c45(FROM(z0))
PLUS(mark(z0), z1) → c54(PLUS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c48(2NDSPOS(z0, z1))
PI(mark(z0)) → c52(PI(z0))
FROM(mark(z0)) → c44(FROM(z0))
RCONS(z0, mark(z1)) → c42(RCONS(z0, z1))
2NDSPOS(z0, mark(z1)) → c47(2NDSPOS(z0, z1))
PI(ok(z0)) → c53(PI(z0))
Defined Rule Symbols:none
Defined Pair Symbols:
S, POSRECIP, NEGRECIP, CONS, CONS2, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE
Compound Symbols:
c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61
(129) SIsEmptyProof (BOTH BOUNDS(ID, ID) transformation)
The set S is empty
(130) BOUNDS(O(1), O(1))