Runtime Complexity (innermost) proof of /tmp/tmpty9L7Q/Ex1_2_AEL03

The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(O(1), O(n^1)).

0 CpxTRS

↳1 CpxTrsToCdtProof (BOTH BOUNDS(ID, ID), 94 ms)

↳2 CdtProblem

↳3 CdtLeafRemovalProof (BOTH BOUNDS(ID, ID), 0 ms)

↳4 CdtProblem

↳5 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID), 0 ms)

↳6 CdtProblem

↳7 CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID), 15 ms)

↳8 CdtProblem

↳9 CdtUsableRulesProof (⇔, 382 ms)

↳10 CdtProblem

↳11 CdtNarrowingProof (BOTH BOUNDS(ID, ID), 43 ms)

↳12 CdtProblem

↳13 CdtNarrowingProof (BOTH BOUNDS(ID, ID), 0 ms)

↳14 CdtProblem

↳15 CdtNarrowingProof (BOTH BOUNDS(ID, ID), 2 ms)

↳16 CdtProblem

↳17 CdtNarrowingProof (BOTH BOUNDS(ID, ID), 0 ms)

↳18 CdtProblem

↳19 CdtNarrowingProof (BOTH BOUNDS(ID, ID), 45 ms)

↳20 CdtProblem

↳21 CdtNarrowingProof (BOTH BOUNDS(ID, ID), 34 ms)

↳22 CdtProblem

↳23 CdtNarrowingProof (BOTH BOUNDS(ID, ID), 0 ms)

↳24 CdtProblem

↳25 CdtNarrowingProof (BOTH BOUNDS(ID, ID), 0 ms)

↳26 CdtProblem

↳27 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID), 0 ms)

↳28 CdtProblem

↳29 CdtNarrowingProof (BOTH BOUNDS(ID, ID), 0 ms)

↳30 CdtProblem

↳31 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID), 0 ms)

↳32 CdtProblem

↳33 CdtNarrowingProof (BOTH BOUNDS(ID, ID), 0 ms)

↳34 CdtProblem

↳35 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID), 0 ms)

↳36 CdtProblem

↳37 CdtNarrowingProof (BOTH BOUNDS(ID, ID), 0 ms)

↳38 CdtProblem

↳39 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID), 0 ms)

↳40 CdtProblem

↳41 CdtNarrowingProof (BOTH BOUNDS(ID, ID), 98 ms)

↳42 CdtProblem

↳43 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID), 0 ms)

↳44 CdtProblem

↳45 CdtNarrowingProof (BOTH BOUNDS(ID, ID), 0 ms)

↳46 CdtProblem

↳47 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID), 0 ms)

↳48 CdtProblem

↳49 CdtNarrowingProof (BOTH BOUNDS(ID, ID), 99 ms)

↳50 CdtProblem

↳51 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID), 0 ms)

↳52 CdtProblem

↳53 CdtNarrowingProof (BOTH BOUNDS(ID, ID), 99 ms)

↳54 CdtProblem

↳55 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID), 26 ms)

↳56 CdtProblem

↳57 CdtNarrowingProof (BOTH BOUNDS(ID, ID), 0 ms)

↳58 CdtProblem

↳59 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID), 0 ms)

↳60 CdtProblem

↳61 CdtNarrowingProof (BOTH BOUNDS(ID, ID), 99 ms)

↳62 CdtProblem

↳63 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID), 2 ms)

↳64 CdtProblem

↳65 CdtNarrowingProof (BOTH BOUNDS(ID, ID), 136 ms)

↳66 CdtProblem

↳67 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID), 0 ms)

↳68 CdtProblem

↳69 CdtNarrowingProof (BOTH BOUNDS(ID, ID), 0 ms)

↳70 CdtProblem

↳71 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID), 0 ms)

↳72 CdtProblem

↳73 CdtNarrowingProof (BOTH BOUNDS(ID, ID), 0 ms)

↳74 CdtProblem

↳75 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID), 0 ms)

↳76 CdtProblem

↳77 CdtNarrowingProof (BOTH BOUNDS(ID, ID), 99 ms)

↳78 CdtProblem

↳79 CdtLeafRemovalProof (BOTH BOUNDS(ID, ID), 39 ms)

↳80 CdtProblem

↳81 CdtUnreachableProof (⇔, 0 ms)

↳82 CdtProblem

↳83 CdtUsableRulesProof (⇔, 0 ms)

↳84 CdtProblem

↳85 CdtRuleRemovalProof (UPPER BOUND (ADD(O(n^1))), 0 ms)

↳86 CdtProblem

↳87 CdtRuleRemovalProof (UPPER BOUND (ADD(O(n^1))), 5 ms)

↳88 CdtProblem

↳89 CdtRuleRemovalProof (UPPER BOUND (ADD(O(n^1))), 6 ms)

↳90 CdtProblem

↳91 CdtRuleRemovalProof (UPPER BOUND (ADD(O(n^1))), 0 ms)

↳92 CdtProblem

↳93 CdtRuleRemovalProof (UPPER BOUND (ADD(O(n^1))), 0 ms)

↳94 CdtProblem

↳95 CdtRuleRemovalProof (UPPER BOUND (ADD(O(n^1))), 0 ms)

↳96 CdtProblem

↳97 CdtRuleRemovalProof (UPPER BOUND (ADD(O(n^1))), 17 ms)

↳98 CdtProblem

↳99 CdtRuleRemovalProof (UPPER BOUND (ADD(O(n^1))), 0 ms)

↳100 CdtProblem

↳101 CdtRuleRemovalProof (UPPER BOUND (ADD(O(n^1))), 10 ms)

↳102 CdtProblem

↳103 CdtRuleRemovalProof (UPPER BOUND (ADD(O(n^1))), 0 ms)

↳104 CdtProblem

↳105 CdtRuleRemovalProof (UPPER BOUND (ADD(O(n^1))), 0 ms)

↳106 CdtProblem

↳107 CdtRuleRemovalProof (UPPER BOUND (ADD(O(n^1))), 0 ms)

↳108 CdtProblem

↳109 CdtRuleRemovalProof (UPPER BOUND (ADD(O(n^1))), 7 ms)

↳110 CdtProblem

↳111 SIsEmptyProof (BOTH BOUNDS(ID, ID), 0 ms)

↳112 BOUNDS(O(1), O(1))

(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, cons(Y, Z)))) → mark(rcons(posrecip(Y), 2ndsneg(N, Z)))
active(2ndsneg(0, Z)) → mark(rnil)
active(2ndsneg(s(N), cons(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(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))
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(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))
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, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(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(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))
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(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, cons(z2, z3)))) → c2(RCONS(posrecip(z2), 2ndsneg(z0, z3)), POSRECIP(z2), 2NDSNEG(z0, z3))
ACTIVE(2ndsneg(0, z0)) → c3
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c4(RCONS(negrecip(z2), 2ndspos(z0, z3)), NEGRECIP(z2), 2NDSPOS(z0, z3))
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)), FROM(0))
ACTIVE(plus(0, z0)) → c6
ACTIVE(plus(s(z0), z1)) → c7(S(plus(z0, z1)), PLUS(z0, z1))
ACTIVE(times(0, z0)) → c8
ACTIVE(times(s(z0), z1)) → c9(PLUS(z1, times(z0, z1)), TIMES(z0, z1))
ACTIVE(square(z0)) → c10(TIMES(z0, z0))
ACTIVE(s(z0)) → c11(S(active(z0)), ACTIVE(z0))
ACTIVE(posrecip(z0)) → c12(POSRECIP(active(z0)), ACTIVE(z0))
ACTIVE(negrecip(z0)) → c13(NEGRECIP(active(z0)), ACTIVE(z0))
ACTIVE(cons(z0, z1)) → c14(CONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(from(z0)) → c17(FROM(active(z0)), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(pi(z0)) → c22(PI(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
ACTIVE(square(z0)) → c27(SQUARE(active(z0)), ACTIVE(z0))
S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))
PROPER(0) → c57
PROPER(s(z0)) → c58(S(proper(z0)), PROPER(z0))
PROPER(posrecip(z0)) → c59(POSRECIP(proper(z0)), PROPER(z0))
PROPER(negrecip(z0)) → c60(NEGRECIP(proper(z0)), PROPER(z0))
PROPER(nil) → c61
PROPER(cons(z0, z1)) → c62(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(rnil) → c63
PROPER(rcons(z0, z1)) → c64(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c73(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, cons(z2, z3)))) → c2(RCONS(posrecip(z2), 2ndsneg(z0, z3)), POSRECIP(z2), 2NDSNEG(z0, z3))
ACTIVE(2ndsneg(0, z0)) → c3
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c4(RCONS(negrecip(z2), 2ndspos(z0, z3)), NEGRECIP(z2), 2NDSPOS(z0, z3))
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)), FROM(0))
ACTIVE(plus(0, z0)) → c6
ACTIVE(plus(s(z0), z1)) → c7(S(plus(z0, z1)), PLUS(z0, z1))
ACTIVE(times(0, z0)) → c8
ACTIVE(times(s(z0), z1)) → c9(PLUS(z1, times(z0, z1)), TIMES(z0, z1))
ACTIVE(square(z0)) → c10(TIMES(z0, z0))
ACTIVE(s(z0)) → c11(S(active(z0)), ACTIVE(z0))
ACTIVE(posrecip(z0)) → c12(POSRECIP(active(z0)), ACTIVE(z0))
ACTIVE(negrecip(z0)) → c13(NEGRECIP(active(z0)), ACTIVE(z0))
ACTIVE(cons(z0, z1)) → c14(CONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(from(z0)) → c17(FROM(active(z0)), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(pi(z0)) → c22(PI(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
ACTIVE(square(z0)) → c27(SQUARE(active(z0)), ACTIVE(z0))
S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))
PROPER(0) → c57
PROPER(s(z0)) → c58(S(proper(z0)), PROPER(z0))
PROPER(posrecip(z0)) → c59(POSRECIP(proper(z0)), PROPER(z0))
PROPER(negrecip(z0)) → c60(NEGRECIP(proper(z0)), PROPER(z0))
PROPER(nil) → c61
PROPER(cons(z0, z1)) → c62(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(rnil) → c63
PROPER(rcons(z0, z1)) → c64(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))

K tuples:none
Defined Rule Symbols:

active, s, posrecip, negrecip, cons, rcons, from, 2ndspos, 2ndsneg, pi, plus, times, square, proper, top

Defined Pair Symbols:

ACTIVE, S, POSRECIP, NEGRECIP, CONS, 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

(3) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID) transformation)

Removed 7 trailing nodes:

PROPER(rnil) → c63
ACTIVE(2ndspos(0, z0)) → c1
PROPER(nil) → c61
ACTIVE(2ndsneg(0, z0)) → c3
ACTIVE(plus(0, z0)) → c6
PROPER(0) → c57
ACTIVE(times(0, z0)) → c8

(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, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(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(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))
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(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, cons(z2, z3)))) → c2(RCONS(posrecip(z2), 2ndsneg(z0, z3)), POSRECIP(z2), 2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c4(RCONS(negrecip(z2), 2ndspos(z0, z3)), NEGRECIP(z2), 2NDSPOS(z0, z3))
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)), FROM(0))
ACTIVE(plus(s(z0), z1)) → c7(S(plus(z0, z1)), PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c9(PLUS(z1, times(z0, z1)), TIMES(z0, z1))
ACTIVE(square(z0)) → c10(TIMES(z0, z0))
ACTIVE(s(z0)) → c11(S(active(z0)), ACTIVE(z0))
ACTIVE(posrecip(z0)) → c12(POSRECIP(active(z0)), ACTIVE(z0))
ACTIVE(negrecip(z0)) → c13(NEGRECIP(active(z0)), ACTIVE(z0))
ACTIVE(cons(z0, z1)) → c14(CONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(from(z0)) → c17(FROM(active(z0)), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(pi(z0)) → c22(PI(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
ACTIVE(square(z0)) → c27(SQUARE(active(z0)), ACTIVE(z0))
S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))
PROPER(s(z0)) → c58(S(proper(z0)), PROPER(z0))
PROPER(posrecip(z0)) → c59(POSRECIP(proper(z0)), PROPER(z0))
PROPER(negrecip(z0)) → c60(NEGRECIP(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c62(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(rcons(z0, z1)) → c64(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c73(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, cons(z2, z3)))) → c2(RCONS(posrecip(z2), 2ndsneg(z0, z3)), POSRECIP(z2), 2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c4(RCONS(negrecip(z2), 2ndspos(z0, z3)), NEGRECIP(z2), 2NDSPOS(z0, z3))
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)), FROM(0))
ACTIVE(plus(s(z0), z1)) → c7(S(plus(z0, z1)), PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c9(PLUS(z1, times(z0, z1)), TIMES(z0, z1))
ACTIVE(square(z0)) → c10(TIMES(z0, z0))
ACTIVE(s(z0)) → c11(S(active(z0)), ACTIVE(z0))
ACTIVE(posrecip(z0)) → c12(POSRECIP(active(z0)), ACTIVE(z0))
ACTIVE(negrecip(z0)) → c13(NEGRECIP(active(z0)), ACTIVE(z0))
ACTIVE(cons(z0, z1)) → c14(CONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(from(z0)) → c17(FROM(active(z0)), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(pi(z0)) → c22(PI(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
ACTIVE(square(z0)) → c27(SQUARE(active(z0)), ACTIVE(z0))
S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))
PROPER(s(z0)) → c58(S(proper(z0)), PROPER(z0))
PROPER(posrecip(z0)) → c59(POSRECIP(proper(z0)), PROPER(z0))
PROPER(negrecip(z0)) → c60(NEGRECIP(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c62(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(rcons(z0, z1)) → c64(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))

K tuples:none
Defined Rule Symbols:

active, s, posrecip, negrecip, cons, rcons, from, 2ndspos, 2ndsneg, pi, plus, times, square, proper, top

Defined Pair Symbols:

ACTIVE, S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP

Compound Symbols:

c, c2, c4, c5, c7, 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, c58, c59, c60, c62, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73

(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, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(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(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))
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(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, cons(z2, z3)))) → c2(RCONS(posrecip(z2), 2ndsneg(z0, z3)), POSRECIP(z2), 2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c4(RCONS(negrecip(z2), 2ndspos(z0, z3)), NEGRECIP(z2), 2NDSPOS(z0, z3))
ACTIVE(square(z0)) → c10(TIMES(z0, z0))
ACTIVE(s(z0)) → c11(S(active(z0)), ACTIVE(z0))
ACTIVE(posrecip(z0)) → c12(POSRECIP(active(z0)), ACTIVE(z0))
ACTIVE(negrecip(z0)) → c13(NEGRECIP(active(z0)), ACTIVE(z0))
ACTIVE(cons(z0, z1)) → c14(CONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(from(z0)) → c17(FROM(active(z0)), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(pi(z0)) → c22(PI(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
ACTIVE(square(z0)) → c27(SQUARE(active(z0)), ACTIVE(z0))
S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))
PROPER(s(z0)) → c58(S(proper(z0)), PROPER(z0))
PROPER(posrecip(z0)) → c59(POSRECIP(proper(z0)), PROPER(z0))
PROPER(negrecip(z0)) → c60(NEGRECIP(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c62(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(rcons(z0, z1)) → c64(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))

S tuples:

ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c2(RCONS(posrecip(z2), 2ndsneg(z0, z3)), POSRECIP(z2), 2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c4(RCONS(negrecip(z2), 2ndspos(z0, z3)), NEGRECIP(z2), 2NDSPOS(z0, z3))
ACTIVE(square(z0)) → c10(TIMES(z0, z0))
ACTIVE(s(z0)) → c11(S(active(z0)), ACTIVE(z0))
ACTIVE(posrecip(z0)) → c12(POSRECIP(active(z0)), ACTIVE(z0))
ACTIVE(negrecip(z0)) → c13(NEGRECIP(active(z0)), ACTIVE(z0))
ACTIVE(cons(z0, z1)) → c14(CONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(from(z0)) → c17(FROM(active(z0)), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(pi(z0)) → c22(PI(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
ACTIVE(square(z0)) → c27(SQUARE(active(z0)), ACTIVE(z0))
S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))
PROPER(s(z0)) → c58(S(proper(z0)), PROPER(z0))
PROPER(posrecip(z0)) → c59(POSRECIP(proper(z0)), PROPER(z0))
PROPER(negrecip(z0)) → c60(NEGRECIP(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c62(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(rcons(z0, z1)) → c64(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))

K tuples:none
Defined Rule Symbols:

active, s, posrecip, negrecip, cons, rcons, from, 2ndspos, 2ndsneg, pi, plus, times, square, proper, top

Defined Pair Symbols:

ACTIVE, S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP

Compound Symbols:

c2, c4, 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, c58, c59, c60, c62, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73, c, c5, c7, c9

(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, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(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(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))
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(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)) → c10(TIMES(z0, z0))
ACTIVE(s(z0)) → c11(S(active(z0)), ACTIVE(z0))
ACTIVE(posrecip(z0)) → c12(POSRECIP(active(z0)), ACTIVE(z0))
ACTIVE(negrecip(z0)) → c13(NEGRECIP(active(z0)), ACTIVE(z0))
ACTIVE(cons(z0, z1)) → c14(CONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(from(z0)) → c17(FROM(active(z0)), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(pi(z0)) → c22(PI(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
ACTIVE(square(z0)) → c27(SQUARE(active(z0)), ACTIVE(z0))
S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))
PROPER(s(z0)) → c58(S(proper(z0)), PROPER(z0))
PROPER(posrecip(z0)) → c59(POSRECIP(proper(z0)), PROPER(z0))
PROPER(negrecip(z0)) → c60(NEGRECIP(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c62(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(rcons(z0, z1)) → c64(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))

S tuples:

ACTIVE(square(z0)) → c10(TIMES(z0, z0))
ACTIVE(s(z0)) → c11(S(active(z0)), ACTIVE(z0))
ACTIVE(posrecip(z0)) → c12(POSRECIP(active(z0)), ACTIVE(z0))
ACTIVE(negrecip(z0)) → c13(NEGRECIP(active(z0)), ACTIVE(z0))
ACTIVE(cons(z0, z1)) → c14(CONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(from(z0)) → c17(FROM(active(z0)), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(pi(z0)) → c22(PI(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
ACTIVE(square(z0)) → c27(SQUARE(active(z0)), ACTIVE(z0))
S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))
PROPER(s(z0)) → c58(S(proper(z0)), PROPER(z0))
PROPER(posrecip(z0)) → c59(POSRECIP(proper(z0)), PROPER(z0))
PROPER(negrecip(z0)) → c60(NEGRECIP(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c62(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(rcons(z0, z1)) → c64(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))

K tuples:none
Defined Rule Symbols:

active, s, posrecip, negrecip, cons, rcons, from, 2ndspos, 2ndsneg, pi, plus, times, square, proper, top

Defined Pair Symbols:

ACTIVE, S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP

Compound Symbols:

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, c58, c59, c60, c62, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73, c, c5, c7, c9, 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, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(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(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))
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))
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))
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(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)) → c10(TIMES(z0, z0))
ACTIVE(s(z0)) → c11(S(active(z0)), ACTIVE(z0))
ACTIVE(posrecip(z0)) → c12(POSRECIP(active(z0)), ACTIVE(z0))
ACTIVE(negrecip(z0)) → c13(NEGRECIP(active(z0)), ACTIVE(z0))
ACTIVE(cons(z0, z1)) → c14(CONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(from(z0)) → c17(FROM(active(z0)), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(pi(z0)) → c22(PI(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
ACTIVE(square(z0)) → c27(SQUARE(active(z0)), ACTIVE(z0))
S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))
PROPER(s(z0)) → c58(S(proper(z0)), PROPER(z0))
PROPER(posrecip(z0)) → c59(POSRECIP(proper(z0)), PROPER(z0))
PROPER(negrecip(z0)) → c60(NEGRECIP(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c62(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(rcons(z0, z1)) → c64(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))

S tuples:

ACTIVE(square(z0)) → c10(TIMES(z0, z0))
ACTIVE(s(z0)) → c11(S(active(z0)), ACTIVE(z0))
ACTIVE(posrecip(z0)) → c12(POSRECIP(active(z0)), ACTIVE(z0))
ACTIVE(negrecip(z0)) → c13(NEGRECIP(active(z0)), ACTIVE(z0))
ACTIVE(cons(z0, z1)) → c14(CONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(from(z0)) → c17(FROM(active(z0)), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(pi(z0)) → c22(PI(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
ACTIVE(square(z0)) → c27(SQUARE(active(z0)), ACTIVE(z0))
S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))
PROPER(s(z0)) → c58(S(proper(z0)), PROPER(z0))
PROPER(posrecip(z0)) → c59(POSRECIP(proper(z0)), PROPER(z0))
PROPER(negrecip(z0)) → c60(NEGRECIP(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c62(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(rcons(z0, z1)) → c64(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))

K tuples:none
Defined Rule Symbols:

active, rcons, posrecip, 2ndsneg, negrecip, 2ndspos, s, cons, from, pi, plus, times, square, proper

Defined Pair Symbols:

ACTIVE, S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP

Compound Symbols:

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, c58, c59, c60, c62, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73, c, c5, c7, c9, c1

(11) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

Use narrowing to replace ACTIVE(s(z0)) → c11(S(active(z0)), ACTIVE(z0)) by

ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c11(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, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(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(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))
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))
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))
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(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)) → c10(TIMES(z0, z0))
ACTIVE(posrecip(z0)) → c12(POSRECIP(active(z0)), ACTIVE(z0))
ACTIVE(negrecip(z0)) → c13(NEGRECIP(active(z0)), ACTIVE(z0))
ACTIVE(cons(z0, z1)) → c14(CONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(from(z0)) → c17(FROM(active(z0)), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(pi(z0)) → c22(PI(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
ACTIVE(square(z0)) → c27(SQUARE(active(z0)), ACTIVE(z0))
S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))
PROPER(s(z0)) → c58(S(proper(z0)), PROPER(z0))
PROPER(posrecip(z0)) → c59(POSRECIP(proper(z0)), PROPER(z0))
PROPER(negrecip(z0)) → c60(NEGRECIP(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c62(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(rcons(z0, z1)) → c64(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))

S tuples:

ACTIVE(square(z0)) → c10(TIMES(z0, z0))
ACTIVE(posrecip(z0)) → c12(POSRECIP(active(z0)), ACTIVE(z0))
ACTIVE(negrecip(z0)) → c13(NEGRECIP(active(z0)), ACTIVE(z0))
ACTIVE(cons(z0, z1)) → c14(CONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(from(z0)) → c17(FROM(active(z0)), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(pi(z0)) → c22(PI(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
ACTIVE(square(z0)) → c27(SQUARE(active(z0)), ACTIVE(z0))
S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))
PROPER(s(z0)) → c58(S(proper(z0)), PROPER(z0))
PROPER(posrecip(z0)) → c59(POSRECIP(proper(z0)), PROPER(z0))
PROPER(negrecip(z0)) → c60(NEGRECIP(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c62(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(rcons(z0, z1)) → c64(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))

K tuples:none
Defined Rule Symbols:

active, rcons, posrecip, 2ndsneg, negrecip, 2ndspos, s, cons, from, pi, plus, times, square, proper

Defined Pair Symbols:

ACTIVE, S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP

Compound Symbols:

c10, 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, c58, c59, c60, c62, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73, c, c5, c7, c9, c1, c11

(13) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

Use narrowing to replace ACTIVE(posrecip(z0)) → c12(POSRECIP(active(z0)), ACTIVE(z0)) by

ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c12(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, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(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(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))
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))
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))
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(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)) → c10(TIMES(z0, z0))
ACTIVE(negrecip(z0)) → c13(NEGRECIP(active(z0)), ACTIVE(z0))
ACTIVE(cons(z0, z1)) → c14(CONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(from(z0)) → c17(FROM(active(z0)), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(pi(z0)) → c22(PI(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
ACTIVE(square(z0)) → c27(SQUARE(active(z0)), ACTIVE(z0))
S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))
PROPER(s(z0)) → c58(S(proper(z0)), PROPER(z0))
PROPER(posrecip(z0)) → c59(POSRECIP(proper(z0)), PROPER(z0))
PROPER(negrecip(z0)) → c60(NEGRECIP(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c62(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(rcons(z0, z1)) → c64(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))

S tuples:

ACTIVE(square(z0)) → c10(TIMES(z0, z0))
ACTIVE(negrecip(z0)) → c13(NEGRECIP(active(z0)), ACTIVE(z0))
ACTIVE(cons(z0, z1)) → c14(CONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(from(z0)) → c17(FROM(active(z0)), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(pi(z0)) → c22(PI(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
ACTIVE(square(z0)) → c27(SQUARE(active(z0)), ACTIVE(z0))
S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))
PROPER(s(z0)) → c58(S(proper(z0)), PROPER(z0))
PROPER(posrecip(z0)) → c59(POSRECIP(proper(z0)), PROPER(z0))
PROPER(negrecip(z0)) → c60(NEGRECIP(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c62(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(rcons(z0, z1)) → c64(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))

K tuples:none
Defined Rule Symbols:

active, rcons, posrecip, 2ndsneg, negrecip, 2ndspos, s, cons, from, pi, plus, times, square, proper

Defined Pair Symbols:

ACTIVE, S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP

Compound Symbols:

c10, 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, c58, c59, c60, c62, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73, c, c5, c7, c9, c1, c11, c12

(15) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

Use narrowing to replace ACTIVE(negrecip(z0)) → c13(NEGRECIP(active(z0)), ACTIVE(z0)) by

ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c13(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, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(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(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))
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))
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))
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(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)) → c10(TIMES(z0, z0))
ACTIVE(cons(z0, z1)) → c14(CONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(from(z0)) → c17(FROM(active(z0)), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(pi(z0)) → c22(PI(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
ACTIVE(square(z0)) → c27(SQUARE(active(z0)), ACTIVE(z0))
S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))
PROPER(s(z0)) → c58(S(proper(z0)), PROPER(z0))
PROPER(posrecip(z0)) → c59(POSRECIP(proper(z0)), PROPER(z0))
PROPER(negrecip(z0)) → c60(NEGRECIP(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c62(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(rcons(z0, z1)) → c64(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))

S tuples:

ACTIVE(square(z0)) → c10(TIMES(z0, z0))
ACTIVE(cons(z0, z1)) → c14(CONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(from(z0)) → c17(FROM(active(z0)), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(pi(z0)) → c22(PI(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
ACTIVE(square(z0)) → c27(SQUARE(active(z0)), ACTIVE(z0))
S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))
PROPER(s(z0)) → c58(S(proper(z0)), PROPER(z0))
PROPER(posrecip(z0)) → c59(POSRECIP(proper(z0)), PROPER(z0))
PROPER(negrecip(z0)) → c60(NEGRECIP(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c62(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(rcons(z0, z1)) → c64(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))

K tuples:none
Defined Rule Symbols:

active, rcons, posrecip, 2ndsneg, negrecip, 2ndspos, s, cons, from, pi, plus, times, square, proper

Defined Pair Symbols:

ACTIVE, S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP

Compound Symbols:

c10, 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, c58, c59, c60, c62, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73, c, c5, c7, c9, c1, c11, c12, c13

(17) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

Use narrowing to replace ACTIVE(cons(z0, z1)) → c14(CONS(active(z0), z1), ACTIVE(z0)) by

ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c14(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, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(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(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))
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))
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))
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(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)) → c10(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(from(z0)) → c17(FROM(active(z0)), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(pi(z0)) → c22(PI(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
ACTIVE(square(z0)) → c27(SQUARE(active(z0)), ACTIVE(z0))
S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))
PROPER(s(z0)) → c58(S(proper(z0)), PROPER(z0))
PROPER(posrecip(z0)) → c59(POSRECIP(proper(z0)), PROPER(z0))
PROPER(negrecip(z0)) → c60(NEGRECIP(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c62(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(rcons(z0, z1)) → c64(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))

S tuples:

ACTIVE(square(z0)) → c10(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(from(z0)) → c17(FROM(active(z0)), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(pi(z0)) → c22(PI(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
ACTIVE(square(z0)) → c27(SQUARE(active(z0)), ACTIVE(z0))
S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))
PROPER(s(z0)) → c58(S(proper(z0)), PROPER(z0))
PROPER(posrecip(z0)) → c59(POSRECIP(proper(z0)), PROPER(z0))
PROPER(negrecip(z0)) → c60(NEGRECIP(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c62(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(rcons(z0, z1)) → c64(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))

K tuples:none
Defined Rule Symbols:

active, rcons, posrecip, 2ndsneg, negrecip, 2ndspos, s, cons, from, pi, plus, times, square, proper

Defined Pair Symbols:

ACTIVE, S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP

Compound Symbols:

c10, 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, c58, c59, c60, c62, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73, c, c5, c7, c9, c1, c11, c12, c13, c14

(19) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

Use narrowing to replace ACTIVE(from(z0)) → c17(FROM(active(z0)), ACTIVE(z0)) by

ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c17(FROM(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, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(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(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))
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))
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))
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(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)) → c10(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(pi(z0)) → c22(PI(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
ACTIVE(square(z0)) → c27(SQUARE(active(z0)), ACTIVE(z0))
S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))
PROPER(s(z0)) → c58(S(proper(z0)), PROPER(z0))
PROPER(posrecip(z0)) → c59(POSRECIP(proper(z0)), PROPER(z0))
PROPER(negrecip(z0)) → c60(NEGRECIP(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c62(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(rcons(z0, z1)) → c64(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))

S tuples:

ACTIVE(square(z0)) → c10(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(pi(z0)) → c22(PI(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
ACTIVE(square(z0)) → c27(SQUARE(active(z0)), ACTIVE(z0))
S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))
PROPER(s(z0)) → c58(S(proper(z0)), PROPER(z0))
PROPER(posrecip(z0)) → c59(POSRECIP(proper(z0)), PROPER(z0))
PROPER(negrecip(z0)) → c60(NEGRECIP(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c62(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(rcons(z0, z1)) → c64(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))

K tuples:none
Defined Rule Symbols:

active, rcons, posrecip, 2ndsneg, negrecip, 2ndspos, s, cons, from, pi, plus, times, square, proper

Defined Pair Symbols:

ACTIVE, S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP

Compound Symbols:

c10, c15, c16, 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, c58, c59, c60, c62, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73, c, c5, c7, c9, c1, c11, c12, c13, c14, c17

(21) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

Use narrowing to replace ACTIVE(pi(z0)) → c22(PI(active(z0)), ACTIVE(z0)) by

ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c22(PI(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, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(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(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))
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))
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))
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(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)) → c10(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
ACTIVE(square(z0)) → c27(SQUARE(active(z0)), ACTIVE(z0))
S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))
PROPER(s(z0)) → c58(S(proper(z0)), PROPER(z0))
PROPER(posrecip(z0)) → c59(POSRECIP(proper(z0)), PROPER(z0))
PROPER(negrecip(z0)) → c60(NEGRECIP(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c62(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(rcons(z0, z1)) → c64(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))

S tuples:

ACTIVE(square(z0)) → c10(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
ACTIVE(square(z0)) → c27(SQUARE(active(z0)), ACTIVE(z0))
S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))
PROPER(s(z0)) → c58(S(proper(z0)), PROPER(z0))
PROPER(posrecip(z0)) → c59(POSRECIP(proper(z0)), PROPER(z0))
PROPER(negrecip(z0)) → c60(NEGRECIP(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c62(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(rcons(z0, z1)) → c64(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))

K tuples:none
Defined Rule Symbols:

active, rcons, posrecip, 2ndsneg, negrecip, 2ndspos, s, cons, from, pi, plus, times, square, proper

Defined Pair Symbols:

ACTIVE, S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP

Compound Symbols:

c10, c15, c16, c18, c19, c20, c21, 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, c58, c59, c60, c62, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73, c, c5, c7, c9, c1, c11, c12, c13, c14, c17, c22

(23) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

Use narrowing to replace ACTIVE(square(z0)) → c27(SQUARE(active(z0)), ACTIVE(z0)) by

ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(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, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(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(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))
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))
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))
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(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)) → c10(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))
PROPER(s(z0)) → c58(S(proper(z0)), PROPER(z0))
PROPER(posrecip(z0)) → c59(POSRECIP(proper(z0)), PROPER(z0))
PROPER(negrecip(z0)) → c60(NEGRECIP(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c62(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(rcons(z0, z1)) → c64(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))

S tuples:

ACTIVE(square(z0)) → c10(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))
PROPER(s(z0)) → c58(S(proper(z0)), PROPER(z0))
PROPER(posrecip(z0)) → c59(POSRECIP(proper(z0)), PROPER(z0))
PROPER(negrecip(z0)) → c60(NEGRECIP(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c62(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(rcons(z0, z1)) → c64(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))

K tuples:none
Defined Rule Symbols:

active, rcons, posrecip, 2ndsneg, negrecip, 2ndspos, s, cons, from, pi, plus, times, square, proper

Defined Pair Symbols:

ACTIVE, S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP

Compound Symbols:

c10, c15, c16, c18, c19, c20, c21, c23, c24, c25, c26, 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, c58, c59, c60, c62, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73, c, c5, c7, c9, c1, c11, c12, c13, c14, c17, c22, c27

(25) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

Use narrowing to replace PROPER(s(z0)) → c58(S(proper(z0)), PROPER(z0)) by

PROPER(s(0)) → c58(S(ok(0)), PROPER(0))
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(nil)) → c58(S(ok(nil)), PROPER(nil))
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(rnil)) → c58(S(ok(rnil)), PROPER(rnil))
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(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, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(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(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))
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))
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))
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(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)) → c10(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))
PROPER(posrecip(z0)) → c59(POSRECIP(proper(z0)), PROPER(z0))
PROPER(negrecip(z0)) → c60(NEGRECIP(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c62(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(rcons(z0, z1)) → c64(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(0)) → c58(S(ok(0)), PROPER(0))
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(nil)) → c58(S(ok(nil)), PROPER(nil))
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(rnil)) → c58(S(ok(rnil)), PROPER(rnil))
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))

S tuples:

ACTIVE(square(z0)) → c10(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))
PROPER(posrecip(z0)) → c59(POSRECIP(proper(z0)), PROPER(z0))
PROPER(negrecip(z0)) → c60(NEGRECIP(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c62(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(rcons(z0, z1)) → c64(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(0)) → c58(S(ok(0)), PROPER(0))
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(nil)) → c58(S(ok(nil)), PROPER(nil))
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(rnil)) → c58(S(ok(rnil)), PROPER(rnil))
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))

K tuples:none
Defined Rule Symbols:

active, rcons, posrecip, 2ndsneg, negrecip, 2ndspos, s, cons, from, pi, plus, times, square, proper

Defined Pair Symbols:

ACTIVE, S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP

Compound Symbols:

c10, c15, c16, c18, c19, c20, c21, c23, c24, c25, c26, 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, c59, c60, c62, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73, c, c5, c7, c9, c1, c11, c12, c13, c14, c17, c22, c27, c58

(27) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)

Removed 3 trailing tuple parts

(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, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(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(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))
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))
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))
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(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)) → c10(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))
PROPER(posrecip(z0)) → c59(POSRECIP(proper(z0)), PROPER(z0))
PROPER(negrecip(z0)) → c60(NEGRECIP(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c62(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(rcons(z0, z1)) → c64(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c58(S(ok(0)))
PROPER(s(nil)) → c58(S(ok(nil)))
PROPER(s(rnil)) → c58(S(ok(rnil)))

S tuples:

ACTIVE(square(z0)) → c10(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))
PROPER(posrecip(z0)) → c59(POSRECIP(proper(z0)), PROPER(z0))
PROPER(negrecip(z0)) → c60(NEGRECIP(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c62(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(rcons(z0, z1)) → c64(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c58(S(ok(0)))
PROPER(s(nil)) → c58(S(ok(nil)))
PROPER(s(rnil)) → c58(S(ok(rnil)))

K tuples:none
Defined Rule Symbols:

active, rcons, posrecip, 2ndsneg, negrecip, 2ndspos, s, cons, from, pi, plus, times, square, proper

Defined Pair Symbols:

ACTIVE, S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP

Compound Symbols:

c10, c15, c16, c18, c19, c20, c21, c23, c24, c25, c26, 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, c59, c60, c62, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73, c, c5, c7, c9, c1, c11, c12, c13, c14, c17, c22, c27, c58, c58

(29) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

Use narrowing to replace PROPER(posrecip(z0)) → c59(POSRECIP(proper(z0)), PROPER(z0)) by

PROPER(posrecip(0)) → c59(POSRECIP(ok(0)), PROPER(0))
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)), PROPER(nil))
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)), PROPER(rnil))
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))

(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, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(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(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))
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))
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))
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(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)) → c10(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))
PROPER(negrecip(z0)) → c60(NEGRECIP(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c62(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(rcons(z0, z1)) → c64(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c58(S(ok(0)))
PROPER(s(nil)) → c58(S(ok(nil)))
PROPER(s(rnil)) → c58(S(ok(rnil)))
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)), PROPER(0))
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)), PROPER(nil))
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)), PROPER(rnil))
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))

S tuples:

ACTIVE(square(z0)) → c10(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))
PROPER(negrecip(z0)) → c60(NEGRECIP(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c62(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(rcons(z0, z1)) → c64(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c58(S(ok(0)))
PROPER(s(nil)) → c58(S(ok(nil)))
PROPER(s(rnil)) → c58(S(ok(rnil)))
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)), PROPER(0))
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)), PROPER(nil))
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)), PROPER(rnil))
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))

K tuples:none
Defined Rule Symbols:

active, rcons, posrecip, 2ndsneg, negrecip, 2ndspos, s, cons, from, pi, plus, times, square, proper

Defined Pair Symbols:

ACTIVE, S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP

Compound Symbols:

c10, c15, c16, c18, c19, c20, c21, c23, c24, c25, c26, 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, c60, c62, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73, c, c5, c7, c9, c1, c11, c12, c13, c14, c17, c22, c27, c58, c58, c59

(31) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)

Removed 3 trailing tuple parts

(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, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(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(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))
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))
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))
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(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)) → c10(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))
PROPER(negrecip(z0)) → c60(NEGRECIP(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c62(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(rcons(z0, z1)) → c64(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c58(S(ok(0)))
PROPER(s(nil)) → c58(S(ok(nil)))
PROPER(s(rnil)) → c58(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))

S tuples:

ACTIVE(square(z0)) → c10(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))
PROPER(negrecip(z0)) → c60(NEGRECIP(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c62(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(rcons(z0, z1)) → c64(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c58(S(ok(0)))
PROPER(s(nil)) → c58(S(ok(nil)))
PROPER(s(rnil)) → c58(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))

K tuples:none
Defined Rule Symbols:

active, rcons, posrecip, 2ndsneg, negrecip, 2ndspos, s, cons, from, pi, plus, times, square, proper

Defined Pair Symbols:

ACTIVE, S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP

Compound Symbols:

c10, c15, c16, c18, c19, c20, c21, c23, c24, c25, c26, 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, c60, c62, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73, c, c5, c7, c9, c1, c11, c12, c13, c14, c17, c22, c27, c58, c58, c59, c59

(33) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

Use narrowing to replace PROPER(negrecip(z0)) → c60(NEGRECIP(proper(z0)), PROPER(z0)) by

PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)), PROPER(0))
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)), PROPER(nil))
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)), PROPER(rnil))
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))

(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, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(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(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))
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))
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))
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(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)) → c10(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))
PROPER(cons(z0, z1)) → c62(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(rcons(z0, z1)) → c64(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c58(S(ok(0)))
PROPER(s(nil)) → c58(S(ok(nil)))
PROPER(s(rnil)) → c58(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)), PROPER(0))
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)), PROPER(nil))
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)), PROPER(rnil))
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))

S tuples:

ACTIVE(square(z0)) → c10(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))
PROPER(cons(z0, z1)) → c62(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(rcons(z0, z1)) → c64(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c58(S(ok(0)))
PROPER(s(nil)) → c58(S(ok(nil)))
PROPER(s(rnil)) → c58(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)), PROPER(0))
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)), PROPER(nil))
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)), PROPER(rnil))
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))

K tuples:none
Defined Rule Symbols:

active, rcons, posrecip, 2ndsneg, negrecip, 2ndspos, s, cons, from, pi, plus, times, square, proper

Defined Pair Symbols:

ACTIVE, S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP

Compound Symbols:

c10, c15, c16, c18, c19, c20, c21, c23, c24, c25, c26, 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, c62, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73, c, c5, c7, c9, c1, c11, c12, c13, c14, c17, c22, c27, c58, c58, c59, c59, c60

(35) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)

Removed 3 trailing tuple parts

(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, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(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(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))
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))
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))
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(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)) → c10(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))
PROPER(cons(z0, z1)) → c62(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(rcons(z0, z1)) → c64(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c58(S(ok(0)))
PROPER(s(nil)) → c58(S(ok(nil)))
PROPER(s(rnil)) → c58(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))

S tuples:

ACTIVE(square(z0)) → c10(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))
PROPER(cons(z0, z1)) → c62(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(rcons(z0, z1)) → c64(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c58(S(ok(0)))
PROPER(s(nil)) → c58(S(ok(nil)))
PROPER(s(rnil)) → c58(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))

K tuples:none
Defined Rule Symbols:

active, rcons, posrecip, 2ndsneg, negrecip, 2ndspos, s, cons, from, pi, plus, times, square, proper

Defined Pair Symbols:

ACTIVE, S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP

Compound Symbols:

c10, c15, c16, c18, c19, c20, c21, c23, c24, c25, c26, 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, c62, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73, c, c5, c7, c9, c1, c11, c12, c13, c14, c17, c22, c27, c58, c58, c59, c59, c60, c60

(37) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

Use narrowing to replace PROPER(cons(z0, z1)) → c62(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) by

PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0), PROPER(0))
PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0), PROPER(rnil))
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(0), PROPER(x1))
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(rnil), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))

(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, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(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(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))
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))
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))
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(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)) → c10(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))
PROPER(rcons(z0, z1)) → c64(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c58(S(ok(0)))
PROPER(s(nil)) → c58(S(ok(nil)))
PROPER(s(rnil)) → c58(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0), PROPER(0))
PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0), PROPER(rnil))
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(0), PROPER(x1))
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(rnil), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))

S tuples:

ACTIVE(square(z0)) → c10(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))
PROPER(rcons(z0, z1)) → c64(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c58(S(ok(0)))
PROPER(s(nil)) → c58(S(ok(nil)))
PROPER(s(rnil)) → c58(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0), PROPER(0))
PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0), PROPER(rnil))
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(0), PROPER(x1))
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(rnil), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))

K tuples:none
Defined Rule Symbols:

active, rcons, posrecip, 2ndsneg, negrecip, 2ndspos, s, cons, from, pi, plus, times, square, proper

Defined Pair Symbols:

ACTIVE, S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP

Compound Symbols:

c10, c15, c16, c18, c19, c20, c21, c23, c24, c25, c26, 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, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73, c, c5, c7, c9, c1, c11, c12, c13, c14, c17, c22, c27, c58, c58, c59, c59, c60, c60, c62

(39) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)

Removed 6 trailing tuple parts

(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, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(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(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))
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))
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))
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(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)) → c10(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))
PROPER(rcons(z0, z1)) → c64(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c58(S(ok(0)))
PROPER(s(nil)) → c58(S(ok(nil)))
PROPER(s(rnil)) → c58(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))

S tuples:

ACTIVE(square(z0)) → c10(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))
PROPER(rcons(z0, z1)) → c64(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c58(S(ok(0)))
PROPER(s(nil)) → c58(S(ok(nil)))
PROPER(s(rnil)) → c58(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))

K tuples:none
Defined Rule Symbols:

active, rcons, posrecip, 2ndsneg, negrecip, 2ndspos, s, cons, from, pi, plus, times, square, proper

Defined Pair Symbols:

ACTIVE, S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP

Compound Symbols:

c10, c15, c16, c18, c19, c20, c21, c23, c24, c25, c26, 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, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73, c, c5, c7, c9, c1, c11, c12, c13, c14, c17, c22, c27, c58, c58, c59, c59, c60, c60, c62, c62

(41) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

Use narrowing to replace PROPER(rcons(z0, z1)) → c64(RCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) by

PROPER(rcons(x0, 0)) → c64(RCONS(proper(x0), ok(0)), PROPER(x0), PROPER(0))
PROPER(rcons(x0, s(z0))) → c64(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c64(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c64(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, nil)) → c64(RCONS(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
PROPER(rcons(x0, cons(z0, z1))) → c64(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, rnil)) → c64(RCONS(proper(x0), ok(rnil)), PROPER(x0), PROPER(rnil))
PROPER(rcons(x0, rcons(z0, z1))) → c64(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c64(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c64(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c64(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c64(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c64(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c64(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c64(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(0, x1)) → c64(RCONS(ok(0), proper(x1)), PROPER(0), PROPER(x1))
PROPER(rcons(s(z0), x1)) → c64(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c64(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c64(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(nil, x1)) → c64(RCONS(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c64(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c64(RCONS(ok(rnil), proper(x1)), PROPER(rnil), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c64(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c64(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c64(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c64(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c64(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c64(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c64(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c64(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))

(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, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(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(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))
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))
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))
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(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)) → c10(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))
PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c58(S(ok(0)))
PROPER(s(nil)) → c58(S(ok(nil)))
PROPER(s(rnil)) → c58(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(rcons(x0, 0)) → c64(RCONS(proper(x0), ok(0)), PROPER(x0), PROPER(0))
PROPER(rcons(x0, s(z0))) → c64(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c64(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c64(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, nil)) → c64(RCONS(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
PROPER(rcons(x0, cons(z0, z1))) → c64(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, rnil)) → c64(RCONS(proper(x0), ok(rnil)), PROPER(x0), PROPER(rnil))
PROPER(rcons(x0, rcons(z0, z1))) → c64(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c64(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c64(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c64(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c64(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c64(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c64(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c64(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(0, x1)) → c64(RCONS(ok(0), proper(x1)), PROPER(0), PROPER(x1))
PROPER(rcons(s(z0), x1)) → c64(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c64(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c64(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(nil, x1)) → c64(RCONS(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c64(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c64(RCONS(ok(rnil), proper(x1)), PROPER(rnil), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c64(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c64(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c64(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c64(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c64(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c64(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c64(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c64(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))

S tuples:

ACTIVE(square(z0)) → c10(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))
PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c58(S(ok(0)))
PROPER(s(nil)) → c58(S(ok(nil)))
PROPER(s(rnil)) → c58(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(rcons(x0, 0)) → c64(RCONS(proper(x0), ok(0)), PROPER(x0), PROPER(0))
PROPER(rcons(x0, s(z0))) → c64(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c64(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c64(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, nil)) → c64(RCONS(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
PROPER(rcons(x0, cons(z0, z1))) → c64(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, rnil)) → c64(RCONS(proper(x0), ok(rnil)), PROPER(x0), PROPER(rnil))
PROPER(rcons(x0, rcons(z0, z1))) → c64(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c64(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c64(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c64(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c64(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c64(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c64(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c64(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(0, x1)) → c64(RCONS(ok(0), proper(x1)), PROPER(0), PROPER(x1))
PROPER(rcons(s(z0), x1)) → c64(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c64(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c64(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(nil, x1)) → c64(RCONS(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c64(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c64(RCONS(ok(rnil), proper(x1)), PROPER(rnil), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c64(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c64(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c64(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c64(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c64(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c64(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c64(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c64(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))

K tuples:none
Defined Rule Symbols:

active, rcons, posrecip, 2ndsneg, negrecip, 2ndspos, s, cons, from, pi, plus, times, square, proper

Defined Pair Symbols:

ACTIVE, S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP

Compound Symbols:

c10, c15, c16, c18, c19, c20, c21, c23, c24, c25, c26, 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, c65, c66, c67, c68, c69, c70, c71, c72, c73, c, c5, c7, c9, c1, c11, c12, c13, c14, c17, c22, c27, c58, c58, c59, c59, c60, c60, c62, c62, c64

(43) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)

Removed 6 trailing tuple parts

(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, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(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(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))
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))
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))
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(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)) → c10(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))
PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c58(S(ok(0)))
PROPER(s(nil)) → c58(S(ok(nil)))
PROPER(s(rnil)) → c58(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(rcons(x0, s(z0))) → c64(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c64(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c64(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, cons(z0, z1))) → c64(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, rcons(z0, z1))) → c64(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c64(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c64(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c64(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c64(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c64(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c64(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c64(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(s(z0), x1)) → c64(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c64(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c64(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c64(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c64(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c64(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c64(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c64(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c64(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c64(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c64(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c64(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(rcons(x0, 0)) → c64(RCONS(proper(x0), ok(0)), PROPER(x0))
PROPER(rcons(x0, nil)) → c64(RCONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(rcons(x0, rnil)) → c64(RCONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(rcons(0, x1)) → c64(RCONS(ok(0), proper(x1)), PROPER(x1))
PROPER(rcons(nil, x1)) → c64(RCONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c64(RCONS(ok(rnil), proper(x1)), PROPER(x1))

S tuples:

ACTIVE(square(z0)) → c10(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))
PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0))
PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c58(S(ok(0)))
PROPER(s(nil)) → c58(S(ok(nil)))
PROPER(s(rnil)) → c58(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(rcons(x0, s(z0))) → c64(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c64(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c64(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, cons(z0, z1))) → c64(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, rcons(z0, z1))) → c64(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c64(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c64(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c64(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c64(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c64(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c64(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c64(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(s(z0), x1)) → c64(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c64(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c64(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c64(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c64(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c64(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c64(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c64(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c64(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c64(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c64(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c64(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(rcons(x0, 0)) → c64(RCONS(proper(x0), ok(0)), PROPER(x0))
PROPER(rcons(x0, nil)) → c64(RCONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(rcons(x0, rnil)) → c64(RCONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(rcons(0, x1)) → c64(RCONS(ok(0), proper(x1)), PROPER(x1))
PROPER(rcons(nil, x1)) → c64(RCONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c64(RCONS(ok(rnil), proper(x1)), PROPER(x1))

K tuples:none
Defined Rule Symbols:

active, rcons, posrecip, 2ndsneg, negrecip, 2ndspos, s, cons, from, pi, plus, times, square, proper

Defined Pair Symbols:

ACTIVE, S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP

Compound Symbols:

c10, c15, c16, c18, c19, c20, c21, c23, c24, c25, c26, 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, c65, c66, c67, c68, c69, c70, c71, c72, c73, c, c5, c7, c9, c1, c11, c12, c13, c14, c17, c22, c27, c58, c58, c59, c59, c60, c60, c62, c62, c64, c64

(45) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

Use narrowing to replace PROPER(from(z0)) → c65(FROM(proper(z0)), PROPER(z0)) by

PROPER(from(0)) → c65(FROM(ok(0)), PROPER(0))
PROPER(from(s(z0))) → c65(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(posrecip(z0))) → c65(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(from(negrecip(z0))) → c65(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(from(nil)) → c65(FROM(ok(nil)), PROPER(nil))
PROPER(from(cons(z0, z1))) → c65(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(rnil)) → c65(FROM(ok(rnil)), PROPER(rnil))
PROPER(from(rcons(z0, z1))) → c65(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(from(from(z0))) → c65(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(2ndspos(z0, z1))) → c65(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(from(2ndsneg(z0, z1))) → c65(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(from(pi(z0))) → c65(FROM(pi(proper(z0))), PROPER(pi(z0)))
PROPER(from(plus(z0, z1))) → c65(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(from(times(z0, z1))) → c65(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(from(square(z0))) → c65(FROM(square(proper(z0))), PROPER(square(z0)))

(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, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(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(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))
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))
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))
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(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)) → c10(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))
PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c58(S(ok(0)))
PROPER(s(nil)) → c58(S(ok(nil)))
PROPER(s(rnil)) → c58(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(rcons(x0, s(z0))) → c64(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c64(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c64(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, cons(z0, z1))) → c64(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, rcons(z0, z1))) → c64(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c64(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c64(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c64(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c64(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c64(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c64(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c64(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(s(z0), x1)) → c64(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c64(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c64(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c64(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c64(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c64(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c64(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c64(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c64(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c64(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c64(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c64(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(rcons(x0, 0)) → c64(RCONS(proper(x0), ok(0)), PROPER(x0))
PROPER(rcons(x0, nil)) → c64(RCONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(rcons(x0, rnil)) → c64(RCONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(rcons(0, x1)) → c64(RCONS(ok(0), proper(x1)), PROPER(x1))
PROPER(rcons(nil, x1)) → c64(RCONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c64(RCONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(from(0)) → c65(FROM(ok(0)), PROPER(0))
PROPER(from(s(z0))) → c65(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(posrecip(z0))) → c65(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(from(negrecip(z0))) → c65(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(from(nil)) → c65(FROM(ok(nil)), PROPER(nil))
PROPER(from(cons(z0, z1))) → c65(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(rnil)) → c65(FROM(ok(rnil)), PROPER(rnil))
PROPER(from(rcons(z0, z1))) → c65(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(from(from(z0))) → c65(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(2ndspos(z0, z1))) → c65(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(from(2ndsneg(z0, z1))) → c65(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(from(pi(z0))) → c65(FROM(pi(proper(z0))), PROPER(pi(z0)))
PROPER(from(plus(z0, z1))) → c65(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(from(times(z0, z1))) → c65(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(from(square(z0))) → c65(FROM(square(proper(z0))), PROPER(square(z0)))

S tuples:

ACTIVE(square(z0)) → c10(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))
PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c58(S(ok(0)))
PROPER(s(nil)) → c58(S(ok(nil)))
PROPER(s(rnil)) → c58(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(rcons(x0, s(z0))) → c64(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c64(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c64(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, cons(z0, z1))) → c64(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, rcons(z0, z1))) → c64(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c64(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c64(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c64(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c64(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c64(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c64(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c64(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(s(z0), x1)) → c64(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c64(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c64(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c64(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c64(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c64(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c64(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c64(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c64(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c64(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c64(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c64(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(rcons(x0, 0)) → c64(RCONS(proper(x0), ok(0)), PROPER(x0))
PROPER(rcons(x0, nil)) → c64(RCONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(rcons(x0, rnil)) → c64(RCONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(rcons(0, x1)) → c64(RCONS(ok(0), proper(x1)), PROPER(x1))
PROPER(rcons(nil, x1)) → c64(RCONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c64(RCONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(from(0)) → c65(FROM(ok(0)), PROPER(0))
PROPER(from(s(z0))) → c65(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(posrecip(z0))) → c65(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(from(negrecip(z0))) → c65(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(from(nil)) → c65(FROM(ok(nil)), PROPER(nil))
PROPER(from(cons(z0, z1))) → c65(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(rnil)) → c65(FROM(ok(rnil)), PROPER(rnil))
PROPER(from(rcons(z0, z1))) → c65(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(from(from(z0))) → c65(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(2ndspos(z0, z1))) → c65(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(from(2ndsneg(z0, z1))) → c65(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(from(pi(z0))) → c65(FROM(pi(proper(z0))), PROPER(pi(z0)))
PROPER(from(plus(z0, z1))) → c65(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(from(times(z0, z1))) → c65(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(from(square(z0))) → c65(FROM(square(proper(z0))), PROPER(square(z0)))

K tuples:none
Defined Rule Symbols:

active, rcons, posrecip, 2ndsneg, negrecip, 2ndspos, s, cons, from, pi, plus, times, square, proper

Defined Pair Symbols:

ACTIVE, S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP

Compound Symbols:

c10, c15, c16, c18, c19, c20, c21, c23, c24, c25, c26, 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, c66, c67, c68, c69, c70, c71, c72, c73, c, c5, c7, c9, c1, c11, c12, c13, c14, c17, c22, c27, c58, c58, c59, c59, c60, c60, c62, c62, c64, c64, c65

(47) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)

Removed 3 trailing tuple parts

(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, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(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(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))
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))
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))
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(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)) → c10(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))
PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c58(S(ok(0)))
PROPER(s(nil)) → c58(S(ok(nil)))
PROPER(s(rnil)) → c58(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(rcons(x0, s(z0))) → c64(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c64(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c64(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, cons(z0, z1))) → c64(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, rcons(z0, z1))) → c64(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c64(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c64(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c64(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c64(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c64(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c64(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c64(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(s(z0), x1)) → c64(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c64(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c64(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c64(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c64(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c64(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c64(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c64(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c64(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c64(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c64(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c64(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(rcons(x0, 0)) → c64(RCONS(proper(x0), ok(0)), PROPER(x0))
PROPER(rcons(x0, nil)) → c64(RCONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(rcons(x0, rnil)) → c64(RCONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(rcons(0, x1)) → c64(RCONS(ok(0), proper(x1)), PROPER(x1))
PROPER(rcons(nil, x1)) → c64(RCONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c64(RCONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(from(s(z0))) → c65(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(posrecip(z0))) → c65(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(from(negrecip(z0))) → c65(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(from(cons(z0, z1))) → c65(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(rcons(z0, z1))) → c65(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(from(from(z0))) → c65(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(2ndspos(z0, z1))) → c65(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(from(2ndsneg(z0, z1))) → c65(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(from(pi(z0))) → c65(FROM(pi(proper(z0))), PROPER(pi(z0)))
PROPER(from(plus(z0, z1))) → c65(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(from(times(z0, z1))) → c65(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(from(square(z0))) → c65(FROM(square(proper(z0))), PROPER(square(z0)))
PROPER(from(0)) → c65(FROM(ok(0)))
PROPER(from(nil)) → c65(FROM(ok(nil)))
PROPER(from(rnil)) → c65(FROM(ok(rnil)))

S tuples:

ACTIVE(square(z0)) → c10(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))
PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c58(S(ok(0)))
PROPER(s(nil)) → c58(S(ok(nil)))
PROPER(s(rnil)) → c58(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(rcons(x0, s(z0))) → c64(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c64(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c64(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, cons(z0, z1))) → c64(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, rcons(z0, z1))) → c64(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c64(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c64(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c64(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c64(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c64(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c64(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c64(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(s(z0), x1)) → c64(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c64(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c64(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c64(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c64(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c64(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c64(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c64(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c64(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c64(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c64(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c64(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(rcons(x0, 0)) → c64(RCONS(proper(x0), ok(0)), PROPER(x0))
PROPER(rcons(x0, nil)) → c64(RCONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(rcons(x0, rnil)) → c64(RCONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(rcons(0, x1)) → c64(RCONS(ok(0), proper(x1)), PROPER(x1))
PROPER(rcons(nil, x1)) → c64(RCONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c64(RCONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(from(s(z0))) → c65(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(posrecip(z0))) → c65(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(from(negrecip(z0))) → c65(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(from(cons(z0, z1))) → c65(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(rcons(z0, z1))) → c65(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(from(from(z0))) → c65(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(2ndspos(z0, z1))) → c65(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(from(2ndsneg(z0, z1))) → c65(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(from(pi(z0))) → c65(FROM(pi(proper(z0))), PROPER(pi(z0)))
PROPER(from(plus(z0, z1))) → c65(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(from(times(z0, z1))) → c65(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(from(square(z0))) → c65(FROM(square(proper(z0))), PROPER(square(z0)))
PROPER(from(0)) → c65(FROM(ok(0)))
PROPER(from(nil)) → c65(FROM(ok(nil)))
PROPER(from(rnil)) → c65(FROM(ok(rnil)))

K tuples:none
Defined Rule Symbols:

active, rcons, posrecip, 2ndsneg, negrecip, 2ndspos, s, cons, from, pi, plus, times, square, proper

Defined Pair Symbols:

ACTIVE, S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP

Compound Symbols:

c10, c15, c16, c18, c19, c20, c21, c23, c24, c25, c26, 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, c66, c67, c68, c69, c70, c71, c72, c73, c, c5, c7, c9, c1, c11, c12, c13, c14, c17, c22, c27, c58, c58, c59, c59, c60, c60, c62, c62, c64, c64, c65, c65

(49) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

Use narrowing to replace PROPER(2ndspos(z0, z1)) → c66(2NDSPOS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) by

PROPER(2ndspos(x0, 0)) → c66(2NDSPOS(proper(x0), ok(0)), PROPER(x0), PROPER(0))
PROPER(2ndspos(x0, s(z0))) → c66(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndspos(x0, posrecip(z0))) → c66(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndspos(x0, negrecip(z0))) → c66(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndspos(x0, nil)) → c66(2NDSPOS(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
PROPER(2ndspos(x0, cons(z0, z1))) → c66(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndspos(x0, rnil)) → c66(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0), PROPER(rnil))
PROPER(2ndspos(x0, rcons(z0, z1))) → c66(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndspos(x0, from(z0))) → c66(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndspos(x0, pi(z0))) → c66(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndspos(x0, plus(z0, z1))) → c66(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndspos(x0, times(z0, z1))) → c66(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndspos(x0, square(z0))) → c66(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndspos(0, x1)) → c66(2NDSPOS(ok(0), proper(x1)), PROPER(0), PROPER(x1))
PROPER(2ndspos(s(z0), x1)) → c66(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndspos(posrecip(z0), x1)) → c66(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndspos(negrecip(z0), x1)) → c66(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndspos(nil, x1)) → c66(2NDSPOS(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
PROPER(2ndspos(cons(z0, z1), x1)) → c66(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndspos(rnil, x1)) → c66(2NDSPOS(ok(rnil), proper(x1)), PROPER(rnil), PROPER(x1))
PROPER(2ndspos(rcons(z0, z1), x1)) → c66(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndspos(from(z0), x1)) → c66(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c66(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c66(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndspos(pi(z0), x1)) → c66(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndspos(plus(z0, z1), x1)) → c66(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndspos(times(z0, z1), x1)) → c66(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndspos(square(z0), x1)) → c66(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))

(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, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(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(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))
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))
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))
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(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)) → c10(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))
PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c58(S(ok(0)))
PROPER(s(nil)) → c58(S(ok(nil)))
PROPER(s(rnil)) → c58(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(rcons(x0, s(z0))) → c64(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c64(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c64(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, cons(z0, z1))) → c64(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, rcons(z0, z1))) → c64(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c64(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c64(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c64(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c64(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c64(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c64(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c64(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(s(z0), x1)) → c64(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c64(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c64(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c64(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c64(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c64(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c64(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c64(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c64(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c64(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c64(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c64(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(rcons(x0, 0)) → c64(RCONS(proper(x0), ok(0)), PROPER(x0))
PROPER(rcons(x0, nil)) → c64(RCONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(rcons(x0, rnil)) → c64(RCONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(rcons(0, x1)) → c64(RCONS(ok(0), proper(x1)), PROPER(x1))
PROPER(rcons(nil, x1)) → c64(RCONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c64(RCONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(from(s(z0))) → c65(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(posrecip(z0))) → c65(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(from(negrecip(z0))) → c65(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(from(cons(z0, z1))) → c65(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(rcons(z0, z1))) → c65(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(from(from(z0))) → c65(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(2ndspos(z0, z1))) → c65(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(from(2ndsneg(z0, z1))) → c65(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(from(pi(z0))) → c65(FROM(pi(proper(z0))), PROPER(pi(z0)))
PROPER(from(plus(z0, z1))) → c65(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(from(times(z0, z1))) → c65(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(from(square(z0))) → c65(FROM(square(proper(z0))), PROPER(square(z0)))
PROPER(from(0)) → c65(FROM(ok(0)))
PROPER(from(nil)) → c65(FROM(ok(nil)))
PROPER(from(rnil)) → c65(FROM(ok(rnil)))
PROPER(2ndspos(x0, 0)) → c66(2NDSPOS(proper(x0), ok(0)), PROPER(x0), PROPER(0))
PROPER(2ndspos(x0, s(z0))) → c66(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndspos(x0, posrecip(z0))) → c66(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndspos(x0, negrecip(z0))) → c66(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndspos(x0, nil)) → c66(2NDSPOS(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
PROPER(2ndspos(x0, cons(z0, z1))) → c66(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndspos(x0, rnil)) → c66(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0), PROPER(rnil))
PROPER(2ndspos(x0, rcons(z0, z1))) → c66(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndspos(x0, from(z0))) → c66(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndspos(x0, pi(z0))) → c66(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndspos(x0, plus(z0, z1))) → c66(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndspos(x0, times(z0, z1))) → c66(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndspos(x0, square(z0))) → c66(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndspos(0, x1)) → c66(2NDSPOS(ok(0), proper(x1)), PROPER(0), PROPER(x1))
PROPER(2ndspos(s(z0), x1)) → c66(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndspos(posrecip(z0), x1)) → c66(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndspos(negrecip(z0), x1)) → c66(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndspos(nil, x1)) → c66(2NDSPOS(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
PROPER(2ndspos(cons(z0, z1), x1)) → c66(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndspos(rnil, x1)) → c66(2NDSPOS(ok(rnil), proper(x1)), PROPER(rnil), PROPER(x1))
PROPER(2ndspos(rcons(z0, z1), x1)) → c66(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndspos(from(z0), x1)) → c66(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c66(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c66(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndspos(pi(z0), x1)) → c66(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndspos(plus(z0, z1), x1)) → c66(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndspos(times(z0, z1), x1)) → c66(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndspos(square(z0), x1)) → c66(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))

S tuples:

ACTIVE(square(z0)) → c10(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))
PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c58(S(ok(0)))
PROPER(s(nil)) → c58(S(ok(nil)))
PROPER(s(rnil)) → c58(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(rcons(x0, s(z0))) → c64(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c64(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c64(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, cons(z0, z1))) → c64(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, rcons(z0, z1))) → c64(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c64(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c64(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c64(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c64(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c64(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c64(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c64(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(s(z0), x1)) → c64(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c64(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c64(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c64(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c64(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c64(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c64(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c64(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c64(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c64(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c64(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c64(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(rcons(x0, 0)) → c64(RCONS(proper(x0), ok(0)), PROPER(x0))
PROPER(rcons(x0, nil)) → c64(RCONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(rcons(x0, rnil)) → c64(RCONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(rcons(0, x1)) → c64(RCONS(ok(0), proper(x1)), PROPER(x1))
PROPER(rcons(nil, x1)) → c64(RCONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c64(RCONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(from(s(z0))) → c65(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(posrecip(z0))) → c65(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(from(negrecip(z0))) → c65(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(from(cons(z0, z1))) → c65(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(rcons(z0, z1))) → c65(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(from(from(z0))) → c65(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(2ndspos(z0, z1))) → c65(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(from(2ndsneg(z0, z1))) → c65(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(from(pi(z0))) → c65(FROM(pi(proper(z0))), PROPER(pi(z0)))
PROPER(from(plus(z0, z1))) → c65(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(from(times(z0, z1))) → c65(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(from(square(z0))) → c65(FROM(square(proper(z0))), PROPER(square(z0)))
PROPER(from(0)) → c65(FROM(ok(0)))
PROPER(from(nil)) → c65(FROM(ok(nil)))
PROPER(from(rnil)) → c65(FROM(ok(rnil)))
PROPER(2ndspos(x0, 0)) → c66(2NDSPOS(proper(x0), ok(0)), PROPER(x0), PROPER(0))
PROPER(2ndspos(x0, s(z0))) → c66(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndspos(x0, posrecip(z0))) → c66(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndspos(x0, negrecip(z0))) → c66(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndspos(x0, nil)) → c66(2NDSPOS(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
PROPER(2ndspos(x0, cons(z0, z1))) → c66(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndspos(x0, rnil)) → c66(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0), PROPER(rnil))
PROPER(2ndspos(x0, rcons(z0, z1))) → c66(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndspos(x0, from(z0))) → c66(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndspos(x0, pi(z0))) → c66(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndspos(x0, plus(z0, z1))) → c66(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndspos(x0, times(z0, z1))) → c66(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndspos(x0, square(z0))) → c66(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndspos(0, x1)) → c66(2NDSPOS(ok(0), proper(x1)), PROPER(0), PROPER(x1))
PROPER(2ndspos(s(z0), x1)) → c66(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndspos(posrecip(z0), x1)) → c66(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndspos(negrecip(z0), x1)) → c66(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndspos(nil, x1)) → c66(2NDSPOS(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
PROPER(2ndspos(cons(z0, z1), x1)) → c66(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndspos(rnil, x1)) → c66(2NDSPOS(ok(rnil), proper(x1)), PROPER(rnil), PROPER(x1))
PROPER(2ndspos(rcons(z0, z1), x1)) → c66(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndspos(from(z0), x1)) → c66(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c66(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c66(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndspos(pi(z0), x1)) → c66(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndspos(plus(z0, z1), x1)) → c66(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndspos(times(z0, z1), x1)) → c66(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndspos(square(z0), x1)) → c66(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))

K tuples:none
Defined Rule Symbols:

active, rcons, posrecip, 2ndsneg, negrecip, 2ndspos, s, cons, from, pi, plus, times, square, proper

Defined Pair Symbols:

ACTIVE, S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP

Compound Symbols:

c10, c15, c16, c18, c19, c20, c21, c23, c24, c25, c26, 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, c67, c68, c69, c70, c71, c72, c73, c, c5, c7, c9, c1, c11, c12, c13, c14, c17, c22, c27, c58, c58, c59, c59, c60, c60, c62, c62, c64, c64, c65, c65, c66

(51) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)

Removed 6 trailing tuple parts

(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, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(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(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))
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))
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))
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(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)) → c10(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))
PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c58(S(ok(0)))
PROPER(s(nil)) → c58(S(ok(nil)))
PROPER(s(rnil)) → c58(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(rcons(x0, s(z0))) → c64(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c64(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c64(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, cons(z0, z1))) → c64(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, rcons(z0, z1))) → c64(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c64(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c64(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c64(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c64(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c64(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c64(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c64(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(s(z0), x1)) → c64(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c64(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c64(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c64(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c64(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c64(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c64(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c64(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c64(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c64(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c64(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c64(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(rcons(x0, 0)) → c64(RCONS(proper(x0), ok(0)), PROPER(x0))
PROPER(rcons(x0, nil)) → c64(RCONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(rcons(x0, rnil)) → c64(RCONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(rcons(0, x1)) → c64(RCONS(ok(0), proper(x1)), PROPER(x1))
PROPER(rcons(nil, x1)) → c64(RCONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c64(RCONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(from(s(z0))) → c65(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(posrecip(z0))) → c65(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(from(negrecip(z0))) → c65(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(from(cons(z0, z1))) → c65(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(rcons(z0, z1))) → c65(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(from(from(z0))) → c65(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(2ndspos(z0, z1))) → c65(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(from(2ndsneg(z0, z1))) → c65(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(from(pi(z0))) → c65(FROM(pi(proper(z0))), PROPER(pi(z0)))
PROPER(from(plus(z0, z1))) → c65(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(from(times(z0, z1))) → c65(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(from(square(z0))) → c65(FROM(square(proper(z0))), PROPER(square(z0)))
PROPER(from(0)) → c65(FROM(ok(0)))
PROPER(from(nil)) → c65(FROM(ok(nil)))
PROPER(from(rnil)) → c65(FROM(ok(rnil)))
PROPER(2ndspos(x0, s(z0))) → c66(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndspos(x0, posrecip(z0))) → c66(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndspos(x0, negrecip(z0))) → c66(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndspos(x0, cons(z0, z1))) → c66(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndspos(x0, rcons(z0, z1))) → c66(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndspos(x0, from(z0))) → c66(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndspos(x0, pi(z0))) → c66(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndspos(x0, plus(z0, z1))) → c66(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndspos(x0, times(z0, z1))) → c66(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndspos(x0, square(z0))) → c66(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndspos(s(z0), x1)) → c66(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndspos(posrecip(z0), x1)) → c66(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndspos(negrecip(z0), x1)) → c66(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndspos(cons(z0, z1), x1)) → c66(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndspos(rcons(z0, z1), x1)) → c66(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndspos(from(z0), x1)) → c66(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c66(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c66(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndspos(pi(z0), x1)) → c66(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndspos(plus(z0, z1), x1)) → c66(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndspos(times(z0, z1), x1)) → c66(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndspos(square(z0), x1)) → c66(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndspos(x0, 0)) → c66(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndspos(x0, nil)) → c66(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndspos(x0, rnil)) → c66(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndspos(0, x1)) → c66(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndspos(nil, x1)) → c66(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndspos(rnil, x1)) → c66(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))

S tuples:

ACTIVE(square(z0)) → c10(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))
PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c58(S(ok(0)))
PROPER(s(nil)) → c58(S(ok(nil)))
PROPER(s(rnil)) → c58(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(rcons(x0, s(z0))) → c64(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c64(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c64(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, cons(z0, z1))) → c64(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, rcons(z0, z1))) → c64(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c64(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c64(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c64(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c64(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c64(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c64(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c64(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(s(z0), x1)) → c64(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c64(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c64(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c64(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c64(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c64(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c64(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c64(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c64(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c64(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c64(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c64(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(rcons(x0, 0)) → c64(RCONS(proper(x0), ok(0)), PROPER(x0))
PROPER(rcons(x0, nil)) → c64(RCONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(rcons(x0, rnil)) → c64(RCONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(rcons(0, x1)) → c64(RCONS(ok(0), proper(x1)), PROPER(x1))
PROPER(rcons(nil, x1)) → c64(RCONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c64(RCONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(from(s(z0))) → c65(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(posrecip(z0))) → c65(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(from(negrecip(z0))) → c65(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(from(cons(z0, z1))) → c65(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(rcons(z0, z1))) → c65(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(from(from(z0))) → c65(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(2ndspos(z0, z1))) → c65(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(from(2ndsneg(z0, z1))) → c65(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(from(pi(z0))) → c65(FROM(pi(proper(z0))), PROPER(pi(z0)))
PROPER(from(plus(z0, z1))) → c65(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(from(times(z0, z1))) → c65(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(from(square(z0))) → c65(FROM(square(proper(z0))), PROPER(square(z0)))
PROPER(from(0)) → c65(FROM(ok(0)))
PROPER(from(nil)) → c65(FROM(ok(nil)))
PROPER(from(rnil)) → c65(FROM(ok(rnil)))
PROPER(2ndspos(x0, s(z0))) → c66(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndspos(x0, posrecip(z0))) → c66(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndspos(x0, negrecip(z0))) → c66(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndspos(x0, cons(z0, z1))) → c66(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndspos(x0, rcons(z0, z1))) → c66(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndspos(x0, from(z0))) → c66(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndspos(x0, pi(z0))) → c66(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndspos(x0, plus(z0, z1))) → c66(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndspos(x0, times(z0, z1))) → c66(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndspos(x0, square(z0))) → c66(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndspos(s(z0), x1)) → c66(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndspos(posrecip(z0), x1)) → c66(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndspos(negrecip(z0), x1)) → c66(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndspos(cons(z0, z1), x1)) → c66(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndspos(rcons(z0, z1), x1)) → c66(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndspos(from(z0), x1)) → c66(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c66(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c66(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndspos(pi(z0), x1)) → c66(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndspos(plus(z0, z1), x1)) → c66(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndspos(times(z0, z1), x1)) → c66(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndspos(square(z0), x1)) → c66(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndspos(x0, 0)) → c66(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndspos(x0, nil)) → c66(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndspos(x0, rnil)) → c66(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndspos(0, x1)) → c66(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndspos(nil, x1)) → c66(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndspos(rnil, x1)) → c66(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))

K tuples:none
Defined Rule Symbols:

active, rcons, posrecip, 2ndsneg, negrecip, 2ndspos, s, cons, from, pi, plus, times, square, proper

Defined Pair Symbols:

ACTIVE, S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP

Compound Symbols:

c10, c15, c16, c18, c19, c20, c21, c23, c24, c25, c26, 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, c67, c68, c69, c70, c71, c72, c73, c, c5, c7, c9, c1, c11, c12, c13, c14, c17, c22, c27, c58, c58, c59, c59, c60, c60, c62, c62, c64, c64, c65, c65, c66, c66

(53) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

Use narrowing to replace PROPER(2ndsneg(z0, z1)) → c67(2NDSNEG(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) by

PROPER(2ndsneg(x0, 0)) → c67(2NDSNEG(proper(x0), ok(0)), PROPER(x0), PROPER(0))
PROPER(2ndsneg(x0, s(z0))) → c67(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndsneg(x0, posrecip(z0))) → c67(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndsneg(x0, negrecip(z0))) → c67(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndsneg(x0, nil)) → c67(2NDSNEG(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
PROPER(2ndsneg(x0, cons(z0, z1))) → c67(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndsneg(x0, rnil)) → c67(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0), PROPER(rnil))
PROPER(2ndsneg(x0, rcons(z0, z1))) → c67(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndsneg(x0, from(z0))) → c67(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndsneg(x0, pi(z0))) → c67(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndsneg(x0, plus(z0, z1))) → c67(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndsneg(x0, times(z0, z1))) → c67(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndsneg(x0, square(z0))) → c67(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndsneg(0, x1)) → c67(2NDSNEG(ok(0), proper(x1)), PROPER(0), PROPER(x1))
PROPER(2ndsneg(s(z0), x1)) → c67(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndsneg(posrecip(z0), x1)) → c67(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndsneg(negrecip(z0), x1)) → c67(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndsneg(nil, x1)) → c67(2NDSNEG(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
PROPER(2ndsneg(cons(z0, z1), x1)) → c67(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(rnil, x1)) → c67(2NDSNEG(ok(rnil), proper(x1)), PROPER(rnil), PROPER(x1))
PROPER(2ndsneg(rcons(z0, z1), x1)) → c67(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(from(z0), x1)) → c67(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c67(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c67(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndsneg(pi(z0), x1)) → c67(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndsneg(plus(z0, z1), x1)) → c67(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndsneg(times(z0, z1), x1)) → c67(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndsneg(square(z0), x1)) → c67(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))

(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, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(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(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))
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))
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))
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(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)) → c10(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))
PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c58(S(ok(0)))
PROPER(s(nil)) → c58(S(ok(nil)))
PROPER(s(rnil)) → c58(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(rcons(x0, s(z0))) → c64(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c64(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c64(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, cons(z0, z1))) → c64(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, rcons(z0, z1))) → c64(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c64(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c64(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c64(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c64(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c64(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c64(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c64(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(s(z0), x1)) → c64(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c64(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c64(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c64(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c64(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c64(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c64(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c64(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c64(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c64(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c64(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c64(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(rcons(x0, 0)) → c64(RCONS(proper(x0), ok(0)), PROPER(x0))
PROPER(rcons(x0, nil)) → c64(RCONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(rcons(x0, rnil)) → c64(RCONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(rcons(0, x1)) → c64(RCONS(ok(0), proper(x1)), PROPER(x1))
PROPER(rcons(nil, x1)) → c64(RCONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c64(RCONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(from(s(z0))) → c65(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(posrecip(z0))) → c65(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(from(negrecip(z0))) → c65(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(from(cons(z0, z1))) → c65(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(rcons(z0, z1))) → c65(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(from(from(z0))) → c65(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(2ndspos(z0, z1))) → c65(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(from(2ndsneg(z0, z1))) → c65(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(from(pi(z0))) → c65(FROM(pi(proper(z0))), PROPER(pi(z0)))
PROPER(from(plus(z0, z1))) → c65(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(from(times(z0, z1))) → c65(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(from(square(z0))) → c65(FROM(square(proper(z0))), PROPER(square(z0)))
PROPER(from(0)) → c65(FROM(ok(0)))
PROPER(from(nil)) → c65(FROM(ok(nil)))
PROPER(from(rnil)) → c65(FROM(ok(rnil)))
PROPER(2ndspos(x0, s(z0))) → c66(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndspos(x0, posrecip(z0))) → c66(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndspos(x0, negrecip(z0))) → c66(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndspos(x0, cons(z0, z1))) → c66(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndspos(x0, rcons(z0, z1))) → c66(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndspos(x0, from(z0))) → c66(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndspos(x0, pi(z0))) → c66(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndspos(x0, plus(z0, z1))) → c66(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndspos(x0, times(z0, z1))) → c66(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndspos(x0, square(z0))) → c66(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndspos(s(z0), x1)) → c66(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndspos(posrecip(z0), x1)) → c66(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndspos(negrecip(z0), x1)) → c66(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndspos(cons(z0, z1), x1)) → c66(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndspos(rcons(z0, z1), x1)) → c66(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndspos(from(z0), x1)) → c66(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c66(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c66(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndspos(pi(z0), x1)) → c66(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndspos(plus(z0, z1), x1)) → c66(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndspos(times(z0, z1), x1)) → c66(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndspos(square(z0), x1)) → c66(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndspos(x0, 0)) → c66(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndspos(x0, nil)) → c66(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndspos(x0, rnil)) → c66(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndspos(0, x1)) → c66(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndspos(nil, x1)) → c66(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndspos(rnil, x1)) → c66(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(x0, 0)) → c67(2NDSNEG(proper(x0), ok(0)), PROPER(x0), PROPER(0))
PROPER(2ndsneg(x0, s(z0))) → c67(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndsneg(x0, posrecip(z0))) → c67(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndsneg(x0, negrecip(z0))) → c67(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndsneg(x0, nil)) → c67(2NDSNEG(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
PROPER(2ndsneg(x0, cons(z0, z1))) → c67(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndsneg(x0, rnil)) → c67(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0), PROPER(rnil))
PROPER(2ndsneg(x0, rcons(z0, z1))) → c67(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndsneg(x0, from(z0))) → c67(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndsneg(x0, pi(z0))) → c67(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndsneg(x0, plus(z0, z1))) → c67(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndsneg(x0, times(z0, z1))) → c67(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndsneg(x0, square(z0))) → c67(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndsneg(0, x1)) → c67(2NDSNEG(ok(0), proper(x1)), PROPER(0), PROPER(x1))
PROPER(2ndsneg(s(z0), x1)) → c67(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndsneg(posrecip(z0), x1)) → c67(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndsneg(negrecip(z0), x1)) → c67(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndsneg(nil, x1)) → c67(2NDSNEG(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
PROPER(2ndsneg(cons(z0, z1), x1)) → c67(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(rnil, x1)) → c67(2NDSNEG(ok(rnil), proper(x1)), PROPER(rnil), PROPER(x1))
PROPER(2ndsneg(rcons(z0, z1), x1)) → c67(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(from(z0), x1)) → c67(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c67(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c67(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndsneg(pi(z0), x1)) → c67(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndsneg(plus(z0, z1), x1)) → c67(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndsneg(times(z0, z1), x1)) → c67(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndsneg(square(z0), x1)) → c67(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))

S tuples:

ACTIVE(square(z0)) → c10(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))
PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c58(S(ok(0)))
PROPER(s(nil)) → c58(S(ok(nil)))
PROPER(s(rnil)) → c58(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(rcons(x0, s(z0))) → c64(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c64(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c64(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, cons(z0, z1))) → c64(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, rcons(z0, z1))) → c64(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c64(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c64(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c64(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c64(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c64(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c64(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c64(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(s(z0), x1)) → c64(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c64(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c64(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c64(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c64(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c64(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c64(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c64(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c64(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c64(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c64(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c64(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(rcons(x0, 0)) → c64(RCONS(proper(x0), ok(0)), PROPER(x0))
PROPER(rcons(x0, nil)) → c64(RCONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(rcons(x0, rnil)) → c64(RCONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(rcons(0, x1)) → c64(RCONS(ok(0), proper(x1)), PROPER(x1))
PROPER(rcons(nil, x1)) → c64(RCONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c64(RCONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(from(s(z0))) → c65(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(posrecip(z0))) → c65(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(from(negrecip(z0))) → c65(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(from(cons(z0, z1))) → c65(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(rcons(z0, z1))) → c65(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(from(from(z0))) → c65(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(2ndspos(z0, z1))) → c65(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(from(2ndsneg(z0, z1))) → c65(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(from(pi(z0))) → c65(FROM(pi(proper(z0))), PROPER(pi(z0)))
PROPER(from(plus(z0, z1))) → c65(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(from(times(z0, z1))) → c65(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(from(square(z0))) → c65(FROM(square(proper(z0))), PROPER(square(z0)))
PROPER(from(0)) → c65(FROM(ok(0)))
PROPER(from(nil)) → c65(FROM(ok(nil)))
PROPER(from(rnil)) → c65(FROM(ok(rnil)))
PROPER(2ndspos(x0, s(z0))) → c66(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndspos(x0, posrecip(z0))) → c66(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndspos(x0, negrecip(z0))) → c66(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndspos(x0, cons(z0, z1))) → c66(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndspos(x0, rcons(z0, z1))) → c66(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndspos(x0, from(z0))) → c66(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndspos(x0, pi(z0))) → c66(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndspos(x0, plus(z0, z1))) → c66(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndspos(x0, times(z0, z1))) → c66(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndspos(x0, square(z0))) → c66(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndspos(s(z0), x1)) → c66(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndspos(posrecip(z0), x1)) → c66(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndspos(negrecip(z0), x1)) → c66(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndspos(cons(z0, z1), x1)) → c66(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndspos(rcons(z0, z1), x1)) → c66(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndspos(from(z0), x1)) → c66(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c66(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c66(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndspos(pi(z0), x1)) → c66(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndspos(plus(z0, z1), x1)) → c66(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndspos(times(z0, z1), x1)) → c66(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndspos(square(z0), x1)) → c66(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndspos(x0, 0)) → c66(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndspos(x0, nil)) → c66(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndspos(x0, rnil)) → c66(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndspos(0, x1)) → c66(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndspos(nil, x1)) → c66(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndspos(rnil, x1)) → c66(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(x0, 0)) → c67(2NDSNEG(proper(x0), ok(0)), PROPER(x0), PROPER(0))
PROPER(2ndsneg(x0, s(z0))) → c67(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndsneg(x0, posrecip(z0))) → c67(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndsneg(x0, negrecip(z0))) → c67(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndsneg(x0, nil)) → c67(2NDSNEG(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
PROPER(2ndsneg(x0, cons(z0, z1))) → c67(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndsneg(x0, rnil)) → c67(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0), PROPER(rnil))
PROPER(2ndsneg(x0, rcons(z0, z1))) → c67(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndsneg(x0, from(z0))) → c67(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndsneg(x0, pi(z0))) → c67(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndsneg(x0, plus(z0, z1))) → c67(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndsneg(x0, times(z0, z1))) → c67(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndsneg(x0, square(z0))) → c67(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndsneg(0, x1)) → c67(2NDSNEG(ok(0), proper(x1)), PROPER(0), PROPER(x1))
PROPER(2ndsneg(s(z0), x1)) → c67(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndsneg(posrecip(z0), x1)) → c67(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndsneg(negrecip(z0), x1)) → c67(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndsneg(nil, x1)) → c67(2NDSNEG(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
PROPER(2ndsneg(cons(z0, z1), x1)) → c67(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(rnil, x1)) → c67(2NDSNEG(ok(rnil), proper(x1)), PROPER(rnil), PROPER(x1))
PROPER(2ndsneg(rcons(z0, z1), x1)) → c67(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(from(z0), x1)) → c67(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c67(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c67(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndsneg(pi(z0), x1)) → c67(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndsneg(plus(z0, z1), x1)) → c67(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndsneg(times(z0, z1), x1)) → c67(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndsneg(square(z0), x1)) → c67(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))

K tuples:none
Defined Rule Symbols:

active, rcons, posrecip, 2ndsneg, negrecip, 2ndspos, s, cons, from, pi, plus, times, square, proper

Defined Pair Symbols:

ACTIVE, S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP

Compound Symbols:

c10, c15, c16, c18, c19, c20, c21, c23, c24, c25, c26, 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, c68, c69, c70, c71, c72, c73, c, c5, c7, c9, c1, c11, c12, c13, c14, c17, c22, c27, c58, c58, c59, c59, c60, c60, c62, c62, c64, c64, c65, c65, c66, c66, c67

(55) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)

Removed 6 trailing tuple parts

(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, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(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(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))
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))
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))
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(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)) → c10(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))
PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c58(S(ok(0)))
PROPER(s(nil)) → c58(S(ok(nil)))
PROPER(s(rnil)) → c58(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(rcons(x0, s(z0))) → c64(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c64(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c64(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, cons(z0, z1))) → c64(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, rcons(z0, z1))) → c64(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c64(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c64(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c64(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c64(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c64(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c64(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c64(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(s(z0), x1)) → c64(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c64(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c64(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c64(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c64(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c64(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c64(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c64(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c64(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c64(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c64(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c64(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(rcons(x0, 0)) → c64(RCONS(proper(x0), ok(0)), PROPER(x0))
PROPER(rcons(x0, nil)) → c64(RCONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(rcons(x0, rnil)) → c64(RCONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(rcons(0, x1)) → c64(RCONS(ok(0), proper(x1)), PROPER(x1))
PROPER(rcons(nil, x1)) → c64(RCONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c64(RCONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(from(s(z0))) → c65(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(posrecip(z0))) → c65(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(from(negrecip(z0))) → c65(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(from(cons(z0, z1))) → c65(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(rcons(z0, z1))) → c65(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(from(from(z0))) → c65(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(2ndspos(z0, z1))) → c65(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(from(2ndsneg(z0, z1))) → c65(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(from(pi(z0))) → c65(FROM(pi(proper(z0))), PROPER(pi(z0)))
PROPER(from(plus(z0, z1))) → c65(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(from(times(z0, z1))) → c65(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(from(square(z0))) → c65(FROM(square(proper(z0))), PROPER(square(z0)))
PROPER(from(0)) → c65(FROM(ok(0)))
PROPER(from(nil)) → c65(FROM(ok(nil)))
PROPER(from(rnil)) → c65(FROM(ok(rnil)))
PROPER(2ndspos(x0, s(z0))) → c66(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndspos(x0, posrecip(z0))) → c66(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndspos(x0, negrecip(z0))) → c66(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndspos(x0, cons(z0, z1))) → c66(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndspos(x0, rcons(z0, z1))) → c66(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndspos(x0, from(z0))) → c66(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndspos(x0, pi(z0))) → c66(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndspos(x0, plus(z0, z1))) → c66(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndspos(x0, times(z0, z1))) → c66(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndspos(x0, square(z0))) → c66(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndspos(s(z0), x1)) → c66(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndspos(posrecip(z0), x1)) → c66(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndspos(negrecip(z0), x1)) → c66(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndspos(cons(z0, z1), x1)) → c66(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndspos(rcons(z0, z1), x1)) → c66(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndspos(from(z0), x1)) → c66(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c66(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c66(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndspos(pi(z0), x1)) → c66(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndspos(plus(z0, z1), x1)) → c66(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndspos(times(z0, z1), x1)) → c66(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndspos(square(z0), x1)) → c66(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndspos(x0, 0)) → c66(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndspos(x0, nil)) → c66(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndspos(x0, rnil)) → c66(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndspos(0, x1)) → c66(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndspos(nil, x1)) → c66(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndspos(rnil, x1)) → c66(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(x0, s(z0))) → c67(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndsneg(x0, posrecip(z0))) → c67(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndsneg(x0, negrecip(z0))) → c67(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndsneg(x0, cons(z0, z1))) → c67(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndsneg(x0, rcons(z0, z1))) → c67(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndsneg(x0, from(z0))) → c67(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndsneg(x0, pi(z0))) → c67(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndsneg(x0, plus(z0, z1))) → c67(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndsneg(x0, times(z0, z1))) → c67(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndsneg(x0, square(z0))) → c67(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndsneg(s(z0), x1)) → c67(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndsneg(posrecip(z0), x1)) → c67(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndsneg(negrecip(z0), x1)) → c67(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndsneg(cons(z0, z1), x1)) → c67(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(rcons(z0, z1), x1)) → c67(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(from(z0), x1)) → c67(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c67(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c67(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndsneg(pi(z0), x1)) → c67(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndsneg(plus(z0, z1), x1)) → c67(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndsneg(times(z0, z1), x1)) → c67(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndsneg(square(z0), x1)) → c67(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndsneg(x0, 0)) → c67(2NDSNEG(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndsneg(x0, nil)) → c67(2NDSNEG(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndsneg(x0, rnil)) → c67(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndsneg(0, x1)) → c67(2NDSNEG(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndsneg(nil, x1)) → c67(2NDSNEG(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(rnil, x1)) → c67(2NDSNEG(ok(rnil), proper(x1)), PROPER(x1))

S tuples:

ACTIVE(square(z0)) → c10(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))
PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c58(S(ok(0)))
PROPER(s(nil)) → c58(S(ok(nil)))
PROPER(s(rnil)) → c58(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(rcons(x0, s(z0))) → c64(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c64(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c64(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, cons(z0, z1))) → c64(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, rcons(z0, z1))) → c64(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c64(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c64(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c64(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c64(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c64(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c64(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c64(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(s(z0), x1)) → c64(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c64(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c64(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c64(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c64(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c64(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c64(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c64(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c64(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c64(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c64(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c64(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(rcons(x0, 0)) → c64(RCONS(proper(x0), ok(0)), PROPER(x0))
PROPER(rcons(x0, nil)) → c64(RCONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(rcons(x0, rnil)) → c64(RCONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(rcons(0, x1)) → c64(RCONS(ok(0), proper(x1)), PROPER(x1))
PROPER(rcons(nil, x1)) → c64(RCONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c64(RCONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(from(s(z0))) → c65(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(posrecip(z0))) → c65(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(from(negrecip(z0))) → c65(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(from(cons(z0, z1))) → c65(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(rcons(z0, z1))) → c65(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(from(from(z0))) → c65(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(2ndspos(z0, z1))) → c65(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(from(2ndsneg(z0, z1))) → c65(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(from(pi(z0))) → c65(FROM(pi(proper(z0))), PROPER(pi(z0)))
PROPER(from(plus(z0, z1))) → c65(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(from(times(z0, z1))) → c65(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(from(square(z0))) → c65(FROM(square(proper(z0))), PROPER(square(z0)))
PROPER(from(0)) → c65(FROM(ok(0)))
PROPER(from(nil)) → c65(FROM(ok(nil)))
PROPER(from(rnil)) → c65(FROM(ok(rnil)))
PROPER(2ndspos(x0, s(z0))) → c66(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndspos(x0, posrecip(z0))) → c66(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndspos(x0, negrecip(z0))) → c66(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndspos(x0, cons(z0, z1))) → c66(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndspos(x0, rcons(z0, z1))) → c66(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndspos(x0, from(z0))) → c66(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndspos(x0, pi(z0))) → c66(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndspos(x0, plus(z0, z1))) → c66(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndspos(x0, times(z0, z1))) → c66(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndspos(x0, square(z0))) → c66(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndspos(s(z0), x1)) → c66(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndspos(posrecip(z0), x1)) → c66(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndspos(negrecip(z0), x1)) → c66(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndspos(cons(z0, z1), x1)) → c66(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndspos(rcons(z0, z1), x1)) → c66(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndspos(from(z0), x1)) → c66(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c66(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c66(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndspos(pi(z0), x1)) → c66(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndspos(plus(z0, z1), x1)) → c66(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndspos(times(z0, z1), x1)) → c66(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndspos(square(z0), x1)) → c66(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndspos(x0, 0)) → c66(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndspos(x0, nil)) → c66(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndspos(x0, rnil)) → c66(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndspos(0, x1)) → c66(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndspos(nil, x1)) → c66(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndspos(rnil, x1)) → c66(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(x0, s(z0))) → c67(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndsneg(x0, posrecip(z0))) → c67(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndsneg(x0, negrecip(z0))) → c67(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndsneg(x0, cons(z0, z1))) → c67(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndsneg(x0, rcons(z0, z1))) → c67(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndsneg(x0, from(z0))) → c67(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndsneg(x0, pi(z0))) → c67(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndsneg(x0, plus(z0, z1))) → c67(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndsneg(x0, times(z0, z1))) → c67(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndsneg(x0, square(z0))) → c67(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndsneg(s(z0), x1)) → c67(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndsneg(posrecip(z0), x1)) → c67(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndsneg(negrecip(z0), x1)) → c67(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndsneg(cons(z0, z1), x1)) → c67(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(rcons(z0, z1), x1)) → c67(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(from(z0), x1)) → c67(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c67(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c67(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndsneg(pi(z0), x1)) → c67(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndsneg(plus(z0, z1), x1)) → c67(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndsneg(times(z0, z1), x1)) → c67(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndsneg(square(z0), x1)) → c67(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndsneg(x0, 0)) → c67(2NDSNEG(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndsneg(x0, nil)) → c67(2NDSNEG(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndsneg(x0, rnil)) → c67(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndsneg(0, x1)) → c67(2NDSNEG(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndsneg(nil, x1)) → c67(2NDSNEG(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(rnil, x1)) → c67(2NDSNEG(ok(rnil), proper(x1)), PROPER(x1))

K tuples:none
Defined Rule Symbols:

active, rcons, posrecip, 2ndsneg, negrecip, 2ndspos, s, cons, from, pi, plus, times, square, proper

Defined Pair Symbols:

ACTIVE, S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP

Compound Symbols:

c10, c15, c16, c18, c19, c20, c21, c23, c24, c25, c26, 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, c68, c69, c70, c71, c72, c73, c, c5, c7, c9, c1, c11, c12, c13, c14, c17, c22, c27, c58, c58, c59, c59, c60, c60, c62, c62, c64, c64, c65, c65, c66, c66, c67, c67

(57) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

Use narrowing to replace PROPER(pi(z0)) → c68(PI(proper(z0)), PROPER(z0)) by

PROPER(pi(0)) → c68(PI(ok(0)), PROPER(0))
PROPER(pi(s(z0))) → c68(PI(s(proper(z0))), PROPER(s(z0)))
PROPER(pi(posrecip(z0))) → c68(PI(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(pi(negrecip(z0))) → c68(PI(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(pi(nil)) → c68(PI(ok(nil)), PROPER(nil))
PROPER(pi(cons(z0, z1))) → c68(PI(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(pi(rnil)) → c68(PI(ok(rnil)), PROPER(rnil))
PROPER(pi(rcons(z0, z1))) → c68(PI(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(pi(from(z0))) → c68(PI(from(proper(z0))), PROPER(from(z0)))
PROPER(pi(2ndspos(z0, z1))) → c68(PI(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(pi(2ndsneg(z0, z1))) → c68(PI(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(pi(pi(z0))) → c68(PI(pi(proper(z0))), PROPER(pi(z0)))
PROPER(pi(plus(z0, z1))) → c68(PI(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(pi(times(z0, z1))) → c68(PI(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(pi(square(z0))) → c68(PI(square(proper(z0))), PROPER(square(z0)))

(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, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(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(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))
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))
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))
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(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)) → c10(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))
PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c58(S(ok(0)))
PROPER(s(nil)) → c58(S(ok(nil)))
PROPER(s(rnil)) → c58(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(rcons(x0, s(z0))) → c64(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c64(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c64(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, cons(z0, z1))) → c64(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, rcons(z0, z1))) → c64(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c64(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c64(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c64(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c64(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c64(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c64(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c64(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(s(z0), x1)) → c64(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c64(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c64(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c64(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c64(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c64(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c64(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c64(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c64(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c64(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c64(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c64(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(rcons(x0, 0)) → c64(RCONS(proper(x0), ok(0)), PROPER(x0))
PROPER(rcons(x0, nil)) → c64(RCONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(rcons(x0, rnil)) → c64(RCONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(rcons(0, x1)) → c64(RCONS(ok(0), proper(x1)), PROPER(x1))
PROPER(rcons(nil, x1)) → c64(RCONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c64(RCONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(from(s(z0))) → c65(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(posrecip(z0))) → c65(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(from(negrecip(z0))) → c65(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(from(cons(z0, z1))) → c65(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(rcons(z0, z1))) → c65(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(from(from(z0))) → c65(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(2ndspos(z0, z1))) → c65(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(from(2ndsneg(z0, z1))) → c65(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(from(pi(z0))) → c65(FROM(pi(proper(z0))), PROPER(pi(z0)))
PROPER(from(plus(z0, z1))) → c65(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(from(times(z0, z1))) → c65(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(from(square(z0))) → c65(FROM(square(proper(z0))), PROPER(square(z0)))
PROPER(from(0)) → c65(FROM(ok(0)))
PROPER(from(nil)) → c65(FROM(ok(nil)))
PROPER(from(rnil)) → c65(FROM(ok(rnil)))
PROPER(2ndspos(x0, s(z0))) → c66(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndspos(x0, posrecip(z0))) → c66(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndspos(x0, negrecip(z0))) → c66(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndspos(x0, cons(z0, z1))) → c66(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndspos(x0, rcons(z0, z1))) → c66(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndspos(x0, from(z0))) → c66(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndspos(x0, pi(z0))) → c66(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndspos(x0, plus(z0, z1))) → c66(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndspos(x0, times(z0, z1))) → c66(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndspos(x0, square(z0))) → c66(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndspos(s(z0), x1)) → c66(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndspos(posrecip(z0), x1)) → c66(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndspos(negrecip(z0), x1)) → c66(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndspos(cons(z0, z1), x1)) → c66(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndspos(rcons(z0, z1), x1)) → c66(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndspos(from(z0), x1)) → c66(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c66(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c66(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndspos(pi(z0), x1)) → c66(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndspos(plus(z0, z1), x1)) → c66(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndspos(times(z0, z1), x1)) → c66(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndspos(square(z0), x1)) → c66(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndspos(x0, 0)) → c66(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndspos(x0, nil)) → c66(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndspos(x0, rnil)) → c66(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndspos(0, x1)) → c66(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndspos(nil, x1)) → c66(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndspos(rnil, x1)) → c66(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(x0, s(z0))) → c67(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndsneg(x0, posrecip(z0))) → c67(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndsneg(x0, negrecip(z0))) → c67(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndsneg(x0, cons(z0, z1))) → c67(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndsneg(x0, rcons(z0, z1))) → c67(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndsneg(x0, from(z0))) → c67(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndsneg(x0, pi(z0))) → c67(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndsneg(x0, plus(z0, z1))) → c67(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndsneg(x0, times(z0, z1))) → c67(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndsneg(x0, square(z0))) → c67(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndsneg(s(z0), x1)) → c67(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndsneg(posrecip(z0), x1)) → c67(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndsneg(negrecip(z0), x1)) → c67(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndsneg(cons(z0, z1), x1)) → c67(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(rcons(z0, z1), x1)) → c67(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(from(z0), x1)) → c67(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c67(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c67(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndsneg(pi(z0), x1)) → c67(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndsneg(plus(z0, z1), x1)) → c67(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndsneg(times(z0, z1), x1)) → c67(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndsneg(square(z0), x1)) → c67(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndsneg(x0, 0)) → c67(2NDSNEG(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndsneg(x0, nil)) → c67(2NDSNEG(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndsneg(x0, rnil)) → c67(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndsneg(0, x1)) → c67(2NDSNEG(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndsneg(nil, x1)) → c67(2NDSNEG(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(rnil, x1)) → c67(2NDSNEG(ok(rnil), proper(x1)), PROPER(x1))
PROPER(pi(0)) → c68(PI(ok(0)), PROPER(0))
PROPER(pi(s(z0))) → c68(PI(s(proper(z0))), PROPER(s(z0)))
PROPER(pi(posrecip(z0))) → c68(PI(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(pi(negrecip(z0))) → c68(PI(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(pi(nil)) → c68(PI(ok(nil)), PROPER(nil))
PROPER(pi(cons(z0, z1))) → c68(PI(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(pi(rnil)) → c68(PI(ok(rnil)), PROPER(rnil))
PROPER(pi(rcons(z0, z1))) → c68(PI(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(pi(from(z0))) → c68(PI(from(proper(z0))), PROPER(from(z0)))
PROPER(pi(2ndspos(z0, z1))) → c68(PI(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(pi(2ndsneg(z0, z1))) → c68(PI(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(pi(pi(z0))) → c68(PI(pi(proper(z0))), PROPER(pi(z0)))
PROPER(pi(plus(z0, z1))) → c68(PI(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(pi(times(z0, z1))) → c68(PI(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(pi(square(z0))) → c68(PI(square(proper(z0))), PROPER(square(z0)))

S tuples:

ACTIVE(square(z0)) → c10(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))
PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c58(S(ok(0)))
PROPER(s(nil)) → c58(S(ok(nil)))
PROPER(s(rnil)) → c58(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(rcons(x0, s(z0))) → c64(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c64(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c64(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, cons(z0, z1))) → c64(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, rcons(z0, z1))) → c64(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c64(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c64(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c64(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c64(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c64(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c64(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c64(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(s(z0), x1)) → c64(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c64(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c64(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c64(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c64(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c64(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c64(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c64(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c64(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c64(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c64(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c64(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(rcons(x0, 0)) → c64(RCONS(proper(x0), ok(0)), PROPER(x0))
PROPER(rcons(x0, nil)) → c64(RCONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(rcons(x0, rnil)) → c64(RCONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(rcons(0, x1)) → c64(RCONS(ok(0), proper(x1)), PROPER(x1))
PROPER(rcons(nil, x1)) → c64(RCONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c64(RCONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(from(s(z0))) → c65(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(posrecip(z0))) → c65(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(from(negrecip(z0))) → c65(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(from(cons(z0, z1))) → c65(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(rcons(z0, z1))) → c65(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(from(from(z0))) → c65(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(2ndspos(z0, z1))) → c65(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(from(2ndsneg(z0, z1))) → c65(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(from(pi(z0))) → c65(FROM(pi(proper(z0))), PROPER(pi(z0)))
PROPER(from(plus(z0, z1))) → c65(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(from(times(z0, z1))) → c65(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(from(square(z0))) → c65(FROM(square(proper(z0))), PROPER(square(z0)))
PROPER(from(0)) → c65(FROM(ok(0)))
PROPER(from(nil)) → c65(FROM(ok(nil)))
PROPER(from(rnil)) → c65(FROM(ok(rnil)))
PROPER(2ndspos(x0, s(z0))) → c66(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndspos(x0, posrecip(z0))) → c66(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndspos(x0, negrecip(z0))) → c66(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndspos(x0, cons(z0, z1))) → c66(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndspos(x0, rcons(z0, z1))) → c66(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndspos(x0, from(z0))) → c66(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndspos(x0, pi(z0))) → c66(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndspos(x0, plus(z0, z1))) → c66(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndspos(x0, times(z0, z1))) → c66(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndspos(x0, square(z0))) → c66(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndspos(s(z0), x1)) → c66(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndspos(posrecip(z0), x1)) → c66(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndspos(negrecip(z0), x1)) → c66(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndspos(cons(z0, z1), x1)) → c66(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndspos(rcons(z0, z1), x1)) → c66(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndspos(from(z0), x1)) → c66(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c66(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c66(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndspos(pi(z0), x1)) → c66(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndspos(plus(z0, z1), x1)) → c66(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndspos(times(z0, z1), x1)) → c66(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndspos(square(z0), x1)) → c66(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndspos(x0, 0)) → c66(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndspos(x0, nil)) → c66(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndspos(x0, rnil)) → c66(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndspos(0, x1)) → c66(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndspos(nil, x1)) → c66(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndspos(rnil, x1)) → c66(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(x0, s(z0))) → c67(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndsneg(x0, posrecip(z0))) → c67(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndsneg(x0, negrecip(z0))) → c67(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndsneg(x0, cons(z0, z1))) → c67(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndsneg(x0, rcons(z0, z1))) → c67(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndsneg(x0, from(z0))) → c67(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndsneg(x0, pi(z0))) → c67(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndsneg(x0, plus(z0, z1))) → c67(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndsneg(x0, times(z0, z1))) → c67(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndsneg(x0, square(z0))) → c67(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndsneg(s(z0), x1)) → c67(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndsneg(posrecip(z0), x1)) → c67(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndsneg(negrecip(z0), x1)) → c67(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndsneg(cons(z0, z1), x1)) → c67(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(rcons(z0, z1), x1)) → c67(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(from(z0), x1)) → c67(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c67(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c67(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndsneg(pi(z0), x1)) → c67(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndsneg(plus(z0, z1), x1)) → c67(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndsneg(times(z0, z1), x1)) → c67(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndsneg(square(z0), x1)) → c67(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndsneg(x0, 0)) → c67(2NDSNEG(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndsneg(x0, nil)) → c67(2NDSNEG(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndsneg(x0, rnil)) → c67(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndsneg(0, x1)) → c67(2NDSNEG(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndsneg(nil, x1)) → c67(2NDSNEG(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(rnil, x1)) → c67(2NDSNEG(ok(rnil), proper(x1)), PROPER(x1))
PROPER(pi(0)) → c68(PI(ok(0)), PROPER(0))
PROPER(pi(s(z0))) → c68(PI(s(proper(z0))), PROPER(s(z0)))
PROPER(pi(posrecip(z0))) → c68(PI(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(pi(negrecip(z0))) → c68(PI(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(pi(nil)) → c68(PI(ok(nil)), PROPER(nil))
PROPER(pi(cons(z0, z1))) → c68(PI(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(pi(rnil)) → c68(PI(ok(rnil)), PROPER(rnil))
PROPER(pi(rcons(z0, z1))) → c68(PI(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(pi(from(z0))) → c68(PI(from(proper(z0))), PROPER(from(z0)))
PROPER(pi(2ndspos(z0, z1))) → c68(PI(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(pi(2ndsneg(z0, z1))) → c68(PI(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(pi(pi(z0))) → c68(PI(pi(proper(z0))), PROPER(pi(z0)))
PROPER(pi(plus(z0, z1))) → c68(PI(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(pi(times(z0, z1))) → c68(PI(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(pi(square(z0))) → c68(PI(square(proper(z0))), PROPER(square(z0)))

K tuples:none
Defined Rule Symbols:

active, rcons, posrecip, 2ndsneg, negrecip, 2ndspos, s, cons, from, pi, plus, times, square, proper

Defined Pair Symbols:

ACTIVE, S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP

Compound Symbols:

c10, c15, c16, c18, c19, c20, c21, c23, c24, c25, c26, 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, c69, c70, c71, c72, c73, c, c5, c7, c9, c1, c11, c12, c13, c14, c17, c22, c27, c58, c58, c59, c59, c60, c60, c62, c62, c64, c64, c65, c65, c66, c66, c67, c67, c68

(59) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)

Removed 3 trailing tuple parts

(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, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(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(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))
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))
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))
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(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)) → c10(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))
PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c58(S(ok(0)))
PROPER(s(nil)) → c58(S(ok(nil)))
PROPER(s(rnil)) → c58(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(rcons(x0, s(z0))) → c64(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c64(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c64(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, cons(z0, z1))) → c64(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, rcons(z0, z1))) → c64(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c64(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c64(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c64(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c64(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c64(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c64(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c64(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(s(z0), x1)) → c64(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c64(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c64(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c64(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c64(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c64(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c64(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c64(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c64(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c64(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c64(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c64(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(rcons(x0, 0)) → c64(RCONS(proper(x0), ok(0)), PROPER(x0))
PROPER(rcons(x0, nil)) → c64(RCONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(rcons(x0, rnil)) → c64(RCONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(rcons(0, x1)) → c64(RCONS(ok(0), proper(x1)), PROPER(x1))
PROPER(rcons(nil, x1)) → c64(RCONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c64(RCONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(from(s(z0))) → c65(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(posrecip(z0))) → c65(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(from(negrecip(z0))) → c65(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(from(cons(z0, z1))) → c65(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(rcons(z0, z1))) → c65(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(from(from(z0))) → c65(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(2ndspos(z0, z1))) → c65(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(from(2ndsneg(z0, z1))) → c65(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(from(pi(z0))) → c65(FROM(pi(proper(z0))), PROPER(pi(z0)))
PROPER(from(plus(z0, z1))) → c65(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(from(times(z0, z1))) → c65(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(from(square(z0))) → c65(FROM(square(proper(z0))), PROPER(square(z0)))
PROPER(from(0)) → c65(FROM(ok(0)))
PROPER(from(nil)) → c65(FROM(ok(nil)))
PROPER(from(rnil)) → c65(FROM(ok(rnil)))
PROPER(2ndspos(x0, s(z0))) → c66(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndspos(x0, posrecip(z0))) → c66(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndspos(x0, negrecip(z0))) → c66(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndspos(x0, cons(z0, z1))) → c66(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndspos(x0, rcons(z0, z1))) → c66(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndspos(x0, from(z0))) → c66(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndspos(x0, pi(z0))) → c66(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndspos(x0, plus(z0, z1))) → c66(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndspos(x0, times(z0, z1))) → c66(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndspos(x0, square(z0))) → c66(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndspos(s(z0), x1)) → c66(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndspos(posrecip(z0), x1)) → c66(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndspos(negrecip(z0), x1)) → c66(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndspos(cons(z0, z1), x1)) → c66(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndspos(rcons(z0, z1), x1)) → c66(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndspos(from(z0), x1)) → c66(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c66(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c66(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndspos(pi(z0), x1)) → c66(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndspos(plus(z0, z1), x1)) → c66(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndspos(times(z0, z1), x1)) → c66(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndspos(square(z0), x1)) → c66(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndspos(x0, 0)) → c66(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndspos(x0, nil)) → c66(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndspos(x0, rnil)) → c66(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndspos(0, x1)) → c66(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndspos(nil, x1)) → c66(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndspos(rnil, x1)) → c66(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(x0, s(z0))) → c67(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndsneg(x0, posrecip(z0))) → c67(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndsneg(x0, negrecip(z0))) → c67(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndsneg(x0, cons(z0, z1))) → c67(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndsneg(x0, rcons(z0, z1))) → c67(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndsneg(x0, from(z0))) → c67(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndsneg(x0, pi(z0))) → c67(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndsneg(x0, plus(z0, z1))) → c67(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndsneg(x0, times(z0, z1))) → c67(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndsneg(x0, square(z0))) → c67(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndsneg(s(z0), x1)) → c67(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndsneg(posrecip(z0), x1)) → c67(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndsneg(negrecip(z0), x1)) → c67(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndsneg(cons(z0, z1), x1)) → c67(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(rcons(z0, z1), x1)) → c67(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(from(z0), x1)) → c67(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c67(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c67(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndsneg(pi(z0), x1)) → c67(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndsneg(plus(z0, z1), x1)) → c67(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndsneg(times(z0, z1), x1)) → c67(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndsneg(square(z0), x1)) → c67(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndsneg(x0, 0)) → c67(2NDSNEG(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndsneg(x0, nil)) → c67(2NDSNEG(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndsneg(x0, rnil)) → c67(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndsneg(0, x1)) → c67(2NDSNEG(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndsneg(nil, x1)) → c67(2NDSNEG(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(rnil, x1)) → c67(2NDSNEG(ok(rnil), proper(x1)), PROPER(x1))
PROPER(pi(s(z0))) → c68(PI(s(proper(z0))), PROPER(s(z0)))
PROPER(pi(posrecip(z0))) → c68(PI(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(pi(negrecip(z0))) → c68(PI(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(pi(cons(z0, z1))) → c68(PI(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(pi(rcons(z0, z1))) → c68(PI(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(pi(from(z0))) → c68(PI(from(proper(z0))), PROPER(from(z0)))
PROPER(pi(2ndspos(z0, z1))) → c68(PI(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(pi(2ndsneg(z0, z1))) → c68(PI(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(pi(pi(z0))) → c68(PI(pi(proper(z0))), PROPER(pi(z0)))
PROPER(pi(plus(z0, z1))) → c68(PI(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(pi(times(z0, z1))) → c68(PI(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(pi(square(z0))) → c68(PI(square(proper(z0))), PROPER(square(z0)))
PROPER(pi(0)) → c68(PI(ok(0)))
PROPER(pi(nil)) → c68(PI(ok(nil)))
PROPER(pi(rnil)) → c68(PI(ok(rnil)))

S tuples:

ACTIVE(square(z0)) → c10(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))
PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c58(S(ok(0)))
PROPER(s(nil)) → c58(S(ok(nil)))
PROPER(s(rnil)) → c58(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(rcons(x0, s(z0))) → c64(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c64(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c64(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, cons(z0, z1))) → c64(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, rcons(z0, z1))) → c64(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c64(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c64(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c64(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c64(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c64(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c64(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c64(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(s(z0), x1)) → c64(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c64(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c64(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c64(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c64(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c64(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c64(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c64(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c64(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c64(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c64(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c64(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(rcons(x0, 0)) → c64(RCONS(proper(x0), ok(0)), PROPER(x0))
PROPER(rcons(x0, nil)) → c64(RCONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(rcons(x0, rnil)) → c64(RCONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(rcons(0, x1)) → c64(RCONS(ok(0), proper(x1)), PROPER(x1))
PROPER(rcons(nil, x1)) → c64(RCONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c64(RCONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(from(s(z0))) → c65(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(posrecip(z0))) → c65(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(from(negrecip(z0))) → c65(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(from(cons(z0, z1))) → c65(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(rcons(z0, z1))) → c65(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(from(from(z0))) → c65(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(2ndspos(z0, z1))) → c65(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(from(2ndsneg(z0, z1))) → c65(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(from(pi(z0))) → c65(FROM(pi(proper(z0))), PROPER(pi(z0)))
PROPER(from(plus(z0, z1))) → c65(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(from(times(z0, z1))) → c65(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(from(square(z0))) → c65(FROM(square(proper(z0))), PROPER(square(z0)))
PROPER(from(0)) → c65(FROM(ok(0)))
PROPER(from(nil)) → c65(FROM(ok(nil)))
PROPER(from(rnil)) → c65(FROM(ok(rnil)))
PROPER(2ndspos(x0, s(z0))) → c66(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndspos(x0, posrecip(z0))) → c66(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndspos(x0, negrecip(z0))) → c66(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndspos(x0, cons(z0, z1))) → c66(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndspos(x0, rcons(z0, z1))) → c66(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndspos(x0, from(z0))) → c66(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndspos(x0, pi(z0))) → c66(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndspos(x0, plus(z0, z1))) → c66(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndspos(x0, times(z0, z1))) → c66(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndspos(x0, square(z0))) → c66(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndspos(s(z0), x1)) → c66(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndspos(posrecip(z0), x1)) → c66(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndspos(negrecip(z0), x1)) → c66(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndspos(cons(z0, z1), x1)) → c66(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndspos(rcons(z0, z1), x1)) → c66(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndspos(from(z0), x1)) → c66(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c66(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c66(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndspos(pi(z0), x1)) → c66(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndspos(plus(z0, z1), x1)) → c66(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndspos(times(z0, z1), x1)) → c66(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndspos(square(z0), x1)) → c66(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndspos(x0, 0)) → c66(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndspos(x0, nil)) → c66(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndspos(x0, rnil)) → c66(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndspos(0, x1)) → c66(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndspos(nil, x1)) → c66(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndspos(rnil, x1)) → c66(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(x0, s(z0))) → c67(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndsneg(x0, posrecip(z0))) → c67(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndsneg(x0, negrecip(z0))) → c67(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndsneg(x0, cons(z0, z1))) → c67(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndsneg(x0, rcons(z0, z1))) → c67(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndsneg(x0, from(z0))) → c67(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndsneg(x0, pi(z0))) → c67(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndsneg(x0, plus(z0, z1))) → c67(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndsneg(x0, times(z0, z1))) → c67(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndsneg(x0, square(z0))) → c67(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndsneg(s(z0), x1)) → c67(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndsneg(posrecip(z0), x1)) → c67(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndsneg(negrecip(z0), x1)) → c67(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndsneg(cons(z0, z1), x1)) → c67(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(rcons(z0, z1), x1)) → c67(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(from(z0), x1)) → c67(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c67(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c67(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndsneg(pi(z0), x1)) → c67(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndsneg(plus(z0, z1), x1)) → c67(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndsneg(times(z0, z1), x1)) → c67(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndsneg(square(z0), x1)) → c67(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndsneg(x0, 0)) → c67(2NDSNEG(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndsneg(x0, nil)) → c67(2NDSNEG(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndsneg(x0, rnil)) → c67(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndsneg(0, x1)) → c67(2NDSNEG(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndsneg(nil, x1)) → c67(2NDSNEG(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(rnil, x1)) → c67(2NDSNEG(ok(rnil), proper(x1)), PROPER(x1))
PROPER(pi(s(z0))) → c68(PI(s(proper(z0))), PROPER(s(z0)))
PROPER(pi(posrecip(z0))) → c68(PI(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(pi(negrecip(z0))) → c68(PI(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(pi(cons(z0, z1))) → c68(PI(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(pi(rcons(z0, z1))) → c68(PI(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(pi(from(z0))) → c68(PI(from(proper(z0))), PROPER(from(z0)))
PROPER(pi(2ndspos(z0, z1))) → c68(PI(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(pi(2ndsneg(z0, z1))) → c68(PI(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(pi(pi(z0))) → c68(PI(pi(proper(z0))), PROPER(pi(z0)))
PROPER(pi(plus(z0, z1))) → c68(PI(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(pi(times(z0, z1))) → c68(PI(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(pi(square(z0))) → c68(PI(square(proper(z0))), PROPER(square(z0)))
PROPER(pi(0)) → c68(PI(ok(0)))
PROPER(pi(nil)) → c68(PI(ok(nil)))
PROPER(pi(rnil)) → c68(PI(ok(rnil)))

K tuples:none
Defined Rule Symbols:

active, rcons, posrecip, 2ndsneg, negrecip, 2ndspos, s, cons, from, pi, plus, times, square, proper

Defined Pair Symbols:

ACTIVE, S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP

Compound Symbols:

c10, c15, c16, c18, c19, c20, c21, c23, c24, c25, c26, 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, c69, c70, c71, c72, c73, c, c5, c7, c9, c1, c11, c12, c13, c14, c17, c22, c27, c58, c58, c59, c59, c60, c60, c62, c62, c64, c64, c65, c65, c66, c66, c67, c67, c68, c68

(61) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

Use narrowing to replace PROPER(plus(z0, z1)) → c69(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) by

PROPER(plus(x0, 0)) → c69(PLUS(proper(x0), ok(0)), PROPER(x0), PROPER(0))
PROPER(plus(x0, s(z0))) → c69(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(plus(x0, posrecip(z0))) → c69(PLUS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(plus(x0, negrecip(z0))) → c69(PLUS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(plus(x0, nil)) → c69(PLUS(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
PROPER(plus(x0, cons(z0, z1))) → c69(PLUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(plus(x0, rnil)) → c69(PLUS(proper(x0), ok(rnil)), PROPER(x0), PROPER(rnil))
PROPER(plus(x0, rcons(z0, z1))) → c69(PLUS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(plus(x0, from(z0))) → c69(PLUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(plus(x0, 2ndspos(z0, z1))) → c69(PLUS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(plus(x0, 2ndsneg(z0, z1))) → c69(PLUS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(plus(x0, pi(z0))) → c69(PLUS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(plus(x0, plus(z0, z1))) → c69(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(plus(x0, times(z0, z1))) → c69(PLUS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(plus(x0, square(z0))) → c69(PLUS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(plus(0, x1)) → c69(PLUS(ok(0), proper(x1)), PROPER(0), PROPER(x1))
PROPER(plus(s(z0), x1)) → c69(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(plus(posrecip(z0), x1)) → c69(PLUS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(plus(negrecip(z0), x1)) → c69(PLUS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(plus(nil, x1)) → c69(PLUS(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
PROPER(plus(cons(z0, z1), x1)) → c69(PLUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(plus(rnil, x1)) → c69(PLUS(ok(rnil), proper(x1)), PROPER(rnil), PROPER(x1))
PROPER(plus(rcons(z0, z1), x1)) → c69(PLUS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(plus(from(z0), x1)) → c69(PLUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(plus(2ndspos(z0, z1), x1)) → c69(PLUS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(plus(2ndsneg(z0, z1), x1)) → c69(PLUS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(plus(pi(z0), x1)) → c69(PLUS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(plus(plus(z0, z1), x1)) → c69(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(plus(times(z0, z1), x1)) → c69(PLUS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(plus(square(z0), x1)) → c69(PLUS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))

(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, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(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(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))
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))
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))
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(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)) → c10(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))
PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c58(S(ok(0)))
PROPER(s(nil)) → c58(S(ok(nil)))
PROPER(s(rnil)) → c58(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(rcons(x0, s(z0))) → c64(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c64(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c64(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, cons(z0, z1))) → c64(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, rcons(z0, z1))) → c64(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c64(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c64(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c64(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c64(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c64(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c64(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c64(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(s(z0), x1)) → c64(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c64(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c64(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c64(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c64(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c64(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c64(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c64(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c64(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c64(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c64(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c64(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(rcons(x0, 0)) → c64(RCONS(proper(x0), ok(0)), PROPER(x0))
PROPER(rcons(x0, nil)) → c64(RCONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(rcons(x0, rnil)) → c64(RCONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(rcons(0, x1)) → c64(RCONS(ok(0), proper(x1)), PROPER(x1))
PROPER(rcons(nil, x1)) → c64(RCONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c64(RCONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(from(s(z0))) → c65(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(posrecip(z0))) → c65(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(from(negrecip(z0))) → c65(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(from(cons(z0, z1))) → c65(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(rcons(z0, z1))) → c65(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(from(from(z0))) → c65(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(2ndspos(z0, z1))) → c65(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(from(2ndsneg(z0, z1))) → c65(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(from(pi(z0))) → c65(FROM(pi(proper(z0))), PROPER(pi(z0)))
PROPER(from(plus(z0, z1))) → c65(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(from(times(z0, z1))) → c65(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(from(square(z0))) → c65(FROM(square(proper(z0))), PROPER(square(z0)))
PROPER(from(0)) → c65(FROM(ok(0)))
PROPER(from(nil)) → c65(FROM(ok(nil)))
PROPER(from(rnil)) → c65(FROM(ok(rnil)))
PROPER(2ndspos(x0, s(z0))) → c66(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndspos(x0, posrecip(z0))) → c66(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndspos(x0, negrecip(z0))) → c66(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndspos(x0, cons(z0, z1))) → c66(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndspos(x0, rcons(z0, z1))) → c66(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndspos(x0, from(z0))) → c66(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndspos(x0, pi(z0))) → c66(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndspos(x0, plus(z0, z1))) → c66(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndspos(x0, times(z0, z1))) → c66(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndspos(x0, square(z0))) → c66(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndspos(s(z0), x1)) → c66(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndspos(posrecip(z0), x1)) → c66(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndspos(negrecip(z0), x1)) → c66(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndspos(cons(z0, z1), x1)) → c66(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndspos(rcons(z0, z1), x1)) → c66(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndspos(from(z0), x1)) → c66(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c66(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c66(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndspos(pi(z0), x1)) → c66(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndspos(plus(z0, z1), x1)) → c66(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndspos(times(z0, z1), x1)) → c66(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndspos(square(z0), x1)) → c66(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndspos(x0, 0)) → c66(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndspos(x0, nil)) → c66(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndspos(x0, rnil)) → c66(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndspos(0, x1)) → c66(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndspos(nil, x1)) → c66(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndspos(rnil, x1)) → c66(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(x0, s(z0))) → c67(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndsneg(x0, posrecip(z0))) → c67(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndsneg(x0, negrecip(z0))) → c67(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndsneg(x0, cons(z0, z1))) → c67(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndsneg(x0, rcons(z0, z1))) → c67(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndsneg(x0, from(z0))) → c67(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndsneg(x0, pi(z0))) → c67(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndsneg(x0, plus(z0, z1))) → c67(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndsneg(x0, times(z0, z1))) → c67(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndsneg(x0, square(z0))) → c67(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndsneg(s(z0), x1)) → c67(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndsneg(posrecip(z0), x1)) → c67(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndsneg(negrecip(z0), x1)) → c67(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndsneg(cons(z0, z1), x1)) → c67(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(rcons(z0, z1), x1)) → c67(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(from(z0), x1)) → c67(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c67(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c67(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndsneg(pi(z0), x1)) → c67(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndsneg(plus(z0, z1), x1)) → c67(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndsneg(times(z0, z1), x1)) → c67(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndsneg(square(z0), x1)) → c67(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndsneg(x0, 0)) → c67(2NDSNEG(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndsneg(x0, nil)) → c67(2NDSNEG(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndsneg(x0, rnil)) → c67(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndsneg(0, x1)) → c67(2NDSNEG(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndsneg(nil, x1)) → c67(2NDSNEG(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(rnil, x1)) → c67(2NDSNEG(ok(rnil), proper(x1)), PROPER(x1))
PROPER(pi(s(z0))) → c68(PI(s(proper(z0))), PROPER(s(z0)))
PROPER(pi(posrecip(z0))) → c68(PI(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(pi(negrecip(z0))) → c68(PI(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(pi(cons(z0, z1))) → c68(PI(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(pi(rcons(z0, z1))) → c68(PI(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(pi(from(z0))) → c68(PI(from(proper(z0))), PROPER(from(z0)))
PROPER(pi(2ndspos(z0, z1))) → c68(PI(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(pi(2ndsneg(z0, z1))) → c68(PI(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(pi(pi(z0))) → c68(PI(pi(proper(z0))), PROPER(pi(z0)))
PROPER(pi(plus(z0, z1))) → c68(PI(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(pi(times(z0, z1))) → c68(PI(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(pi(square(z0))) → c68(PI(square(proper(z0))), PROPER(square(z0)))
PROPER(pi(0)) → c68(PI(ok(0)))
PROPER(pi(nil)) → c68(PI(ok(nil)))
PROPER(pi(rnil)) → c68(PI(ok(rnil)))
PROPER(plus(x0, 0)) → c69(PLUS(proper(x0), ok(0)), PROPER(x0), PROPER(0))
PROPER(plus(x0, s(z0))) → c69(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(plus(x0, posrecip(z0))) → c69(PLUS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(plus(x0, negrecip(z0))) → c69(PLUS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(plus(x0, nil)) → c69(PLUS(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
PROPER(plus(x0, cons(z0, z1))) → c69(PLUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(plus(x0, rnil)) → c69(PLUS(proper(x0), ok(rnil)), PROPER(x0), PROPER(rnil))
PROPER(plus(x0, rcons(z0, z1))) → c69(PLUS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(plus(x0, from(z0))) → c69(PLUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(plus(x0, 2ndspos(z0, z1))) → c69(PLUS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(plus(x0, 2ndsneg(z0, z1))) → c69(PLUS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(plus(x0, pi(z0))) → c69(PLUS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(plus(x0, plus(z0, z1))) → c69(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(plus(x0, times(z0, z1))) → c69(PLUS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(plus(x0, square(z0))) → c69(PLUS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(plus(0, x1)) → c69(PLUS(ok(0), proper(x1)), PROPER(0), PROPER(x1))
PROPER(plus(s(z0), x1)) → c69(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(plus(posrecip(z0), x1)) → c69(PLUS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(plus(negrecip(z0), x1)) → c69(PLUS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(plus(nil, x1)) → c69(PLUS(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
PROPER(plus(cons(z0, z1), x1)) → c69(PLUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(plus(rnil, x1)) → c69(PLUS(ok(rnil), proper(x1)), PROPER(rnil), PROPER(x1))
PROPER(plus(rcons(z0, z1), x1)) → c69(PLUS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(plus(from(z0), x1)) → c69(PLUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(plus(2ndspos(z0, z1), x1)) → c69(PLUS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(plus(2ndsneg(z0, z1), x1)) → c69(PLUS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(plus(pi(z0), x1)) → c69(PLUS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(plus(plus(z0, z1), x1)) → c69(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(plus(times(z0, z1), x1)) → c69(PLUS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(plus(square(z0), x1)) → c69(PLUS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))

S tuples:

ACTIVE(square(z0)) → c10(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))
PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c58(S(ok(0)))
PROPER(s(nil)) → c58(S(ok(nil)))
PROPER(s(rnil)) → c58(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(rcons(x0, s(z0))) → c64(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c64(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c64(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, cons(z0, z1))) → c64(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, rcons(z0, z1))) → c64(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c64(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c64(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c64(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c64(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c64(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c64(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c64(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(s(z0), x1)) → c64(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c64(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c64(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c64(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c64(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c64(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c64(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c64(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c64(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c64(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c64(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c64(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(rcons(x0, 0)) → c64(RCONS(proper(x0), ok(0)), PROPER(x0))
PROPER(rcons(x0, nil)) → c64(RCONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(rcons(x0, rnil)) → c64(RCONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(rcons(0, x1)) → c64(RCONS(ok(0), proper(x1)), PROPER(x1))
PROPER(rcons(nil, x1)) → c64(RCONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c64(RCONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(from(s(z0))) → c65(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(posrecip(z0))) → c65(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(from(negrecip(z0))) → c65(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(from(cons(z0, z1))) → c65(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(rcons(z0, z1))) → c65(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(from(from(z0))) → c65(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(2ndspos(z0, z1))) → c65(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(from(2ndsneg(z0, z1))) → c65(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(from(pi(z0))) → c65(FROM(pi(proper(z0))), PROPER(pi(z0)))
PROPER(from(plus(z0, z1))) → c65(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(from(times(z0, z1))) → c65(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(from(square(z0))) → c65(FROM(square(proper(z0))), PROPER(square(z0)))
PROPER(from(0)) → c65(FROM(ok(0)))
PROPER(from(nil)) → c65(FROM(ok(nil)))
PROPER(from(rnil)) → c65(FROM(ok(rnil)))
PROPER(2ndspos(x0, s(z0))) → c66(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndspos(x0, posrecip(z0))) → c66(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndspos(x0, negrecip(z0))) → c66(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndspos(x0, cons(z0, z1))) → c66(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndspos(x0, rcons(z0, z1))) → c66(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndspos(x0, from(z0))) → c66(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndspos(x0, pi(z0))) → c66(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndspos(x0, plus(z0, z1))) → c66(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndspos(x0, times(z0, z1))) → c66(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndspos(x0, square(z0))) → c66(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndspos(s(z0), x1)) → c66(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndspos(posrecip(z0), x1)) → c66(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndspos(negrecip(z0), x1)) → c66(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndspos(cons(z0, z1), x1)) → c66(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndspos(rcons(z0, z1), x1)) → c66(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndspos(from(z0), x1)) → c66(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c66(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c66(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndspos(pi(z0), x1)) → c66(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndspos(plus(z0, z1), x1)) → c66(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndspos(times(z0, z1), x1)) → c66(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndspos(square(z0), x1)) → c66(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndspos(x0, 0)) → c66(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndspos(x0, nil)) → c66(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndspos(x0, rnil)) → c66(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndspos(0, x1)) → c66(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndspos(nil, x1)) → c66(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndspos(rnil, x1)) → c66(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(x0, s(z0))) → c67(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndsneg(x0, posrecip(z0))) → c67(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndsneg(x0, negrecip(z0))) → c67(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndsneg(x0, cons(z0, z1))) → c67(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndsneg(x0, rcons(z0, z1))) → c67(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndsneg(x0, from(z0))) → c67(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndsneg(x0, pi(z0))) → c67(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndsneg(x0, plus(z0, z1))) → c67(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndsneg(x0, times(z0, z1))) → c67(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndsneg(x0, square(z0))) → c67(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndsneg(s(z0), x1)) → c67(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndsneg(posrecip(z0), x1)) → c67(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndsneg(negrecip(z0), x1)) → c67(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndsneg(cons(z0, z1), x1)) → c67(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(rcons(z0, z1), x1)) → c67(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(from(z0), x1)) → c67(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c67(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c67(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndsneg(pi(z0), x1)) → c67(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndsneg(plus(z0, z1), x1)) → c67(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndsneg(times(z0, z1), x1)) → c67(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndsneg(square(z0), x1)) → c67(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndsneg(x0, 0)) → c67(2NDSNEG(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndsneg(x0, nil)) → c67(2NDSNEG(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndsneg(x0, rnil)) → c67(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndsneg(0, x1)) → c67(2NDSNEG(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndsneg(nil, x1)) → c67(2NDSNEG(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(rnil, x1)) → c67(2NDSNEG(ok(rnil), proper(x1)), PROPER(x1))
PROPER(pi(s(z0))) → c68(PI(s(proper(z0))), PROPER(s(z0)))
PROPER(pi(posrecip(z0))) → c68(PI(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(pi(negrecip(z0))) → c68(PI(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(pi(cons(z0, z1))) → c68(PI(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(pi(rcons(z0, z1))) → c68(PI(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(pi(from(z0))) → c68(PI(from(proper(z0))), PROPER(from(z0)))
PROPER(pi(2ndspos(z0, z1))) → c68(PI(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(pi(2ndsneg(z0, z1))) → c68(PI(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(pi(pi(z0))) → c68(PI(pi(proper(z0))), PROPER(pi(z0)))
PROPER(pi(plus(z0, z1))) → c68(PI(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(pi(times(z0, z1))) → c68(PI(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(pi(square(z0))) → c68(PI(square(proper(z0))), PROPER(square(z0)))
PROPER(pi(0)) → c68(PI(ok(0)))
PROPER(pi(nil)) → c68(PI(ok(nil)))
PROPER(pi(rnil)) → c68(PI(ok(rnil)))
PROPER(plus(x0, 0)) → c69(PLUS(proper(x0), ok(0)), PROPER(x0), PROPER(0))
PROPER(plus(x0, s(z0))) → c69(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(plus(x0, posrecip(z0))) → c69(PLUS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(plus(x0, negrecip(z0))) → c69(PLUS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(plus(x0, nil)) → c69(PLUS(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
PROPER(plus(x0, cons(z0, z1))) → c69(PLUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(plus(x0, rnil)) → c69(PLUS(proper(x0), ok(rnil)), PROPER(x0), PROPER(rnil))
PROPER(plus(x0, rcons(z0, z1))) → c69(PLUS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(plus(x0, from(z0))) → c69(PLUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(plus(x0, 2ndspos(z0, z1))) → c69(PLUS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(plus(x0, 2ndsneg(z0, z1))) → c69(PLUS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(plus(x0, pi(z0))) → c69(PLUS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(plus(x0, plus(z0, z1))) → c69(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(plus(x0, times(z0, z1))) → c69(PLUS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(plus(x0, square(z0))) → c69(PLUS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(plus(0, x1)) → c69(PLUS(ok(0), proper(x1)), PROPER(0), PROPER(x1))
PROPER(plus(s(z0), x1)) → c69(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(plus(posrecip(z0), x1)) → c69(PLUS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(plus(negrecip(z0), x1)) → c69(PLUS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(plus(nil, x1)) → c69(PLUS(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
PROPER(plus(cons(z0, z1), x1)) → c69(PLUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(plus(rnil, x1)) → c69(PLUS(ok(rnil), proper(x1)), PROPER(rnil), PROPER(x1))
PROPER(plus(rcons(z0, z1), x1)) → c69(PLUS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(plus(from(z0), x1)) → c69(PLUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(plus(2ndspos(z0, z1), x1)) → c69(PLUS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(plus(2ndsneg(z0, z1), x1)) → c69(PLUS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(plus(pi(z0), x1)) → c69(PLUS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(plus(plus(z0, z1), x1)) → c69(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(plus(times(z0, z1), x1)) → c69(PLUS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(plus(square(z0), x1)) → c69(PLUS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))

K tuples:none
Defined Rule Symbols:

active, rcons, posrecip, 2ndsneg, negrecip, 2ndspos, s, cons, from, pi, plus, times, square, proper

Defined Pair Symbols:

ACTIVE, S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP

Compound Symbols:

c10, c15, c16, c18, c19, c20, c21, c23, c24, c25, c26, 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, c70, c71, c72, c73, c, c5, c7, c9, c1, c11, c12, c13, c14, c17, c22, c27, c58, c58, c59, c59, c60, c60, c62, c62, c64, c64, c65, c65, c66, c66, c67, c67, c68, c68, c69

(63) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)

Removed 6 trailing tuple parts

(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, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(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(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))
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))
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))
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(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)) → c10(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))
PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c58(S(ok(0)))
PROPER(s(nil)) → c58(S(ok(nil)))
PROPER(s(rnil)) → c58(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(rcons(x0, s(z0))) → c64(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c64(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c64(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, cons(z0, z1))) → c64(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, rcons(z0, z1))) → c64(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c64(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c64(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c64(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c64(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c64(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c64(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c64(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(s(z0), x1)) → c64(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c64(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c64(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c64(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c64(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c64(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c64(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c64(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c64(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c64(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c64(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c64(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(rcons(x0, 0)) → c64(RCONS(proper(x0), ok(0)), PROPER(x0))
PROPER(rcons(x0, nil)) → c64(RCONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(rcons(x0, rnil)) → c64(RCONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(rcons(0, x1)) → c64(RCONS(ok(0), proper(x1)), PROPER(x1))
PROPER(rcons(nil, x1)) → c64(RCONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c64(RCONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(from(s(z0))) → c65(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(posrecip(z0))) → c65(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(from(negrecip(z0))) → c65(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(from(cons(z0, z1))) → c65(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(rcons(z0, z1))) → c65(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(from(from(z0))) → c65(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(2ndspos(z0, z1))) → c65(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(from(2ndsneg(z0, z1))) → c65(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(from(pi(z0))) → c65(FROM(pi(proper(z0))), PROPER(pi(z0)))
PROPER(from(plus(z0, z1))) → c65(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(from(times(z0, z1))) → c65(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(from(square(z0))) → c65(FROM(square(proper(z0))), PROPER(square(z0)))
PROPER(from(0)) → c65(FROM(ok(0)))
PROPER(from(nil)) → c65(FROM(ok(nil)))
PROPER(from(rnil)) → c65(FROM(ok(rnil)))
PROPER(2ndspos(x0, s(z0))) → c66(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndspos(x0, posrecip(z0))) → c66(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndspos(x0, negrecip(z0))) → c66(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndspos(x0, cons(z0, z1))) → c66(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndspos(x0, rcons(z0, z1))) → c66(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndspos(x0, from(z0))) → c66(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndspos(x0, pi(z0))) → c66(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndspos(x0, plus(z0, z1))) → c66(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndspos(x0, times(z0, z1))) → c66(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndspos(x0, square(z0))) → c66(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndspos(s(z0), x1)) → c66(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndspos(posrecip(z0), x1)) → c66(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndspos(negrecip(z0), x1)) → c66(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndspos(cons(z0, z1), x1)) → c66(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndspos(rcons(z0, z1), x1)) → c66(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndspos(from(z0), x1)) → c66(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c66(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c66(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndspos(pi(z0), x1)) → c66(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndspos(plus(z0, z1), x1)) → c66(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndspos(times(z0, z1), x1)) → c66(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndspos(square(z0), x1)) → c66(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndspos(x0, 0)) → c66(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndspos(x0, nil)) → c66(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndspos(x0, rnil)) → c66(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndspos(0, x1)) → c66(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndspos(nil, x1)) → c66(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndspos(rnil, x1)) → c66(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(x0, s(z0))) → c67(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndsneg(x0, posrecip(z0))) → c67(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndsneg(x0, negrecip(z0))) → c67(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndsneg(x0, cons(z0, z1))) → c67(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndsneg(x0, rcons(z0, z1))) → c67(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndsneg(x0, from(z0))) → c67(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndsneg(x0, pi(z0))) → c67(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndsneg(x0, plus(z0, z1))) → c67(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndsneg(x0, times(z0, z1))) → c67(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndsneg(x0, square(z0))) → c67(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndsneg(s(z0), x1)) → c67(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndsneg(posrecip(z0), x1)) → c67(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndsneg(negrecip(z0), x1)) → c67(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndsneg(cons(z0, z1), x1)) → c67(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(rcons(z0, z1), x1)) → c67(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(from(z0), x1)) → c67(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c67(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c67(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndsneg(pi(z0), x1)) → c67(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndsneg(plus(z0, z1), x1)) → c67(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndsneg(times(z0, z1), x1)) → c67(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndsneg(square(z0), x1)) → c67(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndsneg(x0, 0)) → c67(2NDSNEG(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndsneg(x0, nil)) → c67(2NDSNEG(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndsneg(x0, rnil)) → c67(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndsneg(0, x1)) → c67(2NDSNEG(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndsneg(nil, x1)) → c67(2NDSNEG(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(rnil, x1)) → c67(2NDSNEG(ok(rnil), proper(x1)), PROPER(x1))
PROPER(pi(s(z0))) → c68(PI(s(proper(z0))), PROPER(s(z0)))
PROPER(pi(posrecip(z0))) → c68(PI(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(pi(negrecip(z0))) → c68(PI(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(pi(cons(z0, z1))) → c68(PI(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(pi(rcons(z0, z1))) → c68(PI(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(pi(from(z0))) → c68(PI(from(proper(z0))), PROPER(from(z0)))
PROPER(pi(2ndspos(z0, z1))) → c68(PI(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(pi(2ndsneg(z0, z1))) → c68(PI(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(pi(pi(z0))) → c68(PI(pi(proper(z0))), PROPER(pi(z0)))
PROPER(pi(plus(z0, z1))) → c68(PI(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(pi(times(z0, z1))) → c68(PI(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(pi(square(z0))) → c68(PI(square(proper(z0))), PROPER(square(z0)))
PROPER(pi(0)) → c68(PI(ok(0)))
PROPER(pi(nil)) → c68(PI(ok(nil)))
PROPER(pi(rnil)) → c68(PI(ok(rnil)))
PROPER(plus(x0, s(z0))) → c69(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(plus(x0, posrecip(z0))) → c69(PLUS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(plus(x0, negrecip(z0))) → c69(PLUS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(plus(x0, cons(z0, z1))) → c69(PLUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(plus(x0, rcons(z0, z1))) → c69(PLUS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(plus(x0, from(z0))) → c69(PLUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(plus(x0, 2ndspos(z0, z1))) → c69(PLUS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(plus(x0, 2ndsneg(z0, z1))) → c69(PLUS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(plus(x0, pi(z0))) → c69(PLUS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(plus(x0, plus(z0, z1))) → c69(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(plus(x0, times(z0, z1))) → c69(PLUS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(plus(x0, square(z0))) → c69(PLUS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(plus(s(z0), x1)) → c69(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(plus(posrecip(z0), x1)) → c69(PLUS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(plus(negrecip(z0), x1)) → c69(PLUS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(plus(cons(z0, z1), x1)) → c69(PLUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(plus(rcons(z0, z1), x1)) → c69(PLUS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(plus(from(z0), x1)) → c69(PLUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(plus(2ndspos(z0, z1), x1)) → c69(PLUS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(plus(2ndsneg(z0, z1), x1)) → c69(PLUS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(plus(pi(z0), x1)) → c69(PLUS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(plus(plus(z0, z1), x1)) → c69(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(plus(times(z0, z1), x1)) → c69(PLUS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(plus(square(z0), x1)) → c69(PLUS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(plus(x0, 0)) → c69(PLUS(proper(x0), ok(0)), PROPER(x0))
PROPER(plus(x0, nil)) → c69(PLUS(proper(x0), ok(nil)), PROPER(x0))
PROPER(plus(x0, rnil)) → c69(PLUS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(plus(0, x1)) → c69(PLUS(ok(0), proper(x1)), PROPER(x1))
PROPER(plus(nil, x1)) → c69(PLUS(ok(nil), proper(x1)), PROPER(x1))
PROPER(plus(rnil, x1)) → c69(PLUS(ok(rnil), proper(x1)), PROPER(x1))

S tuples:

ACTIVE(square(z0)) → c10(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))
PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c58(S(ok(0)))
PROPER(s(nil)) → c58(S(ok(nil)))
PROPER(s(rnil)) → c58(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(rcons(x0, s(z0))) → c64(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c64(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c64(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, cons(z0, z1))) → c64(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, rcons(z0, z1))) → c64(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c64(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c64(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c64(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c64(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c64(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c64(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c64(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(s(z0), x1)) → c64(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c64(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c64(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c64(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c64(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c64(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c64(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c64(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c64(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c64(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c64(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c64(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(rcons(x0, 0)) → c64(RCONS(proper(x0), ok(0)), PROPER(x0))
PROPER(rcons(x0, nil)) → c64(RCONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(rcons(x0, rnil)) → c64(RCONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(rcons(0, x1)) → c64(RCONS(ok(0), proper(x1)), PROPER(x1))
PROPER(rcons(nil, x1)) → c64(RCONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c64(RCONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(from(s(z0))) → c65(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(posrecip(z0))) → c65(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(from(negrecip(z0))) → c65(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(from(cons(z0, z1))) → c65(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(rcons(z0, z1))) → c65(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(from(from(z0))) → c65(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(2ndspos(z0, z1))) → c65(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(from(2ndsneg(z0, z1))) → c65(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(from(pi(z0))) → c65(FROM(pi(proper(z0))), PROPER(pi(z0)))
PROPER(from(plus(z0, z1))) → c65(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(from(times(z0, z1))) → c65(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(from(square(z0))) → c65(FROM(square(proper(z0))), PROPER(square(z0)))
PROPER(from(0)) → c65(FROM(ok(0)))
PROPER(from(nil)) → c65(FROM(ok(nil)))
PROPER(from(rnil)) → c65(FROM(ok(rnil)))
PROPER(2ndspos(x0, s(z0))) → c66(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndspos(x0, posrecip(z0))) → c66(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndspos(x0, negrecip(z0))) → c66(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndspos(x0, cons(z0, z1))) → c66(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndspos(x0, rcons(z0, z1))) → c66(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndspos(x0, from(z0))) → c66(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndspos(x0, pi(z0))) → c66(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndspos(x0, plus(z0, z1))) → c66(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndspos(x0, times(z0, z1))) → c66(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndspos(x0, square(z0))) → c66(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndspos(s(z0), x1)) → c66(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndspos(posrecip(z0), x1)) → c66(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndspos(negrecip(z0), x1)) → c66(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndspos(cons(z0, z1), x1)) → c66(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndspos(rcons(z0, z1), x1)) → c66(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndspos(from(z0), x1)) → c66(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c66(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c66(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndspos(pi(z0), x1)) → c66(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndspos(plus(z0, z1), x1)) → c66(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndspos(times(z0, z1), x1)) → c66(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndspos(square(z0), x1)) → c66(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndspos(x0, 0)) → c66(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndspos(x0, nil)) → c66(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndspos(x0, rnil)) → c66(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndspos(0, x1)) → c66(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndspos(nil, x1)) → c66(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndspos(rnil, x1)) → c66(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(x0, s(z0))) → c67(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndsneg(x0, posrecip(z0))) → c67(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndsneg(x0, negrecip(z0))) → c67(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndsneg(x0, cons(z0, z1))) → c67(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndsneg(x0, rcons(z0, z1))) → c67(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndsneg(x0, from(z0))) → c67(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndsneg(x0, pi(z0))) → c67(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndsneg(x0, plus(z0, z1))) → c67(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndsneg(x0, times(z0, z1))) → c67(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndsneg(x0, square(z0))) → c67(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndsneg(s(z0), x1)) → c67(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndsneg(posrecip(z0), x1)) → c67(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndsneg(negrecip(z0), x1)) → c67(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndsneg(cons(z0, z1), x1)) → c67(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(rcons(z0, z1), x1)) → c67(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(from(z0), x1)) → c67(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c67(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c67(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndsneg(pi(z0), x1)) → c67(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndsneg(plus(z0, z1), x1)) → c67(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndsneg(times(z0, z1), x1)) → c67(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndsneg(square(z0), x1)) → c67(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndsneg(x0, 0)) → c67(2NDSNEG(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndsneg(x0, nil)) → c67(2NDSNEG(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndsneg(x0, rnil)) → c67(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndsneg(0, x1)) → c67(2NDSNEG(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndsneg(nil, x1)) → c67(2NDSNEG(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(rnil, x1)) → c67(2NDSNEG(ok(rnil), proper(x1)), PROPER(x1))
PROPER(pi(s(z0))) → c68(PI(s(proper(z0))), PROPER(s(z0)))
PROPER(pi(posrecip(z0))) → c68(PI(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(pi(negrecip(z0))) → c68(PI(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(pi(cons(z0, z1))) → c68(PI(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(pi(rcons(z0, z1))) → c68(PI(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(pi(from(z0))) → c68(PI(from(proper(z0))), PROPER(from(z0)))
PROPER(pi(2ndspos(z0, z1))) → c68(PI(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(pi(2ndsneg(z0, z1))) → c68(PI(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(pi(pi(z0))) → c68(PI(pi(proper(z0))), PROPER(pi(z0)))
PROPER(pi(plus(z0, z1))) → c68(PI(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(pi(times(z0, z1))) → c68(PI(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(pi(square(z0))) → c68(PI(square(proper(z0))), PROPER(square(z0)))
PROPER(pi(0)) → c68(PI(ok(0)))
PROPER(pi(nil)) → c68(PI(ok(nil)))
PROPER(pi(rnil)) → c68(PI(ok(rnil)))
PROPER(plus(x0, s(z0))) → c69(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(plus(x0, posrecip(z0))) → c69(PLUS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(plus(x0, negrecip(z0))) → c69(PLUS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(plus(x0, cons(z0, z1))) → c69(PLUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(plus(x0, rcons(z0, z1))) → c69(PLUS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(plus(x0, from(z0))) → c69(PLUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(plus(x0, 2ndspos(z0, z1))) → c69(PLUS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(plus(x0, 2ndsneg(z0, z1))) → c69(PLUS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(plus(x0, pi(z0))) → c69(PLUS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(plus(x0, plus(z0, z1))) → c69(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(plus(x0, times(z0, z1))) → c69(PLUS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(plus(x0, square(z0))) → c69(PLUS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(plus(s(z0), x1)) → c69(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(plus(posrecip(z0), x1)) → c69(PLUS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(plus(negrecip(z0), x1)) → c69(PLUS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(plus(cons(z0, z1), x1)) → c69(PLUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(plus(rcons(z0, z1), x1)) → c69(PLUS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(plus(from(z0), x1)) → c69(PLUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(plus(2ndspos(z0, z1), x1)) → c69(PLUS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(plus(2ndsneg(z0, z1), x1)) → c69(PLUS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(plus(pi(z0), x1)) → c69(PLUS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(plus(plus(z0, z1), x1)) → c69(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(plus(times(z0, z1), x1)) → c69(PLUS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(plus(square(z0), x1)) → c69(PLUS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(plus(x0, 0)) → c69(PLUS(proper(x0), ok(0)), PROPER(x0))
PROPER(plus(x0, nil)) → c69(PLUS(proper(x0), ok(nil)), PROPER(x0))
PROPER(plus(x0, rnil)) → c69(PLUS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(plus(0, x1)) → c69(PLUS(ok(0), proper(x1)), PROPER(x1))
PROPER(plus(nil, x1)) → c69(PLUS(ok(nil), proper(x1)), PROPER(x1))
PROPER(plus(rnil, x1)) → c69(PLUS(ok(rnil), proper(x1)), PROPER(x1))

K tuples:none
Defined Rule Symbols:

active, rcons, posrecip, 2ndsneg, negrecip, 2ndspos, s, cons, from, pi, plus, times, square, proper

Defined Pair Symbols:

ACTIVE, S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP

Compound Symbols:

c10, c15, c16, c18, c19, c20, c21, c23, c24, c25, c26, 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, c70, c71, c72, c73, c, c5, c7, c9, c1, c11, c12, c13, c14, c17, c22, c27, c58, c58, c59, c59, c60, c60, c62, c62, c64, c64, c65, c65, c66, c66, c67, c67, c68, c68, c69, c69

(65) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

Use narrowing to replace PROPER(times(z0, z1)) → c70(TIMES(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) by

PROPER(times(x0, 0)) → c70(TIMES(proper(x0), ok(0)), PROPER(x0), PROPER(0))
PROPER(times(x0, s(z0))) → c70(TIMES(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(times(x0, posrecip(z0))) → c70(TIMES(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(times(x0, negrecip(z0))) → c70(TIMES(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(times(x0, nil)) → c70(TIMES(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
PROPER(times(x0, cons(z0, z1))) → c70(TIMES(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(times(x0, rnil)) → c70(TIMES(proper(x0), ok(rnil)), PROPER(x0), PROPER(rnil))
PROPER(times(x0, rcons(z0, z1))) → c70(TIMES(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(times(x0, from(z0))) → c70(TIMES(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(times(x0, 2ndspos(z0, z1))) → c70(TIMES(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(times(x0, 2ndsneg(z0, z1))) → c70(TIMES(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(times(x0, pi(z0))) → c70(TIMES(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(times(x0, plus(z0, z1))) → c70(TIMES(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(times(x0, times(z0, z1))) → c70(TIMES(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(times(x0, square(z0))) → c70(TIMES(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(times(0, x1)) → c70(TIMES(ok(0), proper(x1)), PROPER(0), PROPER(x1))
PROPER(times(s(z0), x1)) → c70(TIMES(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(times(posrecip(z0), x1)) → c70(TIMES(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(times(negrecip(z0), x1)) → c70(TIMES(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(times(nil, x1)) → c70(TIMES(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
PROPER(times(cons(z0, z1), x1)) → c70(TIMES(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(times(rnil, x1)) → c70(TIMES(ok(rnil), proper(x1)), PROPER(rnil), PROPER(x1))
PROPER(times(rcons(z0, z1), x1)) → c70(TIMES(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(times(from(z0), x1)) → c70(TIMES(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(times(2ndspos(z0, z1), x1)) → c70(TIMES(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(times(2ndsneg(z0, z1), x1)) → c70(TIMES(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(times(pi(z0), x1)) → c70(TIMES(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(times(plus(z0, z1), x1)) → c70(TIMES(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(times(times(z0, z1), x1)) → c70(TIMES(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(times(square(z0), x1)) → c70(TIMES(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))

(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, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(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(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))
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))
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))
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(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)) → c10(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))
PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c58(S(ok(0)))
PROPER(s(nil)) → c58(S(ok(nil)))
PROPER(s(rnil)) → c58(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(rcons(x0, s(z0))) → c64(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c64(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c64(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, cons(z0, z1))) → c64(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, rcons(z0, z1))) → c64(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c64(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c64(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c64(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c64(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c64(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c64(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c64(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(s(z0), x1)) → c64(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c64(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c64(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c64(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c64(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c64(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c64(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c64(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c64(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c64(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c64(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c64(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(rcons(x0, 0)) → c64(RCONS(proper(x0), ok(0)), PROPER(x0))
PROPER(rcons(x0, nil)) → c64(RCONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(rcons(x0, rnil)) → c64(RCONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(rcons(0, x1)) → c64(RCONS(ok(0), proper(x1)), PROPER(x1))
PROPER(rcons(nil, x1)) → c64(RCONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c64(RCONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(from(s(z0))) → c65(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(posrecip(z0))) → c65(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(from(negrecip(z0))) → c65(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(from(cons(z0, z1))) → c65(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(rcons(z0, z1))) → c65(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(from(from(z0))) → c65(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(2ndspos(z0, z1))) → c65(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(from(2ndsneg(z0, z1))) → c65(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(from(pi(z0))) → c65(FROM(pi(proper(z0))), PROPER(pi(z0)))
PROPER(from(plus(z0, z1))) → c65(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(from(times(z0, z1))) → c65(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(from(square(z0))) → c65(FROM(square(proper(z0))), PROPER(square(z0)))
PROPER(from(0)) → c65(FROM(ok(0)))
PROPER(from(nil)) → c65(FROM(ok(nil)))
PROPER(from(rnil)) → c65(FROM(ok(rnil)))
PROPER(2ndspos(x0, s(z0))) → c66(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndspos(x0, posrecip(z0))) → c66(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndspos(x0, negrecip(z0))) → c66(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndspos(x0, cons(z0, z1))) → c66(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndspos(x0, rcons(z0, z1))) → c66(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndspos(x0, from(z0))) → c66(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndspos(x0, pi(z0))) → c66(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndspos(x0, plus(z0, z1))) → c66(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndspos(x0, times(z0, z1))) → c66(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndspos(x0, square(z0))) → c66(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndspos(s(z0), x1)) → c66(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndspos(posrecip(z0), x1)) → c66(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndspos(negrecip(z0), x1)) → c66(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndspos(cons(z0, z1), x1)) → c66(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndspos(rcons(z0, z1), x1)) → c66(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndspos(from(z0), x1)) → c66(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c66(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c66(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndspos(pi(z0), x1)) → c66(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndspos(plus(z0, z1), x1)) → c66(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndspos(times(z0, z1), x1)) → c66(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndspos(square(z0), x1)) → c66(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndspos(x0, 0)) → c66(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndspos(x0, nil)) → c66(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndspos(x0, rnil)) → c66(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndspos(0, x1)) → c66(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndspos(nil, x1)) → c66(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndspos(rnil, x1)) → c66(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(x0, s(z0))) → c67(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndsneg(x0, posrecip(z0))) → c67(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndsneg(x0, negrecip(z0))) → c67(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndsneg(x0, cons(z0, z1))) → c67(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndsneg(x0, rcons(z0, z1))) → c67(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndsneg(x0, from(z0))) → c67(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndsneg(x0, pi(z0))) → c67(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndsneg(x0, plus(z0, z1))) → c67(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndsneg(x0, times(z0, z1))) → c67(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndsneg(x0, square(z0))) → c67(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndsneg(s(z0), x1)) → c67(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndsneg(posrecip(z0), x1)) → c67(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndsneg(negrecip(z0), x1)) → c67(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndsneg(cons(z0, z1), x1)) → c67(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(rcons(z0, z1), x1)) → c67(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(from(z0), x1)) → c67(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c67(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c67(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndsneg(pi(z0), x1)) → c67(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndsneg(plus(z0, z1), x1)) → c67(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndsneg(times(z0, z1), x1)) → c67(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndsneg(square(z0), x1)) → c67(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndsneg(x0, 0)) → c67(2NDSNEG(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndsneg(x0, nil)) → c67(2NDSNEG(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndsneg(x0, rnil)) → c67(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndsneg(0, x1)) → c67(2NDSNEG(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndsneg(nil, x1)) → c67(2NDSNEG(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(rnil, x1)) → c67(2NDSNEG(ok(rnil), proper(x1)), PROPER(x1))
PROPER(pi(s(z0))) → c68(PI(s(proper(z0))), PROPER(s(z0)))
PROPER(pi(posrecip(z0))) → c68(PI(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(pi(negrecip(z0))) → c68(PI(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(pi(cons(z0, z1))) → c68(PI(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(pi(rcons(z0, z1))) → c68(PI(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(pi(from(z0))) → c68(PI(from(proper(z0))), PROPER(from(z0)))
PROPER(pi(2ndspos(z0, z1))) → c68(PI(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(pi(2ndsneg(z0, z1))) → c68(PI(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(pi(pi(z0))) → c68(PI(pi(proper(z0))), PROPER(pi(z0)))
PROPER(pi(plus(z0, z1))) → c68(PI(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(pi(times(z0, z1))) → c68(PI(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(pi(square(z0))) → c68(PI(square(proper(z0))), PROPER(square(z0)))
PROPER(pi(0)) → c68(PI(ok(0)))
PROPER(pi(nil)) → c68(PI(ok(nil)))
PROPER(pi(rnil)) → c68(PI(ok(rnil)))
PROPER(plus(x0, s(z0))) → c69(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(plus(x0, posrecip(z0))) → c69(PLUS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(plus(x0, negrecip(z0))) → c69(PLUS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(plus(x0, cons(z0, z1))) → c69(PLUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(plus(x0, rcons(z0, z1))) → c69(PLUS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(plus(x0, from(z0))) → c69(PLUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(plus(x0, 2ndspos(z0, z1))) → c69(PLUS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(plus(x0, 2ndsneg(z0, z1))) → c69(PLUS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(plus(x0, pi(z0))) → c69(PLUS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(plus(x0, plus(z0, z1))) → c69(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(plus(x0, times(z0, z1))) → c69(PLUS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(plus(x0, square(z0))) → c69(PLUS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(plus(s(z0), x1)) → c69(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(plus(posrecip(z0), x1)) → c69(PLUS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(plus(negrecip(z0), x1)) → c69(PLUS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(plus(cons(z0, z1), x1)) → c69(PLUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(plus(rcons(z0, z1), x1)) → c69(PLUS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(plus(from(z0), x1)) → c69(PLUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(plus(2ndspos(z0, z1), x1)) → c69(PLUS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(plus(2ndsneg(z0, z1), x1)) → c69(PLUS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(plus(pi(z0), x1)) → c69(PLUS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(plus(plus(z0, z1), x1)) → c69(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(plus(times(z0, z1), x1)) → c69(PLUS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(plus(square(z0), x1)) → c69(PLUS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(plus(x0, 0)) → c69(PLUS(proper(x0), ok(0)), PROPER(x0))
PROPER(plus(x0, nil)) → c69(PLUS(proper(x0), ok(nil)), PROPER(x0))
PROPER(plus(x0, rnil)) → c69(PLUS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(plus(0, x1)) → c69(PLUS(ok(0), proper(x1)), PROPER(x1))
PROPER(plus(nil, x1)) → c69(PLUS(ok(nil), proper(x1)), PROPER(x1))
PROPER(plus(rnil, x1)) → c69(PLUS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(times(x0, 0)) → c70(TIMES(proper(x0), ok(0)), PROPER(x0), PROPER(0))
PROPER(times(x0, s(z0))) → c70(TIMES(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(times(x0, posrecip(z0))) → c70(TIMES(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(times(x0, negrecip(z0))) → c70(TIMES(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(times(x0, nil)) → c70(TIMES(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
PROPER(times(x0, cons(z0, z1))) → c70(TIMES(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(times(x0, rnil)) → c70(TIMES(proper(x0), ok(rnil)), PROPER(x0), PROPER(rnil))
PROPER(times(x0, rcons(z0, z1))) → c70(TIMES(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(times(x0, from(z0))) → c70(TIMES(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(times(x0, 2ndspos(z0, z1))) → c70(TIMES(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(times(x0, 2ndsneg(z0, z1))) → c70(TIMES(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(times(x0, pi(z0))) → c70(TIMES(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(times(x0, plus(z0, z1))) → c70(TIMES(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(times(x0, times(z0, z1))) → c70(TIMES(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(times(x0, square(z0))) → c70(TIMES(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(times(0, x1)) → c70(TIMES(ok(0), proper(x1)), PROPER(0), PROPER(x1))
PROPER(times(s(z0), x1)) → c70(TIMES(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(times(posrecip(z0), x1)) → c70(TIMES(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(times(negrecip(z0), x1)) → c70(TIMES(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(times(nil, x1)) → c70(TIMES(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
PROPER(times(cons(z0, z1), x1)) → c70(TIMES(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(times(rnil, x1)) → c70(TIMES(ok(rnil), proper(x1)), PROPER(rnil), PROPER(x1))
PROPER(times(rcons(z0, z1), x1)) → c70(TIMES(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(times(from(z0), x1)) → c70(TIMES(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(times(2ndspos(z0, z1), x1)) → c70(TIMES(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(times(2ndsneg(z0, z1), x1)) → c70(TIMES(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(times(pi(z0), x1)) → c70(TIMES(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(times(plus(z0, z1), x1)) → c70(TIMES(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(times(times(z0, z1), x1)) → c70(TIMES(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(times(square(z0), x1)) → c70(TIMES(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))

S tuples:

ACTIVE(square(z0)) → c10(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))
PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c58(S(ok(0)))
PROPER(s(nil)) → c58(S(ok(nil)))
PROPER(s(rnil)) → c58(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(rcons(x0, s(z0))) → c64(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c64(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c64(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, cons(z0, z1))) → c64(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, rcons(z0, z1))) → c64(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c64(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c64(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c64(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c64(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c64(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c64(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c64(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(s(z0), x1)) → c64(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c64(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c64(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c64(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c64(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c64(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c64(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c64(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c64(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c64(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c64(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c64(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(rcons(x0, 0)) → c64(RCONS(proper(x0), ok(0)), PROPER(x0))
PROPER(rcons(x0, nil)) → c64(RCONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(rcons(x0, rnil)) → c64(RCONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(rcons(0, x1)) → c64(RCONS(ok(0), proper(x1)), PROPER(x1))
PROPER(rcons(nil, x1)) → c64(RCONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c64(RCONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(from(s(z0))) → c65(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(posrecip(z0))) → c65(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(from(negrecip(z0))) → c65(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(from(cons(z0, z1))) → c65(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(rcons(z0, z1))) → c65(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(from(from(z0))) → c65(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(2ndspos(z0, z1))) → c65(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(from(2ndsneg(z0, z1))) → c65(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(from(pi(z0))) → c65(FROM(pi(proper(z0))), PROPER(pi(z0)))
PROPER(from(plus(z0, z1))) → c65(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(from(times(z0, z1))) → c65(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(from(square(z0))) → c65(FROM(square(proper(z0))), PROPER(square(z0)))
PROPER(from(0)) → c65(FROM(ok(0)))
PROPER(from(nil)) → c65(FROM(ok(nil)))
PROPER(from(rnil)) → c65(FROM(ok(rnil)))
PROPER(2ndspos(x0, s(z0))) → c66(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndspos(x0, posrecip(z0))) → c66(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndspos(x0, negrecip(z0))) → c66(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndspos(x0, cons(z0, z1))) → c66(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndspos(x0, rcons(z0, z1))) → c66(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndspos(x0, from(z0))) → c66(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndspos(x0, pi(z0))) → c66(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndspos(x0, plus(z0, z1))) → c66(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndspos(x0, times(z0, z1))) → c66(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndspos(x0, square(z0))) → c66(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndspos(s(z0), x1)) → c66(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndspos(posrecip(z0), x1)) → c66(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndspos(negrecip(z0), x1)) → c66(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndspos(cons(z0, z1), x1)) → c66(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndspos(rcons(z0, z1), x1)) → c66(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndspos(from(z0), x1)) → c66(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c66(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c66(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndspos(pi(z0), x1)) → c66(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndspos(plus(z0, z1), x1)) → c66(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndspos(times(z0, z1), x1)) → c66(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndspos(square(z0), x1)) → c66(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndspos(x0, 0)) → c66(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndspos(x0, nil)) → c66(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndspos(x0, rnil)) → c66(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndspos(0, x1)) → c66(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndspos(nil, x1)) → c66(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndspos(rnil, x1)) → c66(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(x0, s(z0))) → c67(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndsneg(x0, posrecip(z0))) → c67(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndsneg(x0, negrecip(z0))) → c67(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndsneg(x0, cons(z0, z1))) → c67(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndsneg(x0, rcons(z0, z1))) → c67(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndsneg(x0, from(z0))) → c67(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndsneg(x0, pi(z0))) → c67(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndsneg(x0, plus(z0, z1))) → c67(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndsneg(x0, times(z0, z1))) → c67(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndsneg(x0, square(z0))) → c67(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndsneg(s(z0), x1)) → c67(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndsneg(posrecip(z0), x1)) → c67(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndsneg(negrecip(z0), x1)) → c67(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndsneg(cons(z0, z1), x1)) → c67(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(rcons(z0, z1), x1)) → c67(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(from(z0), x1)) → c67(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c67(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c67(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndsneg(pi(z0), x1)) → c67(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndsneg(plus(z0, z1), x1)) → c67(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndsneg(times(z0, z1), x1)) → c67(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndsneg(square(z0), x1)) → c67(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndsneg(x0, 0)) → c67(2NDSNEG(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndsneg(x0, nil)) → c67(2NDSNEG(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndsneg(x0, rnil)) → c67(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndsneg(0, x1)) → c67(2NDSNEG(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndsneg(nil, x1)) → c67(2NDSNEG(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(rnil, x1)) → c67(2NDSNEG(ok(rnil), proper(x1)), PROPER(x1))
PROPER(pi(s(z0))) → c68(PI(s(proper(z0))), PROPER(s(z0)))
PROPER(pi(posrecip(z0))) → c68(PI(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(pi(negrecip(z0))) → c68(PI(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(pi(cons(z0, z1))) → c68(PI(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(pi(rcons(z0, z1))) → c68(PI(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(pi(from(z0))) → c68(PI(from(proper(z0))), PROPER(from(z0)))
PROPER(pi(2ndspos(z0, z1))) → c68(PI(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(pi(2ndsneg(z0, z1))) → c68(PI(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(pi(pi(z0))) → c68(PI(pi(proper(z0))), PROPER(pi(z0)))
PROPER(pi(plus(z0, z1))) → c68(PI(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(pi(times(z0, z1))) → c68(PI(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(pi(square(z0))) → c68(PI(square(proper(z0))), PROPER(square(z0)))
PROPER(pi(0)) → c68(PI(ok(0)))
PROPER(pi(nil)) → c68(PI(ok(nil)))
PROPER(pi(rnil)) → c68(PI(ok(rnil)))
PROPER(plus(x0, s(z0))) → c69(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(plus(x0, posrecip(z0))) → c69(PLUS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(plus(x0, negrecip(z0))) → c69(PLUS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(plus(x0, cons(z0, z1))) → c69(PLUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(plus(x0, rcons(z0, z1))) → c69(PLUS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(plus(x0, from(z0))) → c69(PLUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(plus(x0, 2ndspos(z0, z1))) → c69(PLUS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(plus(x0, 2ndsneg(z0, z1))) → c69(PLUS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(plus(x0, pi(z0))) → c69(PLUS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(plus(x0, plus(z0, z1))) → c69(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(plus(x0, times(z0, z1))) → c69(PLUS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(plus(x0, square(z0))) → c69(PLUS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(plus(s(z0), x1)) → c69(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(plus(posrecip(z0), x1)) → c69(PLUS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(plus(negrecip(z0), x1)) → c69(PLUS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(plus(cons(z0, z1), x1)) → c69(PLUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(plus(rcons(z0, z1), x1)) → c69(PLUS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(plus(from(z0), x1)) → c69(PLUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(plus(2ndspos(z0, z1), x1)) → c69(PLUS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(plus(2ndsneg(z0, z1), x1)) → c69(PLUS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(plus(pi(z0), x1)) → c69(PLUS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(plus(plus(z0, z1), x1)) → c69(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(plus(times(z0, z1), x1)) → c69(PLUS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(plus(square(z0), x1)) → c69(PLUS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(plus(x0, 0)) → c69(PLUS(proper(x0), ok(0)), PROPER(x0))
PROPER(plus(x0, nil)) → c69(PLUS(proper(x0), ok(nil)), PROPER(x0))
PROPER(plus(x0, rnil)) → c69(PLUS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(plus(0, x1)) → c69(PLUS(ok(0), proper(x1)), PROPER(x1))
PROPER(plus(nil, x1)) → c69(PLUS(ok(nil), proper(x1)), PROPER(x1))
PROPER(plus(rnil, x1)) → c69(PLUS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(times(x0, 0)) → c70(TIMES(proper(x0), ok(0)), PROPER(x0), PROPER(0))
PROPER(times(x0, s(z0))) → c70(TIMES(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(times(x0, posrecip(z0))) → c70(TIMES(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(times(x0, negrecip(z0))) → c70(TIMES(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(times(x0, nil)) → c70(TIMES(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
PROPER(times(x0, cons(z0, z1))) → c70(TIMES(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(times(x0, rnil)) → c70(TIMES(proper(x0), ok(rnil)), PROPER(x0), PROPER(rnil))
PROPER(times(x0, rcons(z0, z1))) → c70(TIMES(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(times(x0, from(z0))) → c70(TIMES(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(times(x0, 2ndspos(z0, z1))) → c70(TIMES(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(times(x0, 2ndsneg(z0, z1))) → c70(TIMES(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(times(x0, pi(z0))) → c70(TIMES(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(times(x0, plus(z0, z1))) → c70(TIMES(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(times(x0, times(z0, z1))) → c70(TIMES(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(times(x0, square(z0))) → c70(TIMES(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(times(0, x1)) → c70(TIMES(ok(0), proper(x1)), PROPER(0), PROPER(x1))
PROPER(times(s(z0), x1)) → c70(TIMES(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(times(posrecip(z0), x1)) → c70(TIMES(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(times(negrecip(z0), x1)) → c70(TIMES(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(times(nil, x1)) → c70(TIMES(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
PROPER(times(cons(z0, z1), x1)) → c70(TIMES(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(times(rnil, x1)) → c70(TIMES(ok(rnil), proper(x1)), PROPER(rnil), PROPER(x1))
PROPER(times(rcons(z0, z1), x1)) → c70(TIMES(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(times(from(z0), x1)) → c70(TIMES(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(times(2ndspos(z0, z1), x1)) → c70(TIMES(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(times(2ndsneg(z0, z1), x1)) → c70(TIMES(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(times(pi(z0), x1)) → c70(TIMES(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(times(plus(z0, z1), x1)) → c70(TIMES(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(times(times(z0, z1), x1)) → c70(TIMES(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(times(square(z0), x1)) → c70(TIMES(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))

K tuples:none
Defined Rule Symbols:

active, rcons, posrecip, 2ndsneg, negrecip, 2ndspos, s, cons, from, pi, plus, times, square, proper

Defined Pair Symbols:

ACTIVE, S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP

Compound Symbols:

c10, c15, c16, c18, c19, c20, c21, c23, c24, c25, c26, 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, c71, c72, c73, c, c5, c7, c9, c1, c11, c12, c13, c14, c17, c22, c27, c58, c58, c59, c59, c60, c60, c62, c62, c64, c64, c65, c65, c66, c66, c67, c67, c68, c68, c69, c69, c70

(67) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)

Removed 6 trailing tuple parts

(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, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(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(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))
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))
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))
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(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)) → c10(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))
PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c58(S(ok(0)))
PROPER(s(nil)) → c58(S(ok(nil)))
PROPER(s(rnil)) → c58(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(rcons(x0, s(z0))) → c64(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c64(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c64(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, cons(z0, z1))) → c64(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, rcons(z0, z1))) → c64(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c64(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c64(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c64(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c64(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c64(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c64(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c64(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(s(z0), x1)) → c64(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c64(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c64(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c64(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c64(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c64(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c64(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c64(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c64(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c64(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c64(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c64(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(rcons(x0, 0)) → c64(RCONS(proper(x0), ok(0)), PROPER(x0))
PROPER(rcons(x0, nil)) → c64(RCONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(rcons(x0, rnil)) → c64(RCONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(rcons(0, x1)) → c64(RCONS(ok(0), proper(x1)), PROPER(x1))
PROPER(rcons(nil, x1)) → c64(RCONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c64(RCONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(from(s(z0))) → c65(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(posrecip(z0))) → c65(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(from(negrecip(z0))) → c65(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(from(cons(z0, z1))) → c65(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(rcons(z0, z1))) → c65(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(from(from(z0))) → c65(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(2ndspos(z0, z1))) → c65(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(from(2ndsneg(z0, z1))) → c65(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(from(pi(z0))) → c65(FROM(pi(proper(z0))), PROPER(pi(z0)))
PROPER(from(plus(z0, z1))) → c65(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(from(times(z0, z1))) → c65(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(from(square(z0))) → c65(FROM(square(proper(z0))), PROPER(square(z0)))
PROPER(from(0)) → c65(FROM(ok(0)))
PROPER(from(nil)) → c65(FROM(ok(nil)))
PROPER(from(rnil)) → c65(FROM(ok(rnil)))
PROPER(2ndspos(x0, s(z0))) → c66(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndspos(x0, posrecip(z0))) → c66(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndspos(x0, negrecip(z0))) → c66(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndspos(x0, cons(z0, z1))) → c66(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndspos(x0, rcons(z0, z1))) → c66(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndspos(x0, from(z0))) → c66(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndspos(x0, pi(z0))) → c66(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndspos(x0, plus(z0, z1))) → c66(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndspos(x0, times(z0, z1))) → c66(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndspos(x0, square(z0))) → c66(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndspos(s(z0), x1)) → c66(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndspos(posrecip(z0), x1)) → c66(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndspos(negrecip(z0), x1)) → c66(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndspos(cons(z0, z1), x1)) → c66(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndspos(rcons(z0, z1), x1)) → c66(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndspos(from(z0), x1)) → c66(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c66(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c66(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndspos(pi(z0), x1)) → c66(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndspos(plus(z0, z1), x1)) → c66(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndspos(times(z0, z1), x1)) → c66(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndspos(square(z0), x1)) → c66(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndspos(x0, 0)) → c66(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndspos(x0, nil)) → c66(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndspos(x0, rnil)) → c66(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndspos(0, x1)) → c66(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndspos(nil, x1)) → c66(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndspos(rnil, x1)) → c66(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(x0, s(z0))) → c67(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndsneg(x0, posrecip(z0))) → c67(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndsneg(x0, negrecip(z0))) → c67(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndsneg(x0, cons(z0, z1))) → c67(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndsneg(x0, rcons(z0, z1))) → c67(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndsneg(x0, from(z0))) → c67(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndsneg(x0, pi(z0))) → c67(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndsneg(x0, plus(z0, z1))) → c67(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndsneg(x0, times(z0, z1))) → c67(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndsneg(x0, square(z0))) → c67(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndsneg(s(z0), x1)) → c67(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndsneg(posrecip(z0), x1)) → c67(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndsneg(negrecip(z0), x1)) → c67(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndsneg(cons(z0, z1), x1)) → c67(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(rcons(z0, z1), x1)) → c67(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(from(z0), x1)) → c67(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c67(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c67(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndsneg(pi(z0), x1)) → c67(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndsneg(plus(z0, z1), x1)) → c67(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndsneg(times(z0, z1), x1)) → c67(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndsneg(square(z0), x1)) → c67(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndsneg(x0, 0)) → c67(2NDSNEG(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndsneg(x0, nil)) → c67(2NDSNEG(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndsneg(x0, rnil)) → c67(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndsneg(0, x1)) → c67(2NDSNEG(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndsneg(nil, x1)) → c67(2NDSNEG(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(rnil, x1)) → c67(2NDSNEG(ok(rnil), proper(x1)), PROPER(x1))
PROPER(pi(s(z0))) → c68(PI(s(proper(z0))), PROPER(s(z0)))
PROPER(pi(posrecip(z0))) → c68(PI(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(pi(negrecip(z0))) → c68(PI(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(pi(cons(z0, z1))) → c68(PI(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(pi(rcons(z0, z1))) → c68(PI(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(pi(from(z0))) → c68(PI(from(proper(z0))), PROPER(from(z0)))
PROPER(pi(2ndspos(z0, z1))) → c68(PI(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(pi(2ndsneg(z0, z1))) → c68(PI(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(pi(pi(z0))) → c68(PI(pi(proper(z0))), PROPER(pi(z0)))
PROPER(pi(plus(z0, z1))) → c68(PI(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(pi(times(z0, z1))) → c68(PI(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(pi(square(z0))) → c68(PI(square(proper(z0))), PROPER(square(z0)))
PROPER(pi(0)) → c68(PI(ok(0)))
PROPER(pi(nil)) → c68(PI(ok(nil)))
PROPER(pi(rnil)) → c68(PI(ok(rnil)))
PROPER(plus(x0, s(z0))) → c69(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(plus(x0, posrecip(z0))) → c69(PLUS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(plus(x0, negrecip(z0))) → c69(PLUS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(plus(x0, cons(z0, z1))) → c69(PLUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(plus(x0, rcons(z0, z1))) → c69(PLUS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(plus(x0, from(z0))) → c69(PLUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(plus(x0, 2ndspos(z0, z1))) → c69(PLUS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(plus(x0, 2ndsneg(z0, z1))) → c69(PLUS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(plus(x0, pi(z0))) → c69(PLUS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(plus(x0, plus(z0, z1))) → c69(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(plus(x0, times(z0, z1))) → c69(PLUS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(plus(x0, square(z0))) → c69(PLUS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(plus(s(z0), x1)) → c69(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(plus(posrecip(z0), x1)) → c69(PLUS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(plus(negrecip(z0), x1)) → c69(PLUS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(plus(cons(z0, z1), x1)) → c69(PLUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(plus(rcons(z0, z1), x1)) → c69(PLUS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(plus(from(z0), x1)) → c69(PLUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(plus(2ndspos(z0, z1), x1)) → c69(PLUS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(plus(2ndsneg(z0, z1), x1)) → c69(PLUS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(plus(pi(z0), x1)) → c69(PLUS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(plus(plus(z0, z1), x1)) → c69(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(plus(times(z0, z1), x1)) → c69(PLUS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(plus(square(z0), x1)) → c69(PLUS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(plus(x0, 0)) → c69(PLUS(proper(x0), ok(0)), PROPER(x0))
PROPER(plus(x0, nil)) → c69(PLUS(proper(x0), ok(nil)), PROPER(x0))
PROPER(plus(x0, rnil)) → c69(PLUS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(plus(0, x1)) → c69(PLUS(ok(0), proper(x1)), PROPER(x1))
PROPER(plus(nil, x1)) → c69(PLUS(ok(nil), proper(x1)), PROPER(x1))
PROPER(plus(rnil, x1)) → c69(PLUS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(times(x0, s(z0))) → c70(TIMES(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(times(x0, posrecip(z0))) → c70(TIMES(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(times(x0, negrecip(z0))) → c70(TIMES(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(times(x0, cons(z0, z1))) → c70(TIMES(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(times(x0, rcons(z0, z1))) → c70(TIMES(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(times(x0, from(z0))) → c70(TIMES(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(times(x0, 2ndspos(z0, z1))) → c70(TIMES(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(times(x0, 2ndsneg(z0, z1))) → c70(TIMES(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(times(x0, pi(z0))) → c70(TIMES(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(times(x0, plus(z0, z1))) → c70(TIMES(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(times(x0, times(z0, z1))) → c70(TIMES(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(times(x0, square(z0))) → c70(TIMES(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(times(s(z0), x1)) → c70(TIMES(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(times(posrecip(z0), x1)) → c70(TIMES(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(times(negrecip(z0), x1)) → c70(TIMES(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(times(cons(z0, z1), x1)) → c70(TIMES(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(times(rcons(z0, z1), x1)) → c70(TIMES(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(times(from(z0), x1)) → c70(TIMES(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(times(2ndspos(z0, z1), x1)) → c70(TIMES(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(times(2ndsneg(z0, z1), x1)) → c70(TIMES(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(times(pi(z0), x1)) → c70(TIMES(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(times(plus(z0, z1), x1)) → c70(TIMES(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(times(times(z0, z1), x1)) → c70(TIMES(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(times(square(z0), x1)) → c70(TIMES(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(times(x0, 0)) → c70(TIMES(proper(x0), ok(0)), PROPER(x0))
PROPER(times(x0, nil)) → c70(TIMES(proper(x0), ok(nil)), PROPER(x0))
PROPER(times(x0, rnil)) → c70(TIMES(proper(x0), ok(rnil)), PROPER(x0))
PROPER(times(0, x1)) → c70(TIMES(ok(0), proper(x1)), PROPER(x1))
PROPER(times(nil, x1)) → c70(TIMES(ok(nil), proper(x1)), PROPER(x1))
PROPER(times(rnil, x1)) → c70(TIMES(ok(rnil), proper(x1)), PROPER(x1))

S tuples:

ACTIVE(square(z0)) → c10(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))
PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0))
TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c58(S(ok(0)))
PROPER(s(nil)) → c58(S(ok(nil)))
PROPER(s(rnil)) → c58(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(rcons(x0, s(z0))) → c64(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c64(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c64(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, cons(z0, z1))) → c64(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, rcons(z0, z1))) → c64(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c64(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c64(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c64(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c64(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c64(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c64(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c64(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(s(z0), x1)) → c64(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c64(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c64(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c64(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c64(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c64(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c64(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c64(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c64(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c64(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c64(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c64(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(rcons(x0, 0)) → c64(RCONS(proper(x0), ok(0)), PROPER(x0))
PROPER(rcons(x0, nil)) → c64(RCONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(rcons(x0, rnil)) → c64(RCONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(rcons(0, x1)) → c64(RCONS(ok(0), proper(x1)), PROPER(x1))
PROPER(rcons(nil, x1)) → c64(RCONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c64(RCONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(from(s(z0))) → c65(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(posrecip(z0))) → c65(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(from(negrecip(z0))) → c65(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(from(cons(z0, z1))) → c65(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(rcons(z0, z1))) → c65(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(from(from(z0))) → c65(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(2ndspos(z0, z1))) → c65(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(from(2ndsneg(z0, z1))) → c65(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(from(pi(z0))) → c65(FROM(pi(proper(z0))), PROPER(pi(z0)))
PROPER(from(plus(z0, z1))) → c65(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(from(times(z0, z1))) → c65(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(from(square(z0))) → c65(FROM(square(proper(z0))), PROPER(square(z0)))
PROPER(from(0)) → c65(FROM(ok(0)))
PROPER(from(nil)) → c65(FROM(ok(nil)))
PROPER(from(rnil)) → c65(FROM(ok(rnil)))
PROPER(2ndspos(x0, s(z0))) → c66(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndspos(x0, posrecip(z0))) → c66(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndspos(x0, negrecip(z0))) → c66(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndspos(x0, cons(z0, z1))) → c66(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndspos(x0, rcons(z0, z1))) → c66(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndspos(x0, from(z0))) → c66(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndspos(x0, pi(z0))) → c66(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndspos(x0, plus(z0, z1))) → c66(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndspos(x0, times(z0, z1))) → c66(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndspos(x0, square(z0))) → c66(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndspos(s(z0), x1)) → c66(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndspos(posrecip(z0), x1)) → c66(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndspos(negrecip(z0), x1)) → c66(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndspos(cons(z0, z1), x1)) → c66(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndspos(rcons(z0, z1), x1)) → c66(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndspos(from(z0), x1)) → c66(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c66(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c66(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndspos(pi(z0), x1)) → c66(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndspos(plus(z0, z1), x1)) → c66(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndspos(times(z0, z1), x1)) → c66(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndspos(square(z0), x1)) → c66(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndspos(x0, 0)) → c66(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndspos(x0, nil)) → c66(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndspos(x0, rnil)) → c66(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndspos(0, x1)) → c66(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndspos(nil, x1)) → c66(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndspos(rnil, x1)) → c66(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(x0, s(z0))) → c67(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndsneg(x0, posrecip(z0))) → c67(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndsneg(x0, negrecip(z0))) → c67(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndsneg(x0, cons(z0, z1))) → c67(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndsneg(x0, rcons(z0, z1))) → c67(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndsneg(x0, from(z0))) → c67(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndsneg(x0, pi(z0))) → c67(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndsneg(x0, plus(z0, z1))) → c67(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndsneg(x0, times(z0, z1))) → c67(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndsneg(x0, square(z0))) → c67(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndsneg(s(z0), x1)) → c67(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndsneg(posrecip(z0), x1)) → c67(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndsneg(negrecip(z0), x1)) → c67(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndsneg(cons(z0, z1), x1)) → c67(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(rcons(z0, z1), x1)) → c67(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(from(z0), x1)) → c67(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c67(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c67(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndsneg(pi(z0), x1)) → c67(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndsneg(plus(z0, z1), x1)) → c67(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndsneg(times(z0, z1), x1)) → c67(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndsneg(square(z0), x1)) → c67(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndsneg(x0, 0)) → c67(2NDSNEG(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndsneg(x0, nil)) → c67(2NDSNEG(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndsneg(x0, rnil)) → c67(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndsneg(0, x1)) → c67(2NDSNEG(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndsneg(nil, x1)) → c67(2NDSNEG(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(rnil, x1)) → c67(2NDSNEG(ok(rnil), proper(x1)), PROPER(x1))
PROPER(pi(s(z0))) → c68(PI(s(proper(z0))), PROPER(s(z0)))
PROPER(pi(posrecip(z0))) → c68(PI(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(pi(negrecip(z0))) → c68(PI(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(pi(cons(z0, z1))) → c68(PI(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(pi(rcons(z0, z1))) → c68(PI(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(pi(from(z0))) → c68(PI(from(proper(z0))), PROPER(from(z0)))
PROPER(pi(2ndspos(z0, z1))) → c68(PI(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(pi(2ndsneg(z0, z1))) → c68(PI(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(pi(pi(z0))) → c68(PI(pi(proper(z0))), PROPER(pi(z0)))
PROPER(pi(plus(z0, z1))) → c68(PI(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(pi(times(z0, z1))) → c68(PI(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(pi(square(z0))) → c68(PI(square(proper(z0))), PROPER(square(z0)))
PROPER(pi(0)) → c68(PI(ok(0)))
PROPER(pi(nil)) → c68(PI(ok(nil)))
PROPER(pi(rnil)) → c68(PI(ok(rnil)))
PROPER(plus(x0, s(z0))) → c69(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(plus(x0, posrecip(z0))) → c69(PLUS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(plus(x0, negrecip(z0))) → c69(PLUS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(plus(x0, cons(z0, z1))) → c69(PLUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(plus(x0, rcons(z0, z1))) → c69(PLUS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(plus(x0, from(z0))) → c69(PLUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(plus(x0, 2ndspos(z0, z1))) → c69(PLUS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(plus(x0, 2ndsneg(z0, z1))) → c69(PLUS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(plus(x0, pi(z0))) → c69(PLUS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(plus(x0, plus(z0, z1))) → c69(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(plus(x0, times(z0, z1))) → c69(PLUS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(plus(x0, square(z0))) → c69(PLUS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(plus(s(z0), x1)) → c69(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(plus(posrecip(z0), x1)) → c69(PLUS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(plus(negrecip(z0), x1)) → c69(PLUS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(plus(cons(z0, z1), x1)) → c69(PLUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(plus(rcons(z0, z1), x1)) → c69(PLUS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(plus(from(z0), x1)) → c69(PLUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(plus(2ndspos(z0, z1), x1)) → c69(PLUS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(plus(2ndsneg(z0, z1), x1)) → c69(PLUS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(plus(pi(z0), x1)) → c69(PLUS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(plus(plus(z0, z1), x1)) → c69(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(plus(times(z0, z1), x1)) → c69(PLUS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(plus(square(z0), x1)) → c69(PLUS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(plus(x0, 0)) → c69(PLUS(proper(x0), ok(0)), PROPER(x0))
PROPER(plus(x0, nil)) → c69(PLUS(proper(x0), ok(nil)), PROPER(x0))
PROPER(plus(x0, rnil)) → c69(PLUS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(plus(0, x1)) → c69(PLUS(ok(0), proper(x1)), PROPER(x1))
PROPER(plus(nil, x1)) → c69(PLUS(ok(nil), proper(x1)), PROPER(x1))
PROPER(plus(rnil, x1)) → c69(PLUS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(times(x0, s(z0))) → c70(TIMES(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(times(x0, posrecip(z0))) → c70(TIMES(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(times(x0, negrecip(z0))) → c70(TIMES(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(times(x0, cons(z0, z1))) → c70(TIMES(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(times(x0, rcons(z0, z1))) → c70(TIMES(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(times(x0, from(z0))) → c70(TIMES(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(times(x0, 2ndspos(z0, z1))) → c70(TIMES(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(times(x0, 2ndsneg(z0, z1))) → c70(TIMES(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(times(x0, pi(z0))) → c70(TIMES(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(times(x0, plus(z0, z1))) → c70(TIMES(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(times(x0, times(z0, z1))) → c70(TIMES(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(times(x0, square(z0))) → c70(TIMES(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(times(s(z0), x1)) → c70(TIMES(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(times(posrecip(z0), x1)) → c70(TIMES(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(times(negrecip(z0), x1)) → c70(TIMES(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(times(cons(z0, z1), x1)) → c70(TIMES(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(times(rcons(z0, z1), x1)) → c70(TIMES(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(times(from(z0), x1)) → c70(TIMES(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(times(2ndspos(z0, z1), x1)) → c70(TIMES(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(times(2ndsneg(z0, z1), x1)) → c70(TIMES(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(times(pi(z0), x1)) → c70(TIMES(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(times(plus(z0, z1), x1)) → c70(TIMES(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(times(times(z0, z1), x1)) → c70(TIMES(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(times(square(z0), x1)) → c70(TIMES(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(times(x0, 0)) → c70(TIMES(proper(x0), ok(0)), PROPER(x0))
PROPER(times(x0, nil)) → c70(TIMES(proper(x0), ok(nil)), PROPER(x0))
PROPER(times(x0, rnil)) → c70(TIMES(proper(x0), ok(rnil)), PROPER(x0))
PROPER(times(0, x1)) → c70(TIMES(ok(0), proper(x1)), PROPER(x1))
PROPER(times(nil, x1)) → c70(TIMES(ok(nil), proper(x1)), PROPER(x1))
PROPER(times(rnil, x1)) → c70(TIMES(ok(rnil), proper(x1)), PROPER(x1))

K tuples:none
Defined Rule Symbols:

active, rcons, posrecip, 2ndsneg, negrecip, 2ndspos, s, cons, from, pi, plus, times, square, proper

Defined Pair Symbols:

ACTIVE, S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP

Compound Symbols:

c10, c15, c16, c18, c19, c20, c21, c23, c24, c25, c26, 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, c71, c72, c73, c, c5, c7, c9, c1, c11, c12, c13, c14, c17, c22, c27, c58, c58, c59, c59, c60, c60, c62, c62, c64, c64, c65, c65, c66, c66, c67, c67, c68, c68, c69, c69, c70, c70

(69) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

Use narrowing to replace PROPER(square(z0)) → c71(SQUARE(proper(z0)), PROPER(z0)) by

PROPER(square(0)) → c71(SQUARE(ok(0)), PROPER(0))
PROPER(square(s(z0))) → c71(SQUARE(s(proper(z0))), PROPER(s(z0)))
PROPER(square(posrecip(z0))) → c71(SQUARE(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(square(negrecip(z0))) → c71(SQUARE(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(square(nil)) → c71(SQUARE(ok(nil)), PROPER(nil))
PROPER(square(cons(z0, z1))) → c71(SQUARE(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(square(rnil)) → c71(SQUARE(ok(rnil)), PROPER(rnil))
PROPER(square(rcons(z0, z1))) → c71(SQUARE(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(square(from(z0))) → c71(SQUARE(from(proper(z0))), PROPER(from(z0)))
PROPER(square(2ndspos(z0, z1))) → c71(SQUARE(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(square(2ndsneg(z0, z1))) → c71(SQUARE(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(square(pi(z0))) → c71(SQUARE(pi(proper(z0))), PROPER(pi(z0)))
PROPER(square(plus(z0, z1))) → c71(SQUARE(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(square(times(z0, z1))) → c71(SQUARE(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(square(square(z0))) → c71(SQUARE(square(proper(z0))), PROPER(square(z0)))

(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, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(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(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))
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))
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))
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(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)) → c10(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))
TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c58(S(ok(0)))
PROPER(s(nil)) → c58(S(ok(nil)))
PROPER(s(rnil)) → c58(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(rcons(x0, s(z0))) → c64(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c64(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c64(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, cons(z0, z1))) → c64(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, rcons(z0, z1))) → c64(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c64(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c64(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c64(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c64(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c64(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c64(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c64(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(s(z0), x1)) → c64(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c64(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c64(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c64(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c64(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c64(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c64(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c64(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c64(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c64(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c64(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c64(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(rcons(x0, 0)) → c64(RCONS(proper(x0), ok(0)), PROPER(x0))
PROPER(rcons(x0, nil)) → c64(RCONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(rcons(x0, rnil)) → c64(RCONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(rcons(0, x1)) → c64(RCONS(ok(0), proper(x1)), PROPER(x1))
PROPER(rcons(nil, x1)) → c64(RCONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c64(RCONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(from(s(z0))) → c65(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(posrecip(z0))) → c65(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(from(negrecip(z0))) → c65(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(from(cons(z0, z1))) → c65(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(rcons(z0, z1))) → c65(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(from(from(z0))) → c65(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(2ndspos(z0, z1))) → c65(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(from(2ndsneg(z0, z1))) → c65(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(from(pi(z0))) → c65(FROM(pi(proper(z0))), PROPER(pi(z0)))
PROPER(from(plus(z0, z1))) → c65(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(from(times(z0, z1))) → c65(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(from(square(z0))) → c65(FROM(square(proper(z0))), PROPER(square(z0)))
PROPER(from(0)) → c65(FROM(ok(0)))
PROPER(from(nil)) → c65(FROM(ok(nil)))
PROPER(from(rnil)) → c65(FROM(ok(rnil)))
PROPER(2ndspos(x0, s(z0))) → c66(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndspos(x0, posrecip(z0))) → c66(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndspos(x0, negrecip(z0))) → c66(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndspos(x0, cons(z0, z1))) → c66(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndspos(x0, rcons(z0, z1))) → c66(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndspos(x0, from(z0))) → c66(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndspos(x0, pi(z0))) → c66(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndspos(x0, plus(z0, z1))) → c66(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndspos(x0, times(z0, z1))) → c66(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndspos(x0, square(z0))) → c66(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndspos(s(z0), x1)) → c66(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndspos(posrecip(z0), x1)) → c66(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndspos(negrecip(z0), x1)) → c66(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndspos(cons(z0, z1), x1)) → c66(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndspos(rcons(z0, z1), x1)) → c66(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndspos(from(z0), x1)) → c66(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c66(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c66(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndspos(pi(z0), x1)) → c66(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndspos(plus(z0, z1), x1)) → c66(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndspos(times(z0, z1), x1)) → c66(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndspos(square(z0), x1)) → c66(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndspos(x0, 0)) → c66(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndspos(x0, nil)) → c66(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndspos(x0, rnil)) → c66(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndspos(0, x1)) → c66(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndspos(nil, x1)) → c66(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndspos(rnil, x1)) → c66(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(x0, s(z0))) → c67(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndsneg(x0, posrecip(z0))) → c67(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndsneg(x0, negrecip(z0))) → c67(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndsneg(x0, cons(z0, z1))) → c67(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndsneg(x0, rcons(z0, z1))) → c67(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndsneg(x0, from(z0))) → c67(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndsneg(x0, pi(z0))) → c67(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndsneg(x0, plus(z0, z1))) → c67(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndsneg(x0, times(z0, z1))) → c67(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndsneg(x0, square(z0))) → c67(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndsneg(s(z0), x1)) → c67(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndsneg(posrecip(z0), x1)) → c67(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndsneg(negrecip(z0), x1)) → c67(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndsneg(cons(z0, z1), x1)) → c67(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(rcons(z0, z1), x1)) → c67(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(from(z0), x1)) → c67(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c67(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c67(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndsneg(pi(z0), x1)) → c67(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndsneg(plus(z0, z1), x1)) → c67(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndsneg(times(z0, z1), x1)) → c67(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndsneg(square(z0), x1)) → c67(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndsneg(x0, 0)) → c67(2NDSNEG(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndsneg(x0, nil)) → c67(2NDSNEG(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndsneg(x0, rnil)) → c67(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndsneg(0, x1)) → c67(2NDSNEG(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndsneg(nil, x1)) → c67(2NDSNEG(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(rnil, x1)) → c67(2NDSNEG(ok(rnil), proper(x1)), PROPER(x1))
PROPER(pi(s(z0))) → c68(PI(s(proper(z0))), PROPER(s(z0)))
PROPER(pi(posrecip(z0))) → c68(PI(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(pi(negrecip(z0))) → c68(PI(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(pi(cons(z0, z1))) → c68(PI(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(pi(rcons(z0, z1))) → c68(PI(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(pi(from(z0))) → c68(PI(from(proper(z0))), PROPER(from(z0)))
PROPER(pi(2ndspos(z0, z1))) → c68(PI(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(pi(2ndsneg(z0, z1))) → c68(PI(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(pi(pi(z0))) → c68(PI(pi(proper(z0))), PROPER(pi(z0)))
PROPER(pi(plus(z0, z1))) → c68(PI(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(pi(times(z0, z1))) → c68(PI(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(pi(square(z0))) → c68(PI(square(proper(z0))), PROPER(square(z0)))
PROPER(pi(0)) → c68(PI(ok(0)))
PROPER(pi(nil)) → c68(PI(ok(nil)))
PROPER(pi(rnil)) → c68(PI(ok(rnil)))
PROPER(plus(x0, s(z0))) → c69(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(plus(x0, posrecip(z0))) → c69(PLUS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(plus(x0, negrecip(z0))) → c69(PLUS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(plus(x0, cons(z0, z1))) → c69(PLUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(plus(x0, rcons(z0, z1))) → c69(PLUS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(plus(x0, from(z0))) → c69(PLUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(plus(x0, 2ndspos(z0, z1))) → c69(PLUS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(plus(x0, 2ndsneg(z0, z1))) → c69(PLUS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(plus(x0, pi(z0))) → c69(PLUS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(plus(x0, plus(z0, z1))) → c69(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(plus(x0, times(z0, z1))) → c69(PLUS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(plus(x0, square(z0))) → c69(PLUS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(plus(s(z0), x1)) → c69(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(plus(posrecip(z0), x1)) → c69(PLUS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(plus(negrecip(z0), x1)) → c69(PLUS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(plus(cons(z0, z1), x1)) → c69(PLUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(plus(rcons(z0, z1), x1)) → c69(PLUS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(plus(from(z0), x1)) → c69(PLUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(plus(2ndspos(z0, z1), x1)) → c69(PLUS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(plus(2ndsneg(z0, z1), x1)) → c69(PLUS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(plus(pi(z0), x1)) → c69(PLUS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(plus(plus(z0, z1), x1)) → c69(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(plus(times(z0, z1), x1)) → c69(PLUS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(plus(square(z0), x1)) → c69(PLUS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(plus(x0, 0)) → c69(PLUS(proper(x0), ok(0)), PROPER(x0))
PROPER(plus(x0, nil)) → c69(PLUS(proper(x0), ok(nil)), PROPER(x0))
PROPER(plus(x0, rnil)) → c69(PLUS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(plus(0, x1)) → c69(PLUS(ok(0), proper(x1)), PROPER(x1))
PROPER(plus(nil, x1)) → c69(PLUS(ok(nil), proper(x1)), PROPER(x1))
PROPER(plus(rnil, x1)) → c69(PLUS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(times(x0, s(z0))) → c70(TIMES(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(times(x0, posrecip(z0))) → c70(TIMES(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(times(x0, negrecip(z0))) → c70(TIMES(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(times(x0, cons(z0, z1))) → c70(TIMES(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(times(x0, rcons(z0, z1))) → c70(TIMES(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(times(x0, from(z0))) → c70(TIMES(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(times(x0, 2ndspos(z0, z1))) → c70(TIMES(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(times(x0, 2ndsneg(z0, z1))) → c70(TIMES(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(times(x0, pi(z0))) → c70(TIMES(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(times(x0, plus(z0, z1))) → c70(TIMES(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(times(x0, times(z0, z1))) → c70(TIMES(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(times(x0, square(z0))) → c70(TIMES(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(times(s(z0), x1)) → c70(TIMES(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(times(posrecip(z0), x1)) → c70(TIMES(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(times(negrecip(z0), x1)) → c70(TIMES(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(times(cons(z0, z1), x1)) → c70(TIMES(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(times(rcons(z0, z1), x1)) → c70(TIMES(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(times(from(z0), x1)) → c70(TIMES(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(times(2ndspos(z0, z1), x1)) → c70(TIMES(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(times(2ndsneg(z0, z1), x1)) → c70(TIMES(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(times(pi(z0), x1)) → c70(TIMES(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(times(plus(z0, z1), x1)) → c70(TIMES(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(times(times(z0, z1), x1)) → c70(TIMES(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(times(square(z0), x1)) → c70(TIMES(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(times(x0, 0)) → c70(TIMES(proper(x0), ok(0)), PROPER(x0))
PROPER(times(x0, nil)) → c70(TIMES(proper(x0), ok(nil)), PROPER(x0))
PROPER(times(x0, rnil)) → c70(TIMES(proper(x0), ok(rnil)), PROPER(x0))
PROPER(times(0, x1)) → c70(TIMES(ok(0), proper(x1)), PROPER(x1))
PROPER(times(nil, x1)) → c70(TIMES(ok(nil), proper(x1)), PROPER(x1))
PROPER(times(rnil, x1)) → c70(TIMES(ok(rnil), proper(x1)), PROPER(x1))
PROPER(square(0)) → c71(SQUARE(ok(0)), PROPER(0))
PROPER(square(s(z0))) → c71(SQUARE(s(proper(z0))), PROPER(s(z0)))
PROPER(square(posrecip(z0))) → c71(SQUARE(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(square(negrecip(z0))) → c71(SQUARE(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(square(nil)) → c71(SQUARE(ok(nil)), PROPER(nil))
PROPER(square(cons(z0, z1))) → c71(SQUARE(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(square(rnil)) → c71(SQUARE(ok(rnil)), PROPER(rnil))
PROPER(square(rcons(z0, z1))) → c71(SQUARE(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(square(from(z0))) → c71(SQUARE(from(proper(z0))), PROPER(from(z0)))
PROPER(square(2ndspos(z0, z1))) → c71(SQUARE(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(square(2ndsneg(z0, z1))) → c71(SQUARE(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(square(pi(z0))) → c71(SQUARE(pi(proper(z0))), PROPER(pi(z0)))
PROPER(square(plus(z0, z1))) → c71(SQUARE(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(square(times(z0, z1))) → c71(SQUARE(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(square(square(z0))) → c71(SQUARE(square(proper(z0))), PROPER(square(z0)))

S tuples:

ACTIVE(square(z0)) → c10(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))
TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c58(S(ok(0)))
PROPER(s(nil)) → c58(S(ok(nil)))
PROPER(s(rnil)) → c58(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(rcons(x0, s(z0))) → c64(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c64(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c64(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, cons(z0, z1))) → c64(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, rcons(z0, z1))) → c64(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c64(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c64(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c64(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c64(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c64(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c64(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c64(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(s(z0), x1)) → c64(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c64(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c64(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c64(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c64(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c64(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c64(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c64(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c64(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c64(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c64(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c64(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(rcons(x0, 0)) → c64(RCONS(proper(x0), ok(0)), PROPER(x0))
PROPER(rcons(x0, nil)) → c64(RCONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(rcons(x0, rnil)) → c64(RCONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(rcons(0, x1)) → c64(RCONS(ok(0), proper(x1)), PROPER(x1))
PROPER(rcons(nil, x1)) → c64(RCONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c64(RCONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(from(s(z0))) → c65(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(posrecip(z0))) → c65(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(from(negrecip(z0))) → c65(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(from(cons(z0, z1))) → c65(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(rcons(z0, z1))) → c65(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(from(from(z0))) → c65(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(2ndspos(z0, z1))) → c65(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(from(2ndsneg(z0, z1))) → c65(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(from(pi(z0))) → c65(FROM(pi(proper(z0))), PROPER(pi(z0)))
PROPER(from(plus(z0, z1))) → c65(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(from(times(z0, z1))) → c65(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(from(square(z0))) → c65(FROM(square(proper(z0))), PROPER(square(z0)))
PROPER(from(0)) → c65(FROM(ok(0)))
PROPER(from(nil)) → c65(FROM(ok(nil)))
PROPER(from(rnil)) → c65(FROM(ok(rnil)))
PROPER(2ndspos(x0, s(z0))) → c66(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndspos(x0, posrecip(z0))) → c66(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndspos(x0, negrecip(z0))) → c66(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndspos(x0, cons(z0, z1))) → c66(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndspos(x0, rcons(z0, z1))) → c66(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndspos(x0, from(z0))) → c66(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndspos(x0, pi(z0))) → c66(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndspos(x0, plus(z0, z1))) → c66(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndspos(x0, times(z0, z1))) → c66(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndspos(x0, square(z0))) → c66(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndspos(s(z0), x1)) → c66(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndspos(posrecip(z0), x1)) → c66(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndspos(negrecip(z0), x1)) → c66(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndspos(cons(z0, z1), x1)) → c66(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndspos(rcons(z0, z1), x1)) → c66(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndspos(from(z0), x1)) → c66(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c66(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c66(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndspos(pi(z0), x1)) → c66(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndspos(plus(z0, z1), x1)) → c66(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndspos(times(z0, z1), x1)) → c66(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndspos(square(z0), x1)) → c66(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndspos(x0, 0)) → c66(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndspos(x0, nil)) → c66(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndspos(x0, rnil)) → c66(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndspos(0, x1)) → c66(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndspos(nil, x1)) → c66(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndspos(rnil, x1)) → c66(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(x0, s(z0))) → c67(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndsneg(x0, posrecip(z0))) → c67(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndsneg(x0, negrecip(z0))) → c67(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndsneg(x0, cons(z0, z1))) → c67(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndsneg(x0, rcons(z0, z1))) → c67(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndsneg(x0, from(z0))) → c67(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndsneg(x0, pi(z0))) → c67(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndsneg(x0, plus(z0, z1))) → c67(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndsneg(x0, times(z0, z1))) → c67(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndsneg(x0, square(z0))) → c67(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndsneg(s(z0), x1)) → c67(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndsneg(posrecip(z0), x1)) → c67(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndsneg(negrecip(z0), x1)) → c67(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndsneg(cons(z0, z1), x1)) → c67(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(rcons(z0, z1), x1)) → c67(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(from(z0), x1)) → c67(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c67(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c67(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndsneg(pi(z0), x1)) → c67(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndsneg(plus(z0, z1), x1)) → c67(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndsneg(times(z0, z1), x1)) → c67(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndsneg(square(z0), x1)) → c67(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndsneg(x0, 0)) → c67(2NDSNEG(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndsneg(x0, nil)) → c67(2NDSNEG(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndsneg(x0, rnil)) → c67(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndsneg(0, x1)) → c67(2NDSNEG(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndsneg(nil, x1)) → c67(2NDSNEG(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(rnil, x1)) → c67(2NDSNEG(ok(rnil), proper(x1)), PROPER(x1))
PROPER(pi(s(z0))) → c68(PI(s(proper(z0))), PROPER(s(z0)))
PROPER(pi(posrecip(z0))) → c68(PI(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(pi(negrecip(z0))) → c68(PI(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(pi(cons(z0, z1))) → c68(PI(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(pi(rcons(z0, z1))) → c68(PI(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(pi(from(z0))) → c68(PI(from(proper(z0))), PROPER(from(z0)))
PROPER(pi(2ndspos(z0, z1))) → c68(PI(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(pi(2ndsneg(z0, z1))) → c68(PI(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(pi(pi(z0))) → c68(PI(pi(proper(z0))), PROPER(pi(z0)))
PROPER(pi(plus(z0, z1))) → c68(PI(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(pi(times(z0, z1))) → c68(PI(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(pi(square(z0))) → c68(PI(square(proper(z0))), PROPER(square(z0)))
PROPER(pi(0)) → c68(PI(ok(0)))
PROPER(pi(nil)) → c68(PI(ok(nil)))
PROPER(pi(rnil)) → c68(PI(ok(rnil)))
PROPER(plus(x0, s(z0))) → c69(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(plus(x0, posrecip(z0))) → c69(PLUS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(plus(x0, negrecip(z0))) → c69(PLUS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(plus(x0, cons(z0, z1))) → c69(PLUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(plus(x0, rcons(z0, z1))) → c69(PLUS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(plus(x0, from(z0))) → c69(PLUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(plus(x0, 2ndspos(z0, z1))) → c69(PLUS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(plus(x0, 2ndsneg(z0, z1))) → c69(PLUS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(plus(x0, pi(z0))) → c69(PLUS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(plus(x0, plus(z0, z1))) → c69(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(plus(x0, times(z0, z1))) → c69(PLUS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(plus(x0, square(z0))) → c69(PLUS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(plus(s(z0), x1)) → c69(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(plus(posrecip(z0), x1)) → c69(PLUS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(plus(negrecip(z0), x1)) → c69(PLUS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(plus(cons(z0, z1), x1)) → c69(PLUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(plus(rcons(z0, z1), x1)) → c69(PLUS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(plus(from(z0), x1)) → c69(PLUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(plus(2ndspos(z0, z1), x1)) → c69(PLUS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(plus(2ndsneg(z0, z1), x1)) → c69(PLUS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(plus(pi(z0), x1)) → c69(PLUS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(plus(plus(z0, z1), x1)) → c69(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(plus(times(z0, z1), x1)) → c69(PLUS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(plus(square(z0), x1)) → c69(PLUS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(plus(x0, 0)) → c69(PLUS(proper(x0), ok(0)), PROPER(x0))
PROPER(plus(x0, nil)) → c69(PLUS(proper(x0), ok(nil)), PROPER(x0))
PROPER(plus(x0, rnil)) → c69(PLUS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(plus(0, x1)) → c69(PLUS(ok(0), proper(x1)), PROPER(x1))
PROPER(plus(nil, x1)) → c69(PLUS(ok(nil), proper(x1)), PROPER(x1))
PROPER(plus(rnil, x1)) → c69(PLUS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(times(x0, s(z0))) → c70(TIMES(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(times(x0, posrecip(z0))) → c70(TIMES(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(times(x0, negrecip(z0))) → c70(TIMES(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(times(x0, cons(z0, z1))) → c70(TIMES(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(times(x0, rcons(z0, z1))) → c70(TIMES(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(times(x0, from(z0))) → c70(TIMES(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(times(x0, 2ndspos(z0, z1))) → c70(TIMES(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(times(x0, 2ndsneg(z0, z1))) → c70(TIMES(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(times(x0, pi(z0))) → c70(TIMES(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(times(x0, plus(z0, z1))) → c70(TIMES(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(times(x0, times(z0, z1))) → c70(TIMES(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(times(x0, square(z0))) → c70(TIMES(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(times(s(z0), x1)) → c70(TIMES(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(times(posrecip(z0), x1)) → c70(TIMES(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(times(negrecip(z0), x1)) → c70(TIMES(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(times(cons(z0, z1), x1)) → c70(TIMES(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(times(rcons(z0, z1), x1)) → c70(TIMES(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(times(from(z0), x1)) → c70(TIMES(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(times(2ndspos(z0, z1), x1)) → c70(TIMES(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(times(2ndsneg(z0, z1), x1)) → c70(TIMES(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(times(pi(z0), x1)) → c70(TIMES(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(times(plus(z0, z1), x1)) → c70(TIMES(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(times(times(z0, z1), x1)) → c70(TIMES(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(times(square(z0), x1)) → c70(TIMES(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(times(x0, 0)) → c70(TIMES(proper(x0), ok(0)), PROPER(x0))
PROPER(times(x0, nil)) → c70(TIMES(proper(x0), ok(nil)), PROPER(x0))
PROPER(times(x0, rnil)) → c70(TIMES(proper(x0), ok(rnil)), PROPER(x0))
PROPER(times(0, x1)) → c70(TIMES(ok(0), proper(x1)), PROPER(x1))
PROPER(times(nil, x1)) → c70(TIMES(ok(nil), proper(x1)), PROPER(x1))
PROPER(times(rnil, x1)) → c70(TIMES(ok(rnil), proper(x1)), PROPER(x1))
PROPER(square(0)) → c71(SQUARE(ok(0)), PROPER(0))
PROPER(square(s(z0))) → c71(SQUARE(s(proper(z0))), PROPER(s(z0)))
PROPER(square(posrecip(z0))) → c71(SQUARE(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(square(negrecip(z0))) → c71(SQUARE(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(square(nil)) → c71(SQUARE(ok(nil)), PROPER(nil))
PROPER(square(cons(z0, z1))) → c71(SQUARE(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(square(rnil)) → c71(SQUARE(ok(rnil)), PROPER(rnil))
PROPER(square(rcons(z0, z1))) → c71(SQUARE(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(square(from(z0))) → c71(SQUARE(from(proper(z0))), PROPER(from(z0)))
PROPER(square(2ndspos(z0, z1))) → c71(SQUARE(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(square(2ndsneg(z0, z1))) → c71(SQUARE(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(square(pi(z0))) → c71(SQUARE(pi(proper(z0))), PROPER(pi(z0)))
PROPER(square(plus(z0, z1))) → c71(SQUARE(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(square(times(z0, z1))) → c71(SQUARE(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(square(square(z0))) → c71(SQUARE(square(proper(z0))), PROPER(square(z0)))

K tuples:none
Defined Rule Symbols:

active, rcons, posrecip, 2ndsneg, negrecip, 2ndspos, s, cons, from, pi, plus, times, square, proper

Defined Pair Symbols:

ACTIVE, S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, TOP, PROPER

Compound Symbols:

c10, c15, c16, c18, c19, c20, c21, c23, c24, c25, c26, 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, c72, c73, c, c5, c7, c9, c1, c11, c12, c13, c14, c17, c22, c27, c58, c58, c59, c59, c60, c60, c62, c62, c64, c64, c65, c65, c66, c66, c67, c67, c68, c68, c69, c69, c70, c70, c71

(71) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)

Removed 3 trailing tuple parts

(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, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(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(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))
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))
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))
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(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)) → c10(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))
TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c58(S(ok(0)))
PROPER(s(nil)) → c58(S(ok(nil)))
PROPER(s(rnil)) → c58(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(rcons(x0, s(z0))) → c64(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c64(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c64(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, cons(z0, z1))) → c64(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, rcons(z0, z1))) → c64(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c64(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c64(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c64(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c64(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c64(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c64(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c64(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(s(z0), x1)) → c64(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c64(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c64(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c64(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c64(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c64(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c64(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c64(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c64(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c64(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c64(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c64(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(rcons(x0, 0)) → c64(RCONS(proper(x0), ok(0)), PROPER(x0))
PROPER(rcons(x0, nil)) → c64(RCONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(rcons(x0, rnil)) → c64(RCONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(rcons(0, x1)) → c64(RCONS(ok(0), proper(x1)), PROPER(x1))
PROPER(rcons(nil, x1)) → c64(RCONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c64(RCONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(from(s(z0))) → c65(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(posrecip(z0))) → c65(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(from(negrecip(z0))) → c65(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(from(cons(z0, z1))) → c65(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(rcons(z0, z1))) → c65(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(from(from(z0))) → c65(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(2ndspos(z0, z1))) → c65(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(from(2ndsneg(z0, z1))) → c65(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(from(pi(z0))) → c65(FROM(pi(proper(z0))), PROPER(pi(z0)))
PROPER(from(plus(z0, z1))) → c65(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(from(times(z0, z1))) → c65(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(from(square(z0))) → c65(FROM(square(proper(z0))), PROPER(square(z0)))
PROPER(from(0)) → c65(FROM(ok(0)))
PROPER(from(nil)) → c65(FROM(ok(nil)))
PROPER(from(rnil)) → c65(FROM(ok(rnil)))
PROPER(2ndspos(x0, s(z0))) → c66(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndspos(x0, posrecip(z0))) → c66(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndspos(x0, negrecip(z0))) → c66(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndspos(x0, cons(z0, z1))) → c66(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndspos(x0, rcons(z0, z1))) → c66(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndspos(x0, from(z0))) → c66(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndspos(x0, pi(z0))) → c66(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndspos(x0, plus(z0, z1))) → c66(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndspos(x0, times(z0, z1))) → c66(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndspos(x0, square(z0))) → c66(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndspos(s(z0), x1)) → c66(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndspos(posrecip(z0), x1)) → c66(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndspos(negrecip(z0), x1)) → c66(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndspos(cons(z0, z1), x1)) → c66(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndspos(rcons(z0, z1), x1)) → c66(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndspos(from(z0), x1)) → c66(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c66(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c66(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndspos(pi(z0), x1)) → c66(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndspos(plus(z0, z1), x1)) → c66(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndspos(times(z0, z1), x1)) → c66(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndspos(square(z0), x1)) → c66(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndspos(x0, 0)) → c66(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndspos(x0, nil)) → c66(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndspos(x0, rnil)) → c66(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndspos(0, x1)) → c66(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndspos(nil, x1)) → c66(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndspos(rnil, x1)) → c66(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(x0, s(z0))) → c67(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndsneg(x0, posrecip(z0))) → c67(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndsneg(x0, negrecip(z0))) → c67(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndsneg(x0, cons(z0, z1))) → c67(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndsneg(x0, rcons(z0, z1))) → c67(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndsneg(x0, from(z0))) → c67(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndsneg(x0, pi(z0))) → c67(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndsneg(x0, plus(z0, z1))) → c67(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndsneg(x0, times(z0, z1))) → c67(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndsneg(x0, square(z0))) → c67(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndsneg(s(z0), x1)) → c67(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndsneg(posrecip(z0), x1)) → c67(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndsneg(negrecip(z0), x1)) → c67(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndsneg(cons(z0, z1), x1)) → c67(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(rcons(z0, z1), x1)) → c67(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(from(z0), x1)) → c67(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c67(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c67(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndsneg(pi(z0), x1)) → c67(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndsneg(plus(z0, z1), x1)) → c67(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndsneg(times(z0, z1), x1)) → c67(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndsneg(square(z0), x1)) → c67(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndsneg(x0, 0)) → c67(2NDSNEG(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndsneg(x0, nil)) → c67(2NDSNEG(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndsneg(x0, rnil)) → c67(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndsneg(0, x1)) → c67(2NDSNEG(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndsneg(nil, x1)) → c67(2NDSNEG(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(rnil, x1)) → c67(2NDSNEG(ok(rnil), proper(x1)), PROPER(x1))
PROPER(pi(s(z0))) → c68(PI(s(proper(z0))), PROPER(s(z0)))
PROPER(pi(posrecip(z0))) → c68(PI(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(pi(negrecip(z0))) → c68(PI(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(pi(cons(z0, z1))) → c68(PI(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(pi(rcons(z0, z1))) → c68(PI(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(pi(from(z0))) → c68(PI(from(proper(z0))), PROPER(from(z0)))
PROPER(pi(2ndspos(z0, z1))) → c68(PI(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(pi(2ndsneg(z0, z1))) → c68(PI(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(pi(pi(z0))) → c68(PI(pi(proper(z0))), PROPER(pi(z0)))
PROPER(pi(plus(z0, z1))) → c68(PI(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(pi(times(z0, z1))) → c68(PI(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(pi(square(z0))) → c68(PI(square(proper(z0))), PROPER(square(z0)))
PROPER(pi(0)) → c68(PI(ok(0)))
PROPER(pi(nil)) → c68(PI(ok(nil)))
PROPER(pi(rnil)) → c68(PI(ok(rnil)))
PROPER(plus(x0, s(z0))) → c69(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(plus(x0, posrecip(z0))) → c69(PLUS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(plus(x0, negrecip(z0))) → c69(PLUS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(plus(x0, cons(z0, z1))) → c69(PLUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(plus(x0, rcons(z0, z1))) → c69(PLUS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(plus(x0, from(z0))) → c69(PLUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(plus(x0, 2ndspos(z0, z1))) → c69(PLUS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(plus(x0, 2ndsneg(z0, z1))) → c69(PLUS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(plus(x0, pi(z0))) → c69(PLUS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(plus(x0, plus(z0, z1))) → c69(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(plus(x0, times(z0, z1))) → c69(PLUS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(plus(x0, square(z0))) → c69(PLUS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(plus(s(z0), x1)) → c69(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(plus(posrecip(z0), x1)) → c69(PLUS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(plus(negrecip(z0), x1)) → c69(PLUS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(plus(cons(z0, z1), x1)) → c69(PLUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(plus(rcons(z0, z1), x1)) → c69(PLUS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(plus(from(z0), x1)) → c69(PLUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(plus(2ndspos(z0, z1), x1)) → c69(PLUS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(plus(2ndsneg(z0, z1), x1)) → c69(PLUS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(plus(pi(z0), x1)) → c69(PLUS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(plus(plus(z0, z1), x1)) → c69(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(plus(times(z0, z1), x1)) → c69(PLUS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(plus(square(z0), x1)) → c69(PLUS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(plus(x0, 0)) → c69(PLUS(proper(x0), ok(0)), PROPER(x0))
PROPER(plus(x0, nil)) → c69(PLUS(proper(x0), ok(nil)), PROPER(x0))
PROPER(plus(x0, rnil)) → c69(PLUS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(plus(0, x1)) → c69(PLUS(ok(0), proper(x1)), PROPER(x1))
PROPER(plus(nil, x1)) → c69(PLUS(ok(nil), proper(x1)), PROPER(x1))
PROPER(plus(rnil, x1)) → c69(PLUS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(times(x0, s(z0))) → c70(TIMES(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(times(x0, posrecip(z0))) → c70(TIMES(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(times(x0, negrecip(z0))) → c70(TIMES(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(times(x0, cons(z0, z1))) → c70(TIMES(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(times(x0, rcons(z0, z1))) → c70(TIMES(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(times(x0, from(z0))) → c70(TIMES(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(times(x0, 2ndspos(z0, z1))) → c70(TIMES(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(times(x0, 2ndsneg(z0, z1))) → c70(TIMES(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(times(x0, pi(z0))) → c70(TIMES(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(times(x0, plus(z0, z1))) → c70(TIMES(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(times(x0, times(z0, z1))) → c70(TIMES(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(times(x0, square(z0))) → c70(TIMES(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(times(s(z0), x1)) → c70(TIMES(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(times(posrecip(z0), x1)) → c70(TIMES(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(times(negrecip(z0), x1)) → c70(TIMES(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(times(cons(z0, z1), x1)) → c70(TIMES(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(times(rcons(z0, z1), x1)) → c70(TIMES(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(times(from(z0), x1)) → c70(TIMES(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(times(2ndspos(z0, z1), x1)) → c70(TIMES(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(times(2ndsneg(z0, z1), x1)) → c70(TIMES(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(times(pi(z0), x1)) → c70(TIMES(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(times(plus(z0, z1), x1)) → c70(TIMES(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(times(times(z0, z1), x1)) → c70(TIMES(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(times(square(z0), x1)) → c70(TIMES(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(times(x0, 0)) → c70(TIMES(proper(x0), ok(0)), PROPER(x0))
PROPER(times(x0, nil)) → c70(TIMES(proper(x0), ok(nil)), PROPER(x0))
PROPER(times(x0, rnil)) → c70(TIMES(proper(x0), ok(rnil)), PROPER(x0))
PROPER(times(0, x1)) → c70(TIMES(ok(0), proper(x1)), PROPER(x1))
PROPER(times(nil, x1)) → c70(TIMES(ok(nil), proper(x1)), PROPER(x1))
PROPER(times(rnil, x1)) → c70(TIMES(ok(rnil), proper(x1)), PROPER(x1))
PROPER(square(s(z0))) → c71(SQUARE(s(proper(z0))), PROPER(s(z0)))
PROPER(square(posrecip(z0))) → c71(SQUARE(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(square(negrecip(z0))) → c71(SQUARE(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(square(cons(z0, z1))) → c71(SQUARE(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(square(rcons(z0, z1))) → c71(SQUARE(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(square(from(z0))) → c71(SQUARE(from(proper(z0))), PROPER(from(z0)))
PROPER(square(2ndspos(z0, z1))) → c71(SQUARE(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(square(2ndsneg(z0, z1))) → c71(SQUARE(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(square(pi(z0))) → c71(SQUARE(pi(proper(z0))), PROPER(pi(z0)))
PROPER(square(plus(z0, z1))) → c71(SQUARE(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(square(times(z0, z1))) → c71(SQUARE(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(square(square(z0))) → c71(SQUARE(square(proper(z0))), PROPER(square(z0)))
PROPER(square(0)) → c71(SQUARE(ok(0)))
PROPER(square(nil)) → c71(SQUARE(ok(nil)))
PROPER(square(rnil)) → c71(SQUARE(ok(rnil)))

S tuples:

ACTIVE(square(z0)) → c10(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))
TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c58(S(ok(0)))
PROPER(s(nil)) → c58(S(ok(nil)))
PROPER(s(rnil)) → c58(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(rcons(x0, s(z0))) → c64(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c64(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c64(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, cons(z0, z1))) → c64(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, rcons(z0, z1))) → c64(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c64(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c64(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c64(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c64(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c64(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c64(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c64(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(s(z0), x1)) → c64(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c64(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c64(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c64(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c64(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c64(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c64(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c64(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c64(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c64(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c64(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c64(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(rcons(x0, 0)) → c64(RCONS(proper(x0), ok(0)), PROPER(x0))
PROPER(rcons(x0, nil)) → c64(RCONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(rcons(x0, rnil)) → c64(RCONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(rcons(0, x1)) → c64(RCONS(ok(0), proper(x1)), PROPER(x1))
PROPER(rcons(nil, x1)) → c64(RCONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c64(RCONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(from(s(z0))) → c65(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(posrecip(z0))) → c65(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(from(negrecip(z0))) → c65(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(from(cons(z0, z1))) → c65(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(rcons(z0, z1))) → c65(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(from(from(z0))) → c65(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(2ndspos(z0, z1))) → c65(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(from(2ndsneg(z0, z1))) → c65(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(from(pi(z0))) → c65(FROM(pi(proper(z0))), PROPER(pi(z0)))
PROPER(from(plus(z0, z1))) → c65(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(from(times(z0, z1))) → c65(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(from(square(z0))) → c65(FROM(square(proper(z0))), PROPER(square(z0)))
PROPER(from(0)) → c65(FROM(ok(0)))
PROPER(from(nil)) → c65(FROM(ok(nil)))
PROPER(from(rnil)) → c65(FROM(ok(rnil)))
PROPER(2ndspos(x0, s(z0))) → c66(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndspos(x0, posrecip(z0))) → c66(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndspos(x0, negrecip(z0))) → c66(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndspos(x0, cons(z0, z1))) → c66(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndspos(x0, rcons(z0, z1))) → c66(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndspos(x0, from(z0))) → c66(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndspos(x0, pi(z0))) → c66(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndspos(x0, plus(z0, z1))) → c66(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndspos(x0, times(z0, z1))) → c66(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndspos(x0, square(z0))) → c66(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndspos(s(z0), x1)) → c66(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndspos(posrecip(z0), x1)) → c66(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndspos(negrecip(z0), x1)) → c66(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndspos(cons(z0, z1), x1)) → c66(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndspos(rcons(z0, z1), x1)) → c66(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndspos(from(z0), x1)) → c66(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c66(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c66(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndspos(pi(z0), x1)) → c66(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndspos(plus(z0, z1), x1)) → c66(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndspos(times(z0, z1), x1)) → c66(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndspos(square(z0), x1)) → c66(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndspos(x0, 0)) → c66(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndspos(x0, nil)) → c66(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndspos(x0, rnil)) → c66(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndspos(0, x1)) → c66(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndspos(nil, x1)) → c66(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndspos(rnil, x1)) → c66(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(x0, s(z0))) → c67(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndsneg(x0, posrecip(z0))) → c67(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndsneg(x0, negrecip(z0))) → c67(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndsneg(x0, cons(z0, z1))) → c67(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndsneg(x0, rcons(z0, z1))) → c67(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndsneg(x0, from(z0))) → c67(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndsneg(x0, pi(z0))) → c67(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndsneg(x0, plus(z0, z1))) → c67(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndsneg(x0, times(z0, z1))) → c67(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndsneg(x0, square(z0))) → c67(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndsneg(s(z0), x1)) → c67(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndsneg(posrecip(z0), x1)) → c67(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndsneg(negrecip(z0), x1)) → c67(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndsneg(cons(z0, z1), x1)) → c67(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(rcons(z0, z1), x1)) → c67(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(from(z0), x1)) → c67(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c67(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c67(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndsneg(pi(z0), x1)) → c67(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndsneg(plus(z0, z1), x1)) → c67(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndsneg(times(z0, z1), x1)) → c67(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndsneg(square(z0), x1)) → c67(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndsneg(x0, 0)) → c67(2NDSNEG(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndsneg(x0, nil)) → c67(2NDSNEG(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndsneg(x0, rnil)) → c67(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndsneg(0, x1)) → c67(2NDSNEG(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndsneg(nil, x1)) → c67(2NDSNEG(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(rnil, x1)) → c67(2NDSNEG(ok(rnil), proper(x1)), PROPER(x1))
PROPER(pi(s(z0))) → c68(PI(s(proper(z0))), PROPER(s(z0)))
PROPER(pi(posrecip(z0))) → c68(PI(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(pi(negrecip(z0))) → c68(PI(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(pi(cons(z0, z1))) → c68(PI(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(pi(rcons(z0, z1))) → c68(PI(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(pi(from(z0))) → c68(PI(from(proper(z0))), PROPER(from(z0)))
PROPER(pi(2ndspos(z0, z1))) → c68(PI(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(pi(2ndsneg(z0, z1))) → c68(PI(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(pi(pi(z0))) → c68(PI(pi(proper(z0))), PROPER(pi(z0)))
PROPER(pi(plus(z0, z1))) → c68(PI(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(pi(times(z0, z1))) → c68(PI(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(pi(square(z0))) → c68(PI(square(proper(z0))), PROPER(square(z0)))
PROPER(pi(0)) → c68(PI(ok(0)))
PROPER(pi(nil)) → c68(PI(ok(nil)))
PROPER(pi(rnil)) → c68(PI(ok(rnil)))
PROPER(plus(x0, s(z0))) → c69(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(plus(x0, posrecip(z0))) → c69(PLUS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(plus(x0, negrecip(z0))) → c69(PLUS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(plus(x0, cons(z0, z1))) → c69(PLUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(plus(x0, rcons(z0, z1))) → c69(PLUS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(plus(x0, from(z0))) → c69(PLUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(plus(x0, 2ndspos(z0, z1))) → c69(PLUS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(plus(x0, 2ndsneg(z0, z1))) → c69(PLUS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(plus(x0, pi(z0))) → c69(PLUS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(plus(x0, plus(z0, z1))) → c69(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(plus(x0, times(z0, z1))) → c69(PLUS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(plus(x0, square(z0))) → c69(PLUS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(plus(s(z0), x1)) → c69(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(plus(posrecip(z0), x1)) → c69(PLUS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(plus(negrecip(z0), x1)) → c69(PLUS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(plus(cons(z0, z1), x1)) → c69(PLUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(plus(rcons(z0, z1), x1)) → c69(PLUS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(plus(from(z0), x1)) → c69(PLUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(plus(2ndspos(z0, z1), x1)) → c69(PLUS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(plus(2ndsneg(z0, z1), x1)) → c69(PLUS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(plus(pi(z0), x1)) → c69(PLUS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(plus(plus(z0, z1), x1)) → c69(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(plus(times(z0, z1), x1)) → c69(PLUS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(plus(square(z0), x1)) → c69(PLUS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(plus(x0, 0)) → c69(PLUS(proper(x0), ok(0)), PROPER(x0))
PROPER(plus(x0, nil)) → c69(PLUS(proper(x0), ok(nil)), PROPER(x0))
PROPER(plus(x0, rnil)) → c69(PLUS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(plus(0, x1)) → c69(PLUS(ok(0), proper(x1)), PROPER(x1))
PROPER(plus(nil, x1)) → c69(PLUS(ok(nil), proper(x1)), PROPER(x1))
PROPER(plus(rnil, x1)) → c69(PLUS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(times(x0, s(z0))) → c70(TIMES(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(times(x0, posrecip(z0))) → c70(TIMES(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(times(x0, negrecip(z0))) → c70(TIMES(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(times(x0, cons(z0, z1))) → c70(TIMES(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(times(x0, rcons(z0, z1))) → c70(TIMES(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(times(x0, from(z0))) → c70(TIMES(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(times(x0, 2ndspos(z0, z1))) → c70(TIMES(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(times(x0, 2ndsneg(z0, z1))) → c70(TIMES(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(times(x0, pi(z0))) → c70(TIMES(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(times(x0, plus(z0, z1))) → c70(TIMES(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(times(x0, times(z0, z1))) → c70(TIMES(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(times(x0, square(z0))) → c70(TIMES(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(times(s(z0), x1)) → c70(TIMES(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(times(posrecip(z0), x1)) → c70(TIMES(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(times(negrecip(z0), x1)) → c70(TIMES(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(times(cons(z0, z1), x1)) → c70(TIMES(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(times(rcons(z0, z1), x1)) → c70(TIMES(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(times(from(z0), x1)) → c70(TIMES(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(times(2ndspos(z0, z1), x1)) → c70(TIMES(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(times(2ndsneg(z0, z1), x1)) → c70(TIMES(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(times(pi(z0), x1)) → c70(TIMES(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(times(plus(z0, z1), x1)) → c70(TIMES(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(times(times(z0, z1), x1)) → c70(TIMES(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(times(square(z0), x1)) → c70(TIMES(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(times(x0, 0)) → c70(TIMES(proper(x0), ok(0)), PROPER(x0))
PROPER(times(x0, nil)) → c70(TIMES(proper(x0), ok(nil)), PROPER(x0))
PROPER(times(x0, rnil)) → c70(TIMES(proper(x0), ok(rnil)), PROPER(x0))
PROPER(times(0, x1)) → c70(TIMES(ok(0), proper(x1)), PROPER(x1))
PROPER(times(nil, x1)) → c70(TIMES(ok(nil), proper(x1)), PROPER(x1))
PROPER(times(rnil, x1)) → c70(TIMES(ok(rnil), proper(x1)), PROPER(x1))
PROPER(square(s(z0))) → c71(SQUARE(s(proper(z0))), PROPER(s(z0)))
PROPER(square(posrecip(z0))) → c71(SQUARE(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(square(negrecip(z0))) → c71(SQUARE(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(square(cons(z0, z1))) → c71(SQUARE(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(square(rcons(z0, z1))) → c71(SQUARE(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(square(from(z0))) → c71(SQUARE(from(proper(z0))), PROPER(from(z0)))
PROPER(square(2ndspos(z0, z1))) → c71(SQUARE(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(square(2ndsneg(z0, z1))) → c71(SQUARE(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(square(pi(z0))) → c71(SQUARE(pi(proper(z0))), PROPER(pi(z0)))
PROPER(square(plus(z0, z1))) → c71(SQUARE(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(square(times(z0, z1))) → c71(SQUARE(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(square(square(z0))) → c71(SQUARE(square(proper(z0))), PROPER(square(z0)))
PROPER(square(0)) → c71(SQUARE(ok(0)))
PROPER(square(nil)) → c71(SQUARE(ok(nil)))
PROPER(square(rnil)) → c71(SQUARE(ok(rnil)))

K tuples:none
Defined Rule Symbols:

active, rcons, posrecip, 2ndsneg, negrecip, 2ndspos, s, cons, from, pi, plus, times, square, proper

Defined Pair Symbols:

ACTIVE, S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, TOP, PROPER

Compound Symbols:

c10, c15, c16, c18, c19, c20, c21, c23, c24, c25, c26, 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, c72, c73, c, c5, c7, c9, c1, c11, c12, c13, c14, c17, c22, c27, c58, c58, c59, c59, c60, c60, c62, c62, c64, c64, c65, c65, c66, c66, c67, c67, c68, c68, c69, c69, c70, c70, c71, c71

(73) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

Use narrowing to replace TOP(mark(z0)) → c72(TOP(proper(z0)), PROPER(z0)) by

TOP(mark(0)) → c72(TOP(ok(0)), PROPER(0))
TOP(mark(s(z0))) → c72(TOP(s(proper(z0))), PROPER(s(z0)))
TOP(mark(posrecip(z0))) → c72(TOP(posrecip(proper(z0))), PROPER(posrecip(z0)))
TOP(mark(negrecip(z0))) → c72(TOP(negrecip(proper(z0))), PROPER(negrecip(z0)))
TOP(mark(nil)) → c72(TOP(ok(nil)), PROPER(nil))
TOP(mark(cons(z0, z1))) → c72(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
TOP(mark(rnil)) → c72(TOP(ok(rnil)), PROPER(rnil))
TOP(mark(rcons(z0, z1))) → c72(TOP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
TOP(mark(from(z0))) → c72(TOP(from(proper(z0))), PROPER(from(z0)))
TOP(mark(2ndspos(z0, z1))) → c72(TOP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
TOP(mark(2ndsneg(z0, z1))) → c72(TOP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
TOP(mark(pi(z0))) → c72(TOP(pi(proper(z0))), PROPER(pi(z0)))
TOP(mark(plus(z0, z1))) → c72(TOP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
TOP(mark(times(z0, z1))) → c72(TOP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
TOP(mark(square(z0))) → c72(TOP(square(proper(z0))), PROPER(square(z0)))

(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, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(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(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))
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))
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))
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(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)) → c10(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))
TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c58(S(ok(0)))
PROPER(s(nil)) → c58(S(ok(nil)))
PROPER(s(rnil)) → c58(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(rcons(x0, s(z0))) → c64(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c64(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c64(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, cons(z0, z1))) → c64(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, rcons(z0, z1))) → c64(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c64(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c64(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c64(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c64(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c64(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c64(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c64(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(s(z0), x1)) → c64(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c64(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c64(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c64(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c64(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c64(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c64(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c64(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c64(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c64(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c64(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c64(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(rcons(x0, 0)) → c64(RCONS(proper(x0), ok(0)), PROPER(x0))
PROPER(rcons(x0, nil)) → c64(RCONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(rcons(x0, rnil)) → c64(RCONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(rcons(0, x1)) → c64(RCONS(ok(0), proper(x1)), PROPER(x1))
PROPER(rcons(nil, x1)) → c64(RCONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c64(RCONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(from(s(z0))) → c65(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(posrecip(z0))) → c65(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(from(negrecip(z0))) → c65(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(from(cons(z0, z1))) → c65(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(rcons(z0, z1))) → c65(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(from(from(z0))) → c65(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(2ndspos(z0, z1))) → c65(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(from(2ndsneg(z0, z1))) → c65(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(from(pi(z0))) → c65(FROM(pi(proper(z0))), PROPER(pi(z0)))
PROPER(from(plus(z0, z1))) → c65(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(from(times(z0, z1))) → c65(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(from(square(z0))) → c65(FROM(square(proper(z0))), PROPER(square(z0)))
PROPER(from(0)) → c65(FROM(ok(0)))
PROPER(from(nil)) → c65(FROM(ok(nil)))
PROPER(from(rnil)) → c65(FROM(ok(rnil)))
PROPER(2ndspos(x0, s(z0))) → c66(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndspos(x0, posrecip(z0))) → c66(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndspos(x0, negrecip(z0))) → c66(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndspos(x0, cons(z0, z1))) → c66(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndspos(x0, rcons(z0, z1))) → c66(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndspos(x0, from(z0))) → c66(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndspos(x0, pi(z0))) → c66(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndspos(x0, plus(z0, z1))) → c66(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndspos(x0, times(z0, z1))) → c66(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndspos(x0, square(z0))) → c66(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndspos(s(z0), x1)) → c66(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndspos(posrecip(z0), x1)) → c66(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndspos(negrecip(z0), x1)) → c66(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndspos(cons(z0, z1), x1)) → c66(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndspos(rcons(z0, z1), x1)) → c66(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndspos(from(z0), x1)) → c66(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c66(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c66(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndspos(pi(z0), x1)) → c66(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndspos(plus(z0, z1), x1)) → c66(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndspos(times(z0, z1), x1)) → c66(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndspos(square(z0), x1)) → c66(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndspos(x0, 0)) → c66(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndspos(x0, nil)) → c66(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndspos(x0, rnil)) → c66(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndspos(0, x1)) → c66(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndspos(nil, x1)) → c66(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndspos(rnil, x1)) → c66(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(x0, s(z0))) → c67(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndsneg(x0, posrecip(z0))) → c67(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndsneg(x0, negrecip(z0))) → c67(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndsneg(x0, cons(z0, z1))) → c67(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndsneg(x0, rcons(z0, z1))) → c67(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndsneg(x0, from(z0))) → c67(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndsneg(x0, pi(z0))) → c67(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndsneg(x0, plus(z0, z1))) → c67(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndsneg(x0, times(z0, z1))) → c67(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndsneg(x0, square(z0))) → c67(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndsneg(s(z0), x1)) → c67(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndsneg(posrecip(z0), x1)) → c67(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndsneg(negrecip(z0), x1)) → c67(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndsneg(cons(z0, z1), x1)) → c67(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(rcons(z0, z1), x1)) → c67(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(from(z0), x1)) → c67(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c67(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c67(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndsneg(pi(z0), x1)) → c67(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndsneg(plus(z0, z1), x1)) → c67(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndsneg(times(z0, z1), x1)) → c67(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndsneg(square(z0), x1)) → c67(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndsneg(x0, 0)) → c67(2NDSNEG(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndsneg(x0, nil)) → c67(2NDSNEG(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndsneg(x0, rnil)) → c67(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndsneg(0, x1)) → c67(2NDSNEG(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndsneg(nil, x1)) → c67(2NDSNEG(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(rnil, x1)) → c67(2NDSNEG(ok(rnil), proper(x1)), PROPER(x1))
PROPER(pi(s(z0))) → c68(PI(s(proper(z0))), PROPER(s(z0)))
PROPER(pi(posrecip(z0))) → c68(PI(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(pi(negrecip(z0))) → c68(PI(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(pi(cons(z0, z1))) → c68(PI(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(pi(rcons(z0, z1))) → c68(PI(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(pi(from(z0))) → c68(PI(from(proper(z0))), PROPER(from(z0)))
PROPER(pi(2ndspos(z0, z1))) → c68(PI(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(pi(2ndsneg(z0, z1))) → c68(PI(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(pi(pi(z0))) → c68(PI(pi(proper(z0))), PROPER(pi(z0)))
PROPER(pi(plus(z0, z1))) → c68(PI(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(pi(times(z0, z1))) → c68(PI(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(pi(square(z0))) → c68(PI(square(proper(z0))), PROPER(square(z0)))
PROPER(pi(0)) → c68(PI(ok(0)))
PROPER(pi(nil)) → c68(PI(ok(nil)))
PROPER(pi(rnil)) → c68(PI(ok(rnil)))
PROPER(plus(x0, s(z0))) → c69(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(plus(x0, posrecip(z0))) → c69(PLUS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(plus(x0, negrecip(z0))) → c69(PLUS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(plus(x0, cons(z0, z1))) → c69(PLUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(plus(x0, rcons(z0, z1))) → c69(PLUS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(plus(x0, from(z0))) → c69(PLUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(plus(x0, 2ndspos(z0, z1))) → c69(PLUS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(plus(x0, 2ndsneg(z0, z1))) → c69(PLUS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(plus(x0, pi(z0))) → c69(PLUS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(plus(x0, plus(z0, z1))) → c69(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(plus(x0, times(z0, z1))) → c69(PLUS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(plus(x0, square(z0))) → c69(PLUS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(plus(s(z0), x1)) → c69(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(plus(posrecip(z0), x1)) → c69(PLUS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(plus(negrecip(z0), x1)) → c69(PLUS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(plus(cons(z0, z1), x1)) → c69(PLUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(plus(rcons(z0, z1), x1)) → c69(PLUS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(plus(from(z0), x1)) → c69(PLUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(plus(2ndspos(z0, z1), x1)) → c69(PLUS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(plus(2ndsneg(z0, z1), x1)) → c69(PLUS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(plus(pi(z0), x1)) → c69(PLUS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(plus(plus(z0, z1), x1)) → c69(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(plus(times(z0, z1), x1)) → c69(PLUS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(plus(square(z0), x1)) → c69(PLUS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(plus(x0, 0)) → c69(PLUS(proper(x0), ok(0)), PROPER(x0))
PROPER(plus(x0, nil)) → c69(PLUS(proper(x0), ok(nil)), PROPER(x0))
PROPER(plus(x0, rnil)) → c69(PLUS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(plus(0, x1)) → c69(PLUS(ok(0), proper(x1)), PROPER(x1))
PROPER(plus(nil, x1)) → c69(PLUS(ok(nil), proper(x1)), PROPER(x1))
PROPER(plus(rnil, x1)) → c69(PLUS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(times(x0, s(z0))) → c70(TIMES(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(times(x0, posrecip(z0))) → c70(TIMES(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(times(x0, negrecip(z0))) → c70(TIMES(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(times(x0, cons(z0, z1))) → c70(TIMES(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(times(x0, rcons(z0, z1))) → c70(TIMES(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(times(x0, from(z0))) → c70(TIMES(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(times(x0, 2ndspos(z0, z1))) → c70(TIMES(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(times(x0, 2ndsneg(z0, z1))) → c70(TIMES(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(times(x0, pi(z0))) → c70(TIMES(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(times(x0, plus(z0, z1))) → c70(TIMES(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(times(x0, times(z0, z1))) → c70(TIMES(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(times(x0, square(z0))) → c70(TIMES(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(times(s(z0), x1)) → c70(TIMES(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(times(posrecip(z0), x1)) → c70(TIMES(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(times(negrecip(z0), x1)) → c70(TIMES(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(times(cons(z0, z1), x1)) → c70(TIMES(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(times(rcons(z0, z1), x1)) → c70(TIMES(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(times(from(z0), x1)) → c70(TIMES(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(times(2ndspos(z0, z1), x1)) → c70(TIMES(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(times(2ndsneg(z0, z1), x1)) → c70(TIMES(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(times(pi(z0), x1)) → c70(TIMES(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(times(plus(z0, z1), x1)) → c70(TIMES(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(times(times(z0, z1), x1)) → c70(TIMES(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(times(square(z0), x1)) → c70(TIMES(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(times(x0, 0)) → c70(TIMES(proper(x0), ok(0)), PROPER(x0))
PROPER(times(x0, nil)) → c70(TIMES(proper(x0), ok(nil)), PROPER(x0))
PROPER(times(x0, rnil)) → c70(TIMES(proper(x0), ok(rnil)), PROPER(x0))
PROPER(times(0, x1)) → c70(TIMES(ok(0), proper(x1)), PROPER(x1))
PROPER(times(nil, x1)) → c70(TIMES(ok(nil), proper(x1)), PROPER(x1))
PROPER(times(rnil, x1)) → c70(TIMES(ok(rnil), proper(x1)), PROPER(x1))
PROPER(square(s(z0))) → c71(SQUARE(s(proper(z0))), PROPER(s(z0)))
PROPER(square(posrecip(z0))) → c71(SQUARE(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(square(negrecip(z0))) → c71(SQUARE(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(square(cons(z0, z1))) → c71(SQUARE(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(square(rcons(z0, z1))) → c71(SQUARE(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(square(from(z0))) → c71(SQUARE(from(proper(z0))), PROPER(from(z0)))
PROPER(square(2ndspos(z0, z1))) → c71(SQUARE(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(square(2ndsneg(z0, z1))) → c71(SQUARE(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(square(pi(z0))) → c71(SQUARE(pi(proper(z0))), PROPER(pi(z0)))
PROPER(square(plus(z0, z1))) → c71(SQUARE(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(square(times(z0, z1))) → c71(SQUARE(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(square(square(z0))) → c71(SQUARE(square(proper(z0))), PROPER(square(z0)))
PROPER(square(0)) → c71(SQUARE(ok(0)))
PROPER(square(nil)) → c71(SQUARE(ok(nil)))
PROPER(square(rnil)) → c71(SQUARE(ok(rnil)))
TOP(mark(0)) → c72(TOP(ok(0)), PROPER(0))
TOP(mark(s(z0))) → c72(TOP(s(proper(z0))), PROPER(s(z0)))
TOP(mark(posrecip(z0))) → c72(TOP(posrecip(proper(z0))), PROPER(posrecip(z0)))
TOP(mark(negrecip(z0))) → c72(TOP(negrecip(proper(z0))), PROPER(negrecip(z0)))
TOP(mark(nil)) → c72(TOP(ok(nil)), PROPER(nil))
TOP(mark(cons(z0, z1))) → c72(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
TOP(mark(rnil)) → c72(TOP(ok(rnil)), PROPER(rnil))
TOP(mark(rcons(z0, z1))) → c72(TOP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
TOP(mark(from(z0))) → c72(TOP(from(proper(z0))), PROPER(from(z0)))
TOP(mark(2ndspos(z0, z1))) → c72(TOP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
TOP(mark(2ndsneg(z0, z1))) → c72(TOP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
TOP(mark(pi(z0))) → c72(TOP(pi(proper(z0))), PROPER(pi(z0)))
TOP(mark(plus(z0, z1))) → c72(TOP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
TOP(mark(times(z0, z1))) → c72(TOP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
TOP(mark(square(z0))) → c72(TOP(square(proper(z0))), PROPER(square(z0)))

S tuples:

ACTIVE(square(z0)) → c10(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))
TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c58(S(ok(0)))
PROPER(s(nil)) → c58(S(ok(nil)))
PROPER(s(rnil)) → c58(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(rcons(x0, s(z0))) → c64(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c64(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c64(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, cons(z0, z1))) → c64(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, rcons(z0, z1))) → c64(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c64(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c64(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c64(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c64(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c64(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c64(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c64(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(s(z0), x1)) → c64(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c64(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c64(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c64(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c64(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c64(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c64(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c64(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c64(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c64(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c64(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c64(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(rcons(x0, 0)) → c64(RCONS(proper(x0), ok(0)), PROPER(x0))
PROPER(rcons(x0, nil)) → c64(RCONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(rcons(x0, rnil)) → c64(RCONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(rcons(0, x1)) → c64(RCONS(ok(0), proper(x1)), PROPER(x1))
PROPER(rcons(nil, x1)) → c64(RCONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c64(RCONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(from(s(z0))) → c65(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(posrecip(z0))) → c65(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(from(negrecip(z0))) → c65(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(from(cons(z0, z1))) → c65(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(rcons(z0, z1))) → c65(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(from(from(z0))) → c65(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(2ndspos(z0, z1))) → c65(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(from(2ndsneg(z0, z1))) → c65(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(from(pi(z0))) → c65(FROM(pi(proper(z0))), PROPER(pi(z0)))
PROPER(from(plus(z0, z1))) → c65(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(from(times(z0, z1))) → c65(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(from(square(z0))) → c65(FROM(square(proper(z0))), PROPER(square(z0)))
PROPER(from(0)) → c65(FROM(ok(0)))
PROPER(from(nil)) → c65(FROM(ok(nil)))
PROPER(from(rnil)) → c65(FROM(ok(rnil)))
PROPER(2ndspos(x0, s(z0))) → c66(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndspos(x0, posrecip(z0))) → c66(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndspos(x0, negrecip(z0))) → c66(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndspos(x0, cons(z0, z1))) → c66(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndspos(x0, rcons(z0, z1))) → c66(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndspos(x0, from(z0))) → c66(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndspos(x0, pi(z0))) → c66(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndspos(x0, plus(z0, z1))) → c66(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndspos(x0, times(z0, z1))) → c66(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndspos(x0, square(z0))) → c66(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndspos(s(z0), x1)) → c66(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndspos(posrecip(z0), x1)) → c66(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndspos(negrecip(z0), x1)) → c66(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndspos(cons(z0, z1), x1)) → c66(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndspos(rcons(z0, z1), x1)) → c66(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndspos(from(z0), x1)) → c66(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c66(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c66(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndspos(pi(z0), x1)) → c66(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndspos(plus(z0, z1), x1)) → c66(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndspos(times(z0, z1), x1)) → c66(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndspos(square(z0), x1)) → c66(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndspos(x0, 0)) → c66(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndspos(x0, nil)) → c66(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndspos(x0, rnil)) → c66(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndspos(0, x1)) → c66(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndspos(nil, x1)) → c66(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndspos(rnil, x1)) → c66(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(x0, s(z0))) → c67(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndsneg(x0, posrecip(z0))) → c67(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndsneg(x0, negrecip(z0))) → c67(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndsneg(x0, cons(z0, z1))) → c67(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndsneg(x0, rcons(z0, z1))) → c67(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndsneg(x0, from(z0))) → c67(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndsneg(x0, pi(z0))) → c67(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndsneg(x0, plus(z0, z1))) → c67(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndsneg(x0, times(z0, z1))) → c67(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndsneg(x0, square(z0))) → c67(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndsneg(s(z0), x1)) → c67(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndsneg(posrecip(z0), x1)) → c67(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndsneg(negrecip(z0), x1)) → c67(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndsneg(cons(z0, z1), x1)) → c67(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(rcons(z0, z1), x1)) → c67(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(from(z0), x1)) → c67(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c67(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c67(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndsneg(pi(z0), x1)) → c67(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndsneg(plus(z0, z1), x1)) → c67(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndsneg(times(z0, z1), x1)) → c67(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndsneg(square(z0), x1)) → c67(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndsneg(x0, 0)) → c67(2NDSNEG(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndsneg(x0, nil)) → c67(2NDSNEG(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndsneg(x0, rnil)) → c67(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndsneg(0, x1)) → c67(2NDSNEG(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndsneg(nil, x1)) → c67(2NDSNEG(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(rnil, x1)) → c67(2NDSNEG(ok(rnil), proper(x1)), PROPER(x1))
PROPER(pi(s(z0))) → c68(PI(s(proper(z0))), PROPER(s(z0)))
PROPER(pi(posrecip(z0))) → c68(PI(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(pi(negrecip(z0))) → c68(PI(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(pi(cons(z0, z1))) → c68(PI(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(pi(rcons(z0, z1))) → c68(PI(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(pi(from(z0))) → c68(PI(from(proper(z0))), PROPER(from(z0)))
PROPER(pi(2ndspos(z0, z1))) → c68(PI(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(pi(2ndsneg(z0, z1))) → c68(PI(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(pi(pi(z0))) → c68(PI(pi(proper(z0))), PROPER(pi(z0)))
PROPER(pi(plus(z0, z1))) → c68(PI(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(pi(times(z0, z1))) → c68(PI(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(pi(square(z0))) → c68(PI(square(proper(z0))), PROPER(square(z0)))
PROPER(pi(0)) → c68(PI(ok(0)))
PROPER(pi(nil)) → c68(PI(ok(nil)))
PROPER(pi(rnil)) → c68(PI(ok(rnil)))
PROPER(plus(x0, s(z0))) → c69(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(plus(x0, posrecip(z0))) → c69(PLUS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(plus(x0, negrecip(z0))) → c69(PLUS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(plus(x0, cons(z0, z1))) → c69(PLUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(plus(x0, rcons(z0, z1))) → c69(PLUS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(plus(x0, from(z0))) → c69(PLUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(plus(x0, 2ndspos(z0, z1))) → c69(PLUS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(plus(x0, 2ndsneg(z0, z1))) → c69(PLUS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(plus(x0, pi(z0))) → c69(PLUS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(plus(x0, plus(z0, z1))) → c69(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(plus(x0, times(z0, z1))) → c69(PLUS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(plus(x0, square(z0))) → c69(PLUS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(plus(s(z0), x1)) → c69(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(plus(posrecip(z0), x1)) → c69(PLUS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(plus(negrecip(z0), x1)) → c69(PLUS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(plus(cons(z0, z1), x1)) → c69(PLUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(plus(rcons(z0, z1), x1)) → c69(PLUS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(plus(from(z0), x1)) → c69(PLUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(plus(2ndspos(z0, z1), x1)) → c69(PLUS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(plus(2ndsneg(z0, z1), x1)) → c69(PLUS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(plus(pi(z0), x1)) → c69(PLUS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(plus(plus(z0, z1), x1)) → c69(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(plus(times(z0, z1), x1)) → c69(PLUS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(plus(square(z0), x1)) → c69(PLUS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(plus(x0, 0)) → c69(PLUS(proper(x0), ok(0)), PROPER(x0))
PROPER(plus(x0, nil)) → c69(PLUS(proper(x0), ok(nil)), PROPER(x0))
PROPER(plus(x0, rnil)) → c69(PLUS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(plus(0, x1)) → c69(PLUS(ok(0), proper(x1)), PROPER(x1))
PROPER(plus(nil, x1)) → c69(PLUS(ok(nil), proper(x1)), PROPER(x1))
PROPER(plus(rnil, x1)) → c69(PLUS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(times(x0, s(z0))) → c70(TIMES(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(times(x0, posrecip(z0))) → c70(TIMES(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(times(x0, negrecip(z0))) → c70(TIMES(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(times(x0, cons(z0, z1))) → c70(TIMES(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(times(x0, rcons(z0, z1))) → c70(TIMES(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(times(x0, from(z0))) → c70(TIMES(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(times(x0, 2ndspos(z0, z1))) → c70(TIMES(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(times(x0, 2ndsneg(z0, z1))) → c70(TIMES(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(times(x0, pi(z0))) → c70(TIMES(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(times(x0, plus(z0, z1))) → c70(TIMES(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(times(x0, times(z0, z1))) → c70(TIMES(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(times(x0, square(z0))) → c70(TIMES(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(times(s(z0), x1)) → c70(TIMES(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(times(posrecip(z0), x1)) → c70(TIMES(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(times(negrecip(z0), x1)) → c70(TIMES(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(times(cons(z0, z1), x1)) → c70(TIMES(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(times(rcons(z0, z1), x1)) → c70(TIMES(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(times(from(z0), x1)) → c70(TIMES(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(times(2ndspos(z0, z1), x1)) → c70(TIMES(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(times(2ndsneg(z0, z1), x1)) → c70(TIMES(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(times(pi(z0), x1)) → c70(TIMES(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(times(plus(z0, z1), x1)) → c70(TIMES(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(times(times(z0, z1), x1)) → c70(TIMES(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(times(square(z0), x1)) → c70(TIMES(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(times(x0, 0)) → c70(TIMES(proper(x0), ok(0)), PROPER(x0))
PROPER(times(x0, nil)) → c70(TIMES(proper(x0), ok(nil)), PROPER(x0))
PROPER(times(x0, rnil)) → c70(TIMES(proper(x0), ok(rnil)), PROPER(x0))
PROPER(times(0, x1)) → c70(TIMES(ok(0), proper(x1)), PROPER(x1))
PROPER(times(nil, x1)) → c70(TIMES(ok(nil), proper(x1)), PROPER(x1))
PROPER(times(rnil, x1)) → c70(TIMES(ok(rnil), proper(x1)), PROPER(x1))
PROPER(square(s(z0))) → c71(SQUARE(s(proper(z0))), PROPER(s(z0)))
PROPER(square(posrecip(z0))) → c71(SQUARE(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(square(negrecip(z0))) → c71(SQUARE(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(square(cons(z0, z1))) → c71(SQUARE(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(square(rcons(z0, z1))) → c71(SQUARE(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(square(from(z0))) → c71(SQUARE(from(proper(z0))), PROPER(from(z0)))
PROPER(square(2ndspos(z0, z1))) → c71(SQUARE(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(square(2ndsneg(z0, z1))) → c71(SQUARE(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(square(pi(z0))) → c71(SQUARE(pi(proper(z0))), PROPER(pi(z0)))
PROPER(square(plus(z0, z1))) → c71(SQUARE(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(square(times(z0, z1))) → c71(SQUARE(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(square(square(z0))) → c71(SQUARE(square(proper(z0))), PROPER(square(z0)))
PROPER(square(0)) → c71(SQUARE(ok(0)))
PROPER(square(nil)) → c71(SQUARE(ok(nil)))
PROPER(square(rnil)) → c71(SQUARE(ok(rnil)))
TOP(mark(0)) → c72(TOP(ok(0)), PROPER(0))
TOP(mark(s(z0))) → c72(TOP(s(proper(z0))), PROPER(s(z0)))
TOP(mark(posrecip(z0))) → c72(TOP(posrecip(proper(z0))), PROPER(posrecip(z0)))
TOP(mark(negrecip(z0))) → c72(TOP(negrecip(proper(z0))), PROPER(negrecip(z0)))
TOP(mark(nil)) → c72(TOP(ok(nil)), PROPER(nil))
TOP(mark(cons(z0, z1))) → c72(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
TOP(mark(rnil)) → c72(TOP(ok(rnil)), PROPER(rnil))
TOP(mark(rcons(z0, z1))) → c72(TOP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
TOP(mark(from(z0))) → c72(TOP(from(proper(z0))), PROPER(from(z0)))
TOP(mark(2ndspos(z0, z1))) → c72(TOP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
TOP(mark(2ndsneg(z0, z1))) → c72(TOP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
TOP(mark(pi(z0))) → c72(TOP(pi(proper(z0))), PROPER(pi(z0)))
TOP(mark(plus(z0, z1))) → c72(TOP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
TOP(mark(times(z0, z1))) → c72(TOP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
TOP(mark(square(z0))) → c72(TOP(square(proper(z0))), PROPER(square(z0)))

K tuples:none
Defined Rule Symbols:

active, rcons, posrecip, 2ndsneg, negrecip, 2ndspos, s, cons, from, pi, plus, times, square, proper

Defined Pair Symbols:

ACTIVE, S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, TOP, PROPER

Compound Symbols:

c10, c15, c16, c18, c19, c20, c21, c23, c24, c25, c26, 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, c73, c, c5, c7, c9, c1, c11, c12, c13, c14, c17, c22, c27, c58, c58, c59, c59, c60, c60, c62, c62, c64, c64, c65, c65, c66, c66, c67, c67, c68, c68, c69, c69, c70, c70, c71, c71, c72

(75) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)

Removed 3 trailing tuple parts

(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, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(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(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))
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))
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))
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(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)) → c10(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))
TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c58(S(ok(0)))
PROPER(s(nil)) → c58(S(ok(nil)))
PROPER(s(rnil)) → c58(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(rcons(x0, s(z0))) → c64(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c64(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c64(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, cons(z0, z1))) → c64(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, rcons(z0, z1))) → c64(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c64(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c64(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c64(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c64(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c64(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c64(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c64(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(s(z0), x1)) → c64(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c64(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c64(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c64(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c64(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c64(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c64(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c64(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c64(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c64(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c64(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c64(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(rcons(x0, 0)) → c64(RCONS(proper(x0), ok(0)), PROPER(x0))
PROPER(rcons(x0, nil)) → c64(RCONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(rcons(x0, rnil)) → c64(RCONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(rcons(0, x1)) → c64(RCONS(ok(0), proper(x1)), PROPER(x1))
PROPER(rcons(nil, x1)) → c64(RCONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c64(RCONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(from(s(z0))) → c65(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(posrecip(z0))) → c65(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(from(negrecip(z0))) → c65(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(from(cons(z0, z1))) → c65(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(rcons(z0, z1))) → c65(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(from(from(z0))) → c65(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(2ndspos(z0, z1))) → c65(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(from(2ndsneg(z0, z1))) → c65(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(from(pi(z0))) → c65(FROM(pi(proper(z0))), PROPER(pi(z0)))
PROPER(from(plus(z0, z1))) → c65(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(from(times(z0, z1))) → c65(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(from(square(z0))) → c65(FROM(square(proper(z0))), PROPER(square(z0)))
PROPER(from(0)) → c65(FROM(ok(0)))
PROPER(from(nil)) → c65(FROM(ok(nil)))
PROPER(from(rnil)) → c65(FROM(ok(rnil)))
PROPER(2ndspos(x0, s(z0))) → c66(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndspos(x0, posrecip(z0))) → c66(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndspos(x0, negrecip(z0))) → c66(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndspos(x0, cons(z0, z1))) → c66(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndspos(x0, rcons(z0, z1))) → c66(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndspos(x0, from(z0))) → c66(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndspos(x0, pi(z0))) → c66(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndspos(x0, plus(z0, z1))) → c66(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndspos(x0, times(z0, z1))) → c66(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndspos(x0, square(z0))) → c66(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndspos(s(z0), x1)) → c66(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndspos(posrecip(z0), x1)) → c66(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndspos(negrecip(z0), x1)) → c66(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndspos(cons(z0, z1), x1)) → c66(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndspos(rcons(z0, z1), x1)) → c66(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndspos(from(z0), x1)) → c66(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c66(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c66(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndspos(pi(z0), x1)) → c66(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndspos(plus(z0, z1), x1)) → c66(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndspos(times(z0, z1), x1)) → c66(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndspos(square(z0), x1)) → c66(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndspos(x0, 0)) → c66(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndspos(x0, nil)) → c66(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndspos(x0, rnil)) → c66(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndspos(0, x1)) → c66(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndspos(nil, x1)) → c66(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndspos(rnil, x1)) → c66(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(x0, s(z0))) → c67(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndsneg(x0, posrecip(z0))) → c67(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndsneg(x0, negrecip(z0))) → c67(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndsneg(x0, cons(z0, z1))) → c67(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndsneg(x0, rcons(z0, z1))) → c67(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndsneg(x0, from(z0))) → c67(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndsneg(x0, pi(z0))) → c67(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndsneg(x0, plus(z0, z1))) → c67(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndsneg(x0, times(z0, z1))) → c67(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndsneg(x0, square(z0))) → c67(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndsneg(s(z0), x1)) → c67(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndsneg(posrecip(z0), x1)) → c67(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndsneg(negrecip(z0), x1)) → c67(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndsneg(cons(z0, z1), x1)) → c67(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(rcons(z0, z1), x1)) → c67(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(from(z0), x1)) → c67(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c67(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c67(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndsneg(pi(z0), x1)) → c67(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndsneg(plus(z0, z1), x1)) → c67(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndsneg(times(z0, z1), x1)) → c67(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndsneg(square(z0), x1)) → c67(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndsneg(x0, 0)) → c67(2NDSNEG(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndsneg(x0, nil)) → c67(2NDSNEG(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndsneg(x0, rnil)) → c67(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndsneg(0, x1)) → c67(2NDSNEG(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndsneg(nil, x1)) → c67(2NDSNEG(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(rnil, x1)) → c67(2NDSNEG(ok(rnil), proper(x1)), PROPER(x1))
PROPER(pi(s(z0))) → c68(PI(s(proper(z0))), PROPER(s(z0)))
PROPER(pi(posrecip(z0))) → c68(PI(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(pi(negrecip(z0))) → c68(PI(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(pi(cons(z0, z1))) → c68(PI(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(pi(rcons(z0, z1))) → c68(PI(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(pi(from(z0))) → c68(PI(from(proper(z0))), PROPER(from(z0)))
PROPER(pi(2ndspos(z0, z1))) → c68(PI(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(pi(2ndsneg(z0, z1))) → c68(PI(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(pi(pi(z0))) → c68(PI(pi(proper(z0))), PROPER(pi(z0)))
PROPER(pi(plus(z0, z1))) → c68(PI(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(pi(times(z0, z1))) → c68(PI(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(pi(square(z0))) → c68(PI(square(proper(z0))), PROPER(square(z0)))
PROPER(pi(0)) → c68(PI(ok(0)))
PROPER(pi(nil)) → c68(PI(ok(nil)))
PROPER(pi(rnil)) → c68(PI(ok(rnil)))
PROPER(plus(x0, s(z0))) → c69(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(plus(x0, posrecip(z0))) → c69(PLUS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(plus(x0, negrecip(z0))) → c69(PLUS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(plus(x0, cons(z0, z1))) → c69(PLUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(plus(x0, rcons(z0, z1))) → c69(PLUS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(plus(x0, from(z0))) → c69(PLUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(plus(x0, 2ndspos(z0, z1))) → c69(PLUS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(plus(x0, 2ndsneg(z0, z1))) → c69(PLUS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(plus(x0, pi(z0))) → c69(PLUS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(plus(x0, plus(z0, z1))) → c69(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(plus(x0, times(z0, z1))) → c69(PLUS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(plus(x0, square(z0))) → c69(PLUS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(plus(s(z0), x1)) → c69(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(plus(posrecip(z0), x1)) → c69(PLUS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(plus(negrecip(z0), x1)) → c69(PLUS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(plus(cons(z0, z1), x1)) → c69(PLUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(plus(rcons(z0, z1), x1)) → c69(PLUS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(plus(from(z0), x1)) → c69(PLUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(plus(2ndspos(z0, z1), x1)) → c69(PLUS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(plus(2ndsneg(z0, z1), x1)) → c69(PLUS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(plus(pi(z0), x1)) → c69(PLUS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(plus(plus(z0, z1), x1)) → c69(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(plus(times(z0, z1), x1)) → c69(PLUS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(plus(square(z0), x1)) → c69(PLUS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(plus(x0, 0)) → c69(PLUS(proper(x0), ok(0)), PROPER(x0))
PROPER(plus(x0, nil)) → c69(PLUS(proper(x0), ok(nil)), PROPER(x0))
PROPER(plus(x0, rnil)) → c69(PLUS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(plus(0, x1)) → c69(PLUS(ok(0), proper(x1)), PROPER(x1))
PROPER(plus(nil, x1)) → c69(PLUS(ok(nil), proper(x1)), PROPER(x1))
PROPER(plus(rnil, x1)) → c69(PLUS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(times(x0, s(z0))) → c70(TIMES(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(times(x0, posrecip(z0))) → c70(TIMES(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(times(x0, negrecip(z0))) → c70(TIMES(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(times(x0, cons(z0, z1))) → c70(TIMES(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(times(x0, rcons(z0, z1))) → c70(TIMES(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(times(x0, from(z0))) → c70(TIMES(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(times(x0, 2ndspos(z0, z1))) → c70(TIMES(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(times(x0, 2ndsneg(z0, z1))) → c70(TIMES(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(times(x0, pi(z0))) → c70(TIMES(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(times(x0, plus(z0, z1))) → c70(TIMES(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(times(x0, times(z0, z1))) → c70(TIMES(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(times(x0, square(z0))) → c70(TIMES(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(times(s(z0), x1)) → c70(TIMES(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(times(posrecip(z0), x1)) → c70(TIMES(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(times(negrecip(z0), x1)) → c70(TIMES(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(times(cons(z0, z1), x1)) → c70(TIMES(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(times(rcons(z0, z1), x1)) → c70(TIMES(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(times(from(z0), x1)) → c70(TIMES(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(times(2ndspos(z0, z1), x1)) → c70(TIMES(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(times(2ndsneg(z0, z1), x1)) → c70(TIMES(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(times(pi(z0), x1)) → c70(TIMES(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(times(plus(z0, z1), x1)) → c70(TIMES(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(times(times(z0, z1), x1)) → c70(TIMES(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(times(square(z0), x1)) → c70(TIMES(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(times(x0, 0)) → c70(TIMES(proper(x0), ok(0)), PROPER(x0))
PROPER(times(x0, nil)) → c70(TIMES(proper(x0), ok(nil)), PROPER(x0))
PROPER(times(x0, rnil)) → c70(TIMES(proper(x0), ok(rnil)), PROPER(x0))
PROPER(times(0, x1)) → c70(TIMES(ok(0), proper(x1)), PROPER(x1))
PROPER(times(nil, x1)) → c70(TIMES(ok(nil), proper(x1)), PROPER(x1))
PROPER(times(rnil, x1)) → c70(TIMES(ok(rnil), proper(x1)), PROPER(x1))
PROPER(square(s(z0))) → c71(SQUARE(s(proper(z0))), PROPER(s(z0)))
PROPER(square(posrecip(z0))) → c71(SQUARE(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(square(negrecip(z0))) → c71(SQUARE(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(square(cons(z0, z1))) → c71(SQUARE(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(square(rcons(z0, z1))) → c71(SQUARE(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(square(from(z0))) → c71(SQUARE(from(proper(z0))), PROPER(from(z0)))
PROPER(square(2ndspos(z0, z1))) → c71(SQUARE(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(square(2ndsneg(z0, z1))) → c71(SQUARE(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(square(pi(z0))) → c71(SQUARE(pi(proper(z0))), PROPER(pi(z0)))
PROPER(square(plus(z0, z1))) → c71(SQUARE(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(square(times(z0, z1))) → c71(SQUARE(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(square(square(z0))) → c71(SQUARE(square(proper(z0))), PROPER(square(z0)))
PROPER(square(0)) → c71(SQUARE(ok(0)))
PROPER(square(nil)) → c71(SQUARE(ok(nil)))
PROPER(square(rnil)) → c71(SQUARE(ok(rnil)))
TOP(mark(s(z0))) → c72(TOP(s(proper(z0))), PROPER(s(z0)))
TOP(mark(posrecip(z0))) → c72(TOP(posrecip(proper(z0))), PROPER(posrecip(z0)))
TOP(mark(negrecip(z0))) → c72(TOP(negrecip(proper(z0))), PROPER(negrecip(z0)))
TOP(mark(cons(z0, z1))) → c72(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
TOP(mark(rcons(z0, z1))) → c72(TOP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
TOP(mark(from(z0))) → c72(TOP(from(proper(z0))), PROPER(from(z0)))
TOP(mark(2ndspos(z0, z1))) → c72(TOP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
TOP(mark(2ndsneg(z0, z1))) → c72(TOP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
TOP(mark(pi(z0))) → c72(TOP(pi(proper(z0))), PROPER(pi(z0)))
TOP(mark(plus(z0, z1))) → c72(TOP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
TOP(mark(times(z0, z1))) → c72(TOP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
TOP(mark(square(z0))) → c72(TOP(square(proper(z0))), PROPER(square(z0)))
TOP(mark(0)) → c72(TOP(ok(0)))
TOP(mark(nil)) → c72(TOP(ok(nil)))
TOP(mark(rnil)) → c72(TOP(ok(rnil)))

S tuples:

ACTIVE(square(z0)) → c10(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))
TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c58(S(ok(0)))
PROPER(s(nil)) → c58(S(ok(nil)))
PROPER(s(rnil)) → c58(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(rcons(x0, s(z0))) → c64(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c64(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c64(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, cons(z0, z1))) → c64(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, rcons(z0, z1))) → c64(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c64(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c64(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c64(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c64(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c64(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c64(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c64(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(s(z0), x1)) → c64(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c64(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c64(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c64(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c64(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c64(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c64(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c64(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c64(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c64(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c64(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c64(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(rcons(x0, 0)) → c64(RCONS(proper(x0), ok(0)), PROPER(x0))
PROPER(rcons(x0, nil)) → c64(RCONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(rcons(x0, rnil)) → c64(RCONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(rcons(0, x1)) → c64(RCONS(ok(0), proper(x1)), PROPER(x1))
PROPER(rcons(nil, x1)) → c64(RCONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c64(RCONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(from(s(z0))) → c65(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(posrecip(z0))) → c65(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(from(negrecip(z0))) → c65(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(from(cons(z0, z1))) → c65(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(rcons(z0, z1))) → c65(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(from(from(z0))) → c65(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(2ndspos(z0, z1))) → c65(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(from(2ndsneg(z0, z1))) → c65(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(from(pi(z0))) → c65(FROM(pi(proper(z0))), PROPER(pi(z0)))
PROPER(from(plus(z0, z1))) → c65(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(from(times(z0, z1))) → c65(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(from(square(z0))) → c65(FROM(square(proper(z0))), PROPER(square(z0)))
PROPER(from(0)) → c65(FROM(ok(0)))
PROPER(from(nil)) → c65(FROM(ok(nil)))
PROPER(from(rnil)) → c65(FROM(ok(rnil)))
PROPER(2ndspos(x0, s(z0))) → c66(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndspos(x0, posrecip(z0))) → c66(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndspos(x0, negrecip(z0))) → c66(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndspos(x0, cons(z0, z1))) → c66(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndspos(x0, rcons(z0, z1))) → c66(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndspos(x0, from(z0))) → c66(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndspos(x0, pi(z0))) → c66(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndspos(x0, plus(z0, z1))) → c66(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndspos(x0, times(z0, z1))) → c66(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndspos(x0, square(z0))) → c66(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndspos(s(z0), x1)) → c66(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndspos(posrecip(z0), x1)) → c66(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndspos(negrecip(z0), x1)) → c66(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndspos(cons(z0, z1), x1)) → c66(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndspos(rcons(z0, z1), x1)) → c66(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndspos(from(z0), x1)) → c66(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c66(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c66(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndspos(pi(z0), x1)) → c66(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndspos(plus(z0, z1), x1)) → c66(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndspos(times(z0, z1), x1)) → c66(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndspos(square(z0), x1)) → c66(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndspos(x0, 0)) → c66(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndspos(x0, nil)) → c66(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndspos(x0, rnil)) → c66(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndspos(0, x1)) → c66(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndspos(nil, x1)) → c66(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndspos(rnil, x1)) → c66(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(x0, s(z0))) → c67(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndsneg(x0, posrecip(z0))) → c67(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndsneg(x0, negrecip(z0))) → c67(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndsneg(x0, cons(z0, z1))) → c67(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndsneg(x0, rcons(z0, z1))) → c67(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndsneg(x0, from(z0))) → c67(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndsneg(x0, pi(z0))) → c67(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndsneg(x0, plus(z0, z1))) → c67(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndsneg(x0, times(z0, z1))) → c67(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndsneg(x0, square(z0))) → c67(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndsneg(s(z0), x1)) → c67(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndsneg(posrecip(z0), x1)) → c67(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndsneg(negrecip(z0), x1)) → c67(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndsneg(cons(z0, z1), x1)) → c67(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(rcons(z0, z1), x1)) → c67(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(from(z0), x1)) → c67(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c67(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c67(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndsneg(pi(z0), x1)) → c67(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndsneg(plus(z0, z1), x1)) → c67(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndsneg(times(z0, z1), x1)) → c67(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndsneg(square(z0), x1)) → c67(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndsneg(x0, 0)) → c67(2NDSNEG(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndsneg(x0, nil)) → c67(2NDSNEG(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndsneg(x0, rnil)) → c67(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndsneg(0, x1)) → c67(2NDSNEG(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndsneg(nil, x1)) → c67(2NDSNEG(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(rnil, x1)) → c67(2NDSNEG(ok(rnil), proper(x1)), PROPER(x1))
PROPER(pi(s(z0))) → c68(PI(s(proper(z0))), PROPER(s(z0)))
PROPER(pi(posrecip(z0))) → c68(PI(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(pi(negrecip(z0))) → c68(PI(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(pi(cons(z0, z1))) → c68(PI(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(pi(rcons(z0, z1))) → c68(PI(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(pi(from(z0))) → c68(PI(from(proper(z0))), PROPER(from(z0)))
PROPER(pi(2ndspos(z0, z1))) → c68(PI(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(pi(2ndsneg(z0, z1))) → c68(PI(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(pi(pi(z0))) → c68(PI(pi(proper(z0))), PROPER(pi(z0)))
PROPER(pi(plus(z0, z1))) → c68(PI(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(pi(times(z0, z1))) → c68(PI(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(pi(square(z0))) → c68(PI(square(proper(z0))), PROPER(square(z0)))
PROPER(pi(0)) → c68(PI(ok(0)))
PROPER(pi(nil)) → c68(PI(ok(nil)))
PROPER(pi(rnil)) → c68(PI(ok(rnil)))
PROPER(plus(x0, s(z0))) → c69(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(plus(x0, posrecip(z0))) → c69(PLUS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(plus(x0, negrecip(z0))) → c69(PLUS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(plus(x0, cons(z0, z1))) → c69(PLUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(plus(x0, rcons(z0, z1))) → c69(PLUS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(plus(x0, from(z0))) → c69(PLUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(plus(x0, 2ndspos(z0, z1))) → c69(PLUS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(plus(x0, 2ndsneg(z0, z1))) → c69(PLUS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(plus(x0, pi(z0))) → c69(PLUS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(plus(x0, plus(z0, z1))) → c69(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(plus(x0, times(z0, z1))) → c69(PLUS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(plus(x0, square(z0))) → c69(PLUS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(plus(s(z0), x1)) → c69(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(plus(posrecip(z0), x1)) → c69(PLUS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(plus(negrecip(z0), x1)) → c69(PLUS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(plus(cons(z0, z1), x1)) → c69(PLUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(plus(rcons(z0, z1), x1)) → c69(PLUS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(plus(from(z0), x1)) → c69(PLUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(plus(2ndspos(z0, z1), x1)) → c69(PLUS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(plus(2ndsneg(z0, z1), x1)) → c69(PLUS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(plus(pi(z0), x1)) → c69(PLUS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(plus(plus(z0, z1), x1)) → c69(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(plus(times(z0, z1), x1)) → c69(PLUS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(plus(square(z0), x1)) → c69(PLUS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(plus(x0, 0)) → c69(PLUS(proper(x0), ok(0)), PROPER(x0))
PROPER(plus(x0, nil)) → c69(PLUS(proper(x0), ok(nil)), PROPER(x0))
PROPER(plus(x0, rnil)) → c69(PLUS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(plus(0, x1)) → c69(PLUS(ok(0), proper(x1)), PROPER(x1))
PROPER(plus(nil, x1)) → c69(PLUS(ok(nil), proper(x1)), PROPER(x1))
PROPER(plus(rnil, x1)) → c69(PLUS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(times(x0, s(z0))) → c70(TIMES(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(times(x0, posrecip(z0))) → c70(TIMES(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(times(x0, negrecip(z0))) → c70(TIMES(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(times(x0, cons(z0, z1))) → c70(TIMES(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(times(x0, rcons(z0, z1))) → c70(TIMES(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(times(x0, from(z0))) → c70(TIMES(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(times(x0, 2ndspos(z0, z1))) → c70(TIMES(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(times(x0, 2ndsneg(z0, z1))) → c70(TIMES(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(times(x0, pi(z0))) → c70(TIMES(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(times(x0, plus(z0, z1))) → c70(TIMES(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(times(x0, times(z0, z1))) → c70(TIMES(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(times(x0, square(z0))) → c70(TIMES(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(times(s(z0), x1)) → c70(TIMES(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(times(posrecip(z0), x1)) → c70(TIMES(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(times(negrecip(z0), x1)) → c70(TIMES(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(times(cons(z0, z1), x1)) → c70(TIMES(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(times(rcons(z0, z1), x1)) → c70(TIMES(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(times(from(z0), x1)) → c70(TIMES(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(times(2ndspos(z0, z1), x1)) → c70(TIMES(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(times(2ndsneg(z0, z1), x1)) → c70(TIMES(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(times(pi(z0), x1)) → c70(TIMES(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(times(plus(z0, z1), x1)) → c70(TIMES(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(times(times(z0, z1), x1)) → c70(TIMES(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(times(square(z0), x1)) → c70(TIMES(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(times(x0, 0)) → c70(TIMES(proper(x0), ok(0)), PROPER(x0))
PROPER(times(x0, nil)) → c70(TIMES(proper(x0), ok(nil)), PROPER(x0))
PROPER(times(x0, rnil)) → c70(TIMES(proper(x0), ok(rnil)), PROPER(x0))
PROPER(times(0, x1)) → c70(TIMES(ok(0), proper(x1)), PROPER(x1))
PROPER(times(nil, x1)) → c70(TIMES(ok(nil), proper(x1)), PROPER(x1))
PROPER(times(rnil, x1)) → c70(TIMES(ok(rnil), proper(x1)), PROPER(x1))
PROPER(square(s(z0))) → c71(SQUARE(s(proper(z0))), PROPER(s(z0)))
PROPER(square(posrecip(z0))) → c71(SQUARE(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(square(negrecip(z0))) → c71(SQUARE(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(square(cons(z0, z1))) → c71(SQUARE(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(square(rcons(z0, z1))) → c71(SQUARE(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(square(from(z0))) → c71(SQUARE(from(proper(z0))), PROPER(from(z0)))
PROPER(square(2ndspos(z0, z1))) → c71(SQUARE(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(square(2ndsneg(z0, z1))) → c71(SQUARE(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(square(pi(z0))) → c71(SQUARE(pi(proper(z0))), PROPER(pi(z0)))
PROPER(square(plus(z0, z1))) → c71(SQUARE(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(square(times(z0, z1))) → c71(SQUARE(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(square(square(z0))) → c71(SQUARE(square(proper(z0))), PROPER(square(z0)))
PROPER(square(0)) → c71(SQUARE(ok(0)))
PROPER(square(nil)) → c71(SQUARE(ok(nil)))
PROPER(square(rnil)) → c71(SQUARE(ok(rnil)))
TOP(mark(s(z0))) → c72(TOP(s(proper(z0))), PROPER(s(z0)))
TOP(mark(posrecip(z0))) → c72(TOP(posrecip(proper(z0))), PROPER(posrecip(z0)))
TOP(mark(negrecip(z0))) → c72(TOP(negrecip(proper(z0))), PROPER(negrecip(z0)))
TOP(mark(cons(z0, z1))) → c72(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
TOP(mark(rcons(z0, z1))) → c72(TOP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
TOP(mark(from(z0))) → c72(TOP(from(proper(z0))), PROPER(from(z0)))
TOP(mark(2ndspos(z0, z1))) → c72(TOP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
TOP(mark(2ndsneg(z0, z1))) → c72(TOP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
TOP(mark(pi(z0))) → c72(TOP(pi(proper(z0))), PROPER(pi(z0)))
TOP(mark(plus(z0, z1))) → c72(TOP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
TOP(mark(times(z0, z1))) → c72(TOP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
TOP(mark(square(z0))) → c72(TOP(square(proper(z0))), PROPER(square(z0)))
TOP(mark(0)) → c72(TOP(ok(0)))
TOP(mark(nil)) → c72(TOP(ok(nil)))
TOP(mark(rnil)) → c72(TOP(ok(rnil)))

K tuples:none
Defined Rule Symbols:

active, rcons, posrecip, 2ndsneg, negrecip, 2ndspos, s, cons, from, pi, plus, times, square, proper

Defined Pair Symbols:

ACTIVE, S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, TOP, PROPER

Compound Symbols:

c10, c15, c16, c18, c19, c20, c21, c23, c24, c25, c26, 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, c73, c, c5, c7, c9, c1, c11, c12, c13, c14, c17, c22, c27, c58, c58, c59, c59, c60, c60, c62, c62, c64, c64, c65, c65, c66, c66, c67, c67, c68, c68, c69, c69, c70, c70, c71, c71, c72, c72

(77) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

Use narrowing to replace TOP(ok(z0)) → c73(TOP(active(z0)), ACTIVE(z0)) by

TOP(ok(from(z0))) → c73(TOP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
TOP(ok(2ndspos(0, z0))) → c73(TOP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
TOP(ok(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c73(TOP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
TOP(ok(2ndsneg(0, z0))) → c73(TOP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
TOP(ok(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c73(TOP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
TOP(ok(pi(z0))) → c73(TOP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
TOP(ok(plus(0, z0))) → c73(TOP(mark(z0)), ACTIVE(plus(0, z0)))
TOP(ok(plus(s(z0), z1))) → c73(TOP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
TOP(ok(times(0, z0))) → c73(TOP(mark(0)), ACTIVE(times(0, z0)))
TOP(ok(times(s(z0), z1))) → c73(TOP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
TOP(ok(square(z0))) → c73(TOP(mark(times(z0, z0))), ACTIVE(square(z0)))
TOP(ok(s(z0))) → c73(TOP(s(active(z0))), ACTIVE(s(z0)))
TOP(ok(posrecip(z0))) → c73(TOP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
TOP(ok(negrecip(z0))) → c73(TOP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
TOP(ok(cons(z0, z1))) → c73(TOP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
TOP(ok(rcons(z0, z1))) → c73(TOP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
TOP(ok(rcons(z0, z1))) → c73(TOP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
TOP(ok(from(z0))) → c73(TOP(from(active(z0))), ACTIVE(from(z0)))
TOP(ok(2ndspos(z0, z1))) → c73(TOP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
TOP(ok(2ndspos(z0, z1))) → c73(TOP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
TOP(ok(2ndsneg(z0, z1))) → c73(TOP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
TOP(ok(2ndsneg(z0, z1))) → c73(TOP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
TOP(ok(pi(z0))) → c73(TOP(pi(active(z0))), ACTIVE(pi(z0)))
TOP(ok(plus(z0, z1))) → c73(TOP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
TOP(ok(plus(z0, z1))) → c73(TOP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
TOP(ok(times(z0, z1))) → c73(TOP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
TOP(ok(times(z0, z1))) → c73(TOP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
TOP(ok(square(z0))) → c73(TOP(square(active(z0))), ACTIVE(square(z0)))

(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, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(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(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))
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))
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))
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(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)) → c10(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c58(S(ok(0)))
PROPER(s(nil)) → c58(S(ok(nil)))
PROPER(s(rnil)) → c58(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(rcons(x0, s(z0))) → c64(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c64(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c64(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, cons(z0, z1))) → c64(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, rcons(z0, z1))) → c64(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c64(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c64(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c64(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c64(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c64(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c64(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c64(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(s(z0), x1)) → c64(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c64(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c64(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c64(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c64(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c64(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c64(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c64(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c64(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c64(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c64(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c64(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(rcons(x0, 0)) → c64(RCONS(proper(x0), ok(0)), PROPER(x0))
PROPER(rcons(x0, nil)) → c64(RCONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(rcons(x0, rnil)) → c64(RCONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(rcons(0, x1)) → c64(RCONS(ok(0), proper(x1)), PROPER(x1))
PROPER(rcons(nil, x1)) → c64(RCONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c64(RCONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(from(s(z0))) → c65(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(posrecip(z0))) → c65(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(from(negrecip(z0))) → c65(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(from(cons(z0, z1))) → c65(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(rcons(z0, z1))) → c65(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(from(from(z0))) → c65(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(2ndspos(z0, z1))) → c65(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(from(2ndsneg(z0, z1))) → c65(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(from(pi(z0))) → c65(FROM(pi(proper(z0))), PROPER(pi(z0)))
PROPER(from(plus(z0, z1))) → c65(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(from(times(z0, z1))) → c65(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(from(square(z0))) → c65(FROM(square(proper(z0))), PROPER(square(z0)))
PROPER(from(0)) → c65(FROM(ok(0)))
PROPER(from(nil)) → c65(FROM(ok(nil)))
PROPER(from(rnil)) → c65(FROM(ok(rnil)))
PROPER(2ndspos(x0, s(z0))) → c66(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndspos(x0, posrecip(z0))) → c66(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndspos(x0, negrecip(z0))) → c66(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndspos(x0, cons(z0, z1))) → c66(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndspos(x0, rcons(z0, z1))) → c66(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndspos(x0, from(z0))) → c66(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndspos(x0, pi(z0))) → c66(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndspos(x0, plus(z0, z1))) → c66(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndspos(x0, times(z0, z1))) → c66(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndspos(x0, square(z0))) → c66(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndspos(s(z0), x1)) → c66(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndspos(posrecip(z0), x1)) → c66(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndspos(negrecip(z0), x1)) → c66(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndspos(cons(z0, z1), x1)) → c66(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndspos(rcons(z0, z1), x1)) → c66(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndspos(from(z0), x1)) → c66(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c66(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c66(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndspos(pi(z0), x1)) → c66(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndspos(plus(z0, z1), x1)) → c66(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndspos(times(z0, z1), x1)) → c66(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndspos(square(z0), x1)) → c66(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndspos(x0, 0)) → c66(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndspos(x0, nil)) → c66(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndspos(x0, rnil)) → c66(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndspos(0, x1)) → c66(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndspos(nil, x1)) → c66(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndspos(rnil, x1)) → c66(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(x0, s(z0))) → c67(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndsneg(x0, posrecip(z0))) → c67(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndsneg(x0, negrecip(z0))) → c67(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndsneg(x0, cons(z0, z1))) → c67(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndsneg(x0, rcons(z0, z1))) → c67(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndsneg(x0, from(z0))) → c67(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndsneg(x0, pi(z0))) → c67(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndsneg(x0, plus(z0, z1))) → c67(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndsneg(x0, times(z0, z1))) → c67(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndsneg(x0, square(z0))) → c67(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndsneg(s(z0), x1)) → c67(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndsneg(posrecip(z0), x1)) → c67(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndsneg(negrecip(z0), x1)) → c67(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndsneg(cons(z0, z1), x1)) → c67(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(rcons(z0, z1), x1)) → c67(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(from(z0), x1)) → c67(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c67(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c67(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndsneg(pi(z0), x1)) → c67(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndsneg(plus(z0, z1), x1)) → c67(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndsneg(times(z0, z1), x1)) → c67(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndsneg(square(z0), x1)) → c67(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndsneg(x0, 0)) → c67(2NDSNEG(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndsneg(x0, nil)) → c67(2NDSNEG(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndsneg(x0, rnil)) → c67(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndsneg(0, x1)) → c67(2NDSNEG(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndsneg(nil, x1)) → c67(2NDSNEG(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(rnil, x1)) → c67(2NDSNEG(ok(rnil), proper(x1)), PROPER(x1))
PROPER(pi(s(z0))) → c68(PI(s(proper(z0))), PROPER(s(z0)))
PROPER(pi(posrecip(z0))) → c68(PI(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(pi(negrecip(z0))) → c68(PI(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(pi(cons(z0, z1))) → c68(PI(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(pi(rcons(z0, z1))) → c68(PI(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(pi(from(z0))) → c68(PI(from(proper(z0))), PROPER(from(z0)))
PROPER(pi(2ndspos(z0, z1))) → c68(PI(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(pi(2ndsneg(z0, z1))) → c68(PI(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(pi(pi(z0))) → c68(PI(pi(proper(z0))), PROPER(pi(z0)))
PROPER(pi(plus(z0, z1))) → c68(PI(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(pi(times(z0, z1))) → c68(PI(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(pi(square(z0))) → c68(PI(square(proper(z0))), PROPER(square(z0)))
PROPER(pi(0)) → c68(PI(ok(0)))
PROPER(pi(nil)) → c68(PI(ok(nil)))
PROPER(pi(rnil)) → c68(PI(ok(rnil)))
PROPER(plus(x0, s(z0))) → c69(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(plus(x0, posrecip(z0))) → c69(PLUS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(plus(x0, negrecip(z0))) → c69(PLUS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(plus(x0, cons(z0, z1))) → c69(PLUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(plus(x0, rcons(z0, z1))) → c69(PLUS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(plus(x0, from(z0))) → c69(PLUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(plus(x0, 2ndspos(z0, z1))) → c69(PLUS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(plus(x0, 2ndsneg(z0, z1))) → c69(PLUS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(plus(x0, pi(z0))) → c69(PLUS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(plus(x0, plus(z0, z1))) → c69(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(plus(x0, times(z0, z1))) → c69(PLUS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(plus(x0, square(z0))) → c69(PLUS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(plus(s(z0), x1)) → c69(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(plus(posrecip(z0), x1)) → c69(PLUS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(plus(negrecip(z0), x1)) → c69(PLUS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(plus(cons(z0, z1), x1)) → c69(PLUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(plus(rcons(z0, z1), x1)) → c69(PLUS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(plus(from(z0), x1)) → c69(PLUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(plus(2ndspos(z0, z1), x1)) → c69(PLUS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(plus(2ndsneg(z0, z1), x1)) → c69(PLUS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(plus(pi(z0), x1)) → c69(PLUS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(plus(plus(z0, z1), x1)) → c69(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(plus(times(z0, z1), x1)) → c69(PLUS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(plus(square(z0), x1)) → c69(PLUS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(plus(x0, 0)) → c69(PLUS(proper(x0), ok(0)), PROPER(x0))
PROPER(plus(x0, nil)) → c69(PLUS(proper(x0), ok(nil)), PROPER(x0))
PROPER(plus(x0, rnil)) → c69(PLUS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(plus(0, x1)) → c69(PLUS(ok(0), proper(x1)), PROPER(x1))
PROPER(plus(nil, x1)) → c69(PLUS(ok(nil), proper(x1)), PROPER(x1))
PROPER(plus(rnil, x1)) → c69(PLUS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(times(x0, s(z0))) → c70(TIMES(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(times(x0, posrecip(z0))) → c70(TIMES(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(times(x0, negrecip(z0))) → c70(TIMES(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(times(x0, cons(z0, z1))) → c70(TIMES(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(times(x0, rcons(z0, z1))) → c70(TIMES(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(times(x0, from(z0))) → c70(TIMES(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(times(x0, 2ndspos(z0, z1))) → c70(TIMES(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(times(x0, 2ndsneg(z0, z1))) → c70(TIMES(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(times(x0, pi(z0))) → c70(TIMES(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(times(x0, plus(z0, z1))) → c70(TIMES(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(times(x0, times(z0, z1))) → c70(TIMES(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(times(x0, square(z0))) → c70(TIMES(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(times(s(z0), x1)) → c70(TIMES(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(times(posrecip(z0), x1)) → c70(TIMES(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(times(negrecip(z0), x1)) → c70(TIMES(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(times(cons(z0, z1), x1)) → c70(TIMES(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(times(rcons(z0, z1), x1)) → c70(TIMES(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(times(from(z0), x1)) → c70(TIMES(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(times(2ndspos(z0, z1), x1)) → c70(TIMES(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(times(2ndsneg(z0, z1), x1)) → c70(TIMES(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(times(pi(z0), x1)) → c70(TIMES(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(times(plus(z0, z1), x1)) → c70(TIMES(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(times(times(z0, z1), x1)) → c70(TIMES(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(times(square(z0), x1)) → c70(TIMES(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(times(x0, 0)) → c70(TIMES(proper(x0), ok(0)), PROPER(x0))
PROPER(times(x0, nil)) → c70(TIMES(proper(x0), ok(nil)), PROPER(x0))
PROPER(times(x0, rnil)) → c70(TIMES(proper(x0), ok(rnil)), PROPER(x0))
PROPER(times(0, x1)) → c70(TIMES(ok(0), proper(x1)), PROPER(x1))
PROPER(times(nil, x1)) → c70(TIMES(ok(nil), proper(x1)), PROPER(x1))
PROPER(times(rnil, x1)) → c70(TIMES(ok(rnil), proper(x1)), PROPER(x1))
PROPER(square(s(z0))) → c71(SQUARE(s(proper(z0))), PROPER(s(z0)))
PROPER(square(posrecip(z0))) → c71(SQUARE(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(square(negrecip(z0))) → c71(SQUARE(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(square(cons(z0, z1))) → c71(SQUARE(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(square(rcons(z0, z1))) → c71(SQUARE(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(square(from(z0))) → c71(SQUARE(from(proper(z0))), PROPER(from(z0)))
PROPER(square(2ndspos(z0, z1))) → c71(SQUARE(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(square(2ndsneg(z0, z1))) → c71(SQUARE(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(square(pi(z0))) → c71(SQUARE(pi(proper(z0))), PROPER(pi(z0)))
PROPER(square(plus(z0, z1))) → c71(SQUARE(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(square(times(z0, z1))) → c71(SQUARE(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(square(square(z0))) → c71(SQUARE(square(proper(z0))), PROPER(square(z0)))
PROPER(square(0)) → c71(SQUARE(ok(0)))
PROPER(square(nil)) → c71(SQUARE(ok(nil)))
PROPER(square(rnil)) → c71(SQUARE(ok(rnil)))
TOP(mark(s(z0))) → c72(TOP(s(proper(z0))), PROPER(s(z0)))
TOP(mark(posrecip(z0))) → c72(TOP(posrecip(proper(z0))), PROPER(posrecip(z0)))
TOP(mark(negrecip(z0))) → c72(TOP(negrecip(proper(z0))), PROPER(negrecip(z0)))
TOP(mark(cons(z0, z1))) → c72(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
TOP(mark(rcons(z0, z1))) → c72(TOP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
TOP(mark(from(z0))) → c72(TOP(from(proper(z0))), PROPER(from(z0)))
TOP(mark(2ndspos(z0, z1))) → c72(TOP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
TOP(mark(2ndsneg(z0, z1))) → c72(TOP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
TOP(mark(pi(z0))) → c72(TOP(pi(proper(z0))), PROPER(pi(z0)))
TOP(mark(plus(z0, z1))) → c72(TOP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
TOP(mark(times(z0, z1))) → c72(TOP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
TOP(mark(square(z0))) → c72(TOP(square(proper(z0))), PROPER(square(z0)))
TOP(mark(0)) → c72(TOP(ok(0)))
TOP(mark(nil)) → c72(TOP(ok(nil)))
TOP(mark(rnil)) → c72(TOP(ok(rnil)))
TOP(ok(from(z0))) → c73(TOP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
TOP(ok(2ndspos(0, z0))) → c73(TOP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
TOP(ok(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c73(TOP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
TOP(ok(2ndsneg(0, z0))) → c73(TOP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
TOP(ok(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c73(TOP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
TOP(ok(pi(z0))) → c73(TOP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
TOP(ok(plus(0, z0))) → c73(TOP(mark(z0)), ACTIVE(plus(0, z0)))
TOP(ok(plus(s(z0), z1))) → c73(TOP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
TOP(ok(times(0, z0))) → c73(TOP(mark(0)), ACTIVE(times(0, z0)))
TOP(ok(times(s(z0), z1))) → c73(TOP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
TOP(ok(square(z0))) → c73(TOP(mark(times(z0, z0))), ACTIVE(square(z0)))
TOP(ok(s(z0))) → c73(TOP(s(active(z0))), ACTIVE(s(z0)))
TOP(ok(posrecip(z0))) → c73(TOP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
TOP(ok(negrecip(z0))) → c73(TOP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
TOP(ok(cons(z0, z1))) → c73(TOP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
TOP(ok(rcons(z0, z1))) → c73(TOP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
TOP(ok(rcons(z0, z1))) → c73(TOP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
TOP(ok(from(z0))) → c73(TOP(from(active(z0))), ACTIVE(from(z0)))
TOP(ok(2ndspos(z0, z1))) → c73(TOP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
TOP(ok(2ndspos(z0, z1))) → c73(TOP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
TOP(ok(2ndsneg(z0, z1))) → c73(TOP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
TOP(ok(2ndsneg(z0, z1))) → c73(TOP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
TOP(ok(pi(z0))) → c73(TOP(pi(active(z0))), ACTIVE(pi(z0)))
TOP(ok(plus(z0, z1))) → c73(TOP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
TOP(ok(plus(z0, z1))) → c73(TOP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
TOP(ok(times(z0, z1))) → c73(TOP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
TOP(ok(times(z0, z1))) → c73(TOP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
TOP(ok(square(z0))) → c73(TOP(square(active(z0))), ACTIVE(square(z0)))

S tuples:

ACTIVE(square(z0)) → c10(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c58(S(ok(0)))
PROPER(s(nil)) → c58(S(ok(nil)))
PROPER(s(rnil)) → c58(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(rcons(x0, s(z0))) → c64(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c64(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c64(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, cons(z0, z1))) → c64(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, rcons(z0, z1))) → c64(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c64(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c64(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c64(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c64(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c64(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c64(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c64(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(s(z0), x1)) → c64(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c64(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c64(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c64(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c64(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c64(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c64(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c64(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c64(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c64(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c64(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c64(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(rcons(x0, 0)) → c64(RCONS(proper(x0), ok(0)), PROPER(x0))
PROPER(rcons(x0, nil)) → c64(RCONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(rcons(x0, rnil)) → c64(RCONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(rcons(0, x1)) → c64(RCONS(ok(0), proper(x1)), PROPER(x1))
PROPER(rcons(nil, x1)) → c64(RCONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c64(RCONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(from(s(z0))) → c65(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(posrecip(z0))) → c65(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(from(negrecip(z0))) → c65(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(from(cons(z0, z1))) → c65(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(rcons(z0, z1))) → c65(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(from(from(z0))) → c65(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(2ndspos(z0, z1))) → c65(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(from(2ndsneg(z0, z1))) → c65(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(from(pi(z0))) → c65(FROM(pi(proper(z0))), PROPER(pi(z0)))
PROPER(from(plus(z0, z1))) → c65(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(from(times(z0, z1))) → c65(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(from(square(z0))) → c65(FROM(square(proper(z0))), PROPER(square(z0)))
PROPER(from(0)) → c65(FROM(ok(0)))
PROPER(from(nil)) → c65(FROM(ok(nil)))
PROPER(from(rnil)) → c65(FROM(ok(rnil)))
PROPER(2ndspos(x0, s(z0))) → c66(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndspos(x0, posrecip(z0))) → c66(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndspos(x0, negrecip(z0))) → c66(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndspos(x0, cons(z0, z1))) → c66(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndspos(x0, rcons(z0, z1))) → c66(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndspos(x0, from(z0))) → c66(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndspos(x0, pi(z0))) → c66(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndspos(x0, plus(z0, z1))) → c66(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndspos(x0, times(z0, z1))) → c66(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndspos(x0, square(z0))) → c66(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndspos(s(z0), x1)) → c66(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndspos(posrecip(z0), x1)) → c66(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndspos(negrecip(z0), x1)) → c66(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndspos(cons(z0, z1), x1)) → c66(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndspos(rcons(z0, z1), x1)) → c66(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndspos(from(z0), x1)) → c66(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c66(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c66(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndspos(pi(z0), x1)) → c66(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndspos(plus(z0, z1), x1)) → c66(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndspos(times(z0, z1), x1)) → c66(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndspos(square(z0), x1)) → c66(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndspos(x0, 0)) → c66(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndspos(x0, nil)) → c66(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndspos(x0, rnil)) → c66(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndspos(0, x1)) → c66(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndspos(nil, x1)) → c66(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndspos(rnil, x1)) → c66(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(x0, s(z0))) → c67(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndsneg(x0, posrecip(z0))) → c67(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndsneg(x0, negrecip(z0))) → c67(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndsneg(x0, cons(z0, z1))) → c67(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndsneg(x0, rcons(z0, z1))) → c67(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndsneg(x0, from(z0))) → c67(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndsneg(x0, pi(z0))) → c67(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndsneg(x0, plus(z0, z1))) → c67(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndsneg(x0, times(z0, z1))) → c67(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndsneg(x0, square(z0))) → c67(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndsneg(s(z0), x1)) → c67(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndsneg(posrecip(z0), x1)) → c67(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndsneg(negrecip(z0), x1)) → c67(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndsneg(cons(z0, z1), x1)) → c67(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(rcons(z0, z1), x1)) → c67(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(from(z0), x1)) → c67(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c67(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c67(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndsneg(pi(z0), x1)) → c67(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndsneg(plus(z0, z1), x1)) → c67(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndsneg(times(z0, z1), x1)) → c67(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndsneg(square(z0), x1)) → c67(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndsneg(x0, 0)) → c67(2NDSNEG(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndsneg(x0, nil)) → c67(2NDSNEG(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndsneg(x0, rnil)) → c67(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndsneg(0, x1)) → c67(2NDSNEG(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndsneg(nil, x1)) → c67(2NDSNEG(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(rnil, x1)) → c67(2NDSNEG(ok(rnil), proper(x1)), PROPER(x1))
PROPER(pi(s(z0))) → c68(PI(s(proper(z0))), PROPER(s(z0)))
PROPER(pi(posrecip(z0))) → c68(PI(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(pi(negrecip(z0))) → c68(PI(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(pi(cons(z0, z1))) → c68(PI(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(pi(rcons(z0, z1))) → c68(PI(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(pi(from(z0))) → c68(PI(from(proper(z0))), PROPER(from(z0)))
PROPER(pi(2ndspos(z0, z1))) → c68(PI(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(pi(2ndsneg(z0, z1))) → c68(PI(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(pi(pi(z0))) → c68(PI(pi(proper(z0))), PROPER(pi(z0)))
PROPER(pi(plus(z0, z1))) → c68(PI(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(pi(times(z0, z1))) → c68(PI(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(pi(square(z0))) → c68(PI(square(proper(z0))), PROPER(square(z0)))
PROPER(pi(0)) → c68(PI(ok(0)))
PROPER(pi(nil)) → c68(PI(ok(nil)))
PROPER(pi(rnil)) → c68(PI(ok(rnil)))
PROPER(plus(x0, s(z0))) → c69(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(plus(x0, posrecip(z0))) → c69(PLUS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(plus(x0, negrecip(z0))) → c69(PLUS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(plus(x0, cons(z0, z1))) → c69(PLUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(plus(x0, rcons(z0, z1))) → c69(PLUS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(plus(x0, from(z0))) → c69(PLUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(plus(x0, 2ndspos(z0, z1))) → c69(PLUS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(plus(x0, 2ndsneg(z0, z1))) → c69(PLUS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(plus(x0, pi(z0))) → c69(PLUS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(plus(x0, plus(z0, z1))) → c69(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(plus(x0, times(z0, z1))) → c69(PLUS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(plus(x0, square(z0))) → c69(PLUS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(plus(s(z0), x1)) → c69(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(plus(posrecip(z0), x1)) → c69(PLUS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(plus(negrecip(z0), x1)) → c69(PLUS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(plus(cons(z0, z1), x1)) → c69(PLUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(plus(rcons(z0, z1), x1)) → c69(PLUS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(plus(from(z0), x1)) → c69(PLUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(plus(2ndspos(z0, z1), x1)) → c69(PLUS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(plus(2ndsneg(z0, z1), x1)) → c69(PLUS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(plus(pi(z0), x1)) → c69(PLUS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(plus(plus(z0, z1), x1)) → c69(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(plus(times(z0, z1), x1)) → c69(PLUS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(plus(square(z0), x1)) → c69(PLUS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(plus(x0, 0)) → c69(PLUS(proper(x0), ok(0)), PROPER(x0))
PROPER(plus(x0, nil)) → c69(PLUS(proper(x0), ok(nil)), PROPER(x0))
PROPER(plus(x0, rnil)) → c69(PLUS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(plus(0, x1)) → c69(PLUS(ok(0), proper(x1)), PROPER(x1))
PROPER(plus(nil, x1)) → c69(PLUS(ok(nil), proper(x1)), PROPER(x1))
PROPER(plus(rnil, x1)) → c69(PLUS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(times(x0, s(z0))) → c70(TIMES(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(times(x0, posrecip(z0))) → c70(TIMES(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(times(x0, negrecip(z0))) → c70(TIMES(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(times(x0, cons(z0, z1))) → c70(TIMES(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(times(x0, rcons(z0, z1))) → c70(TIMES(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(times(x0, from(z0))) → c70(TIMES(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(times(x0, 2ndspos(z0, z1))) → c70(TIMES(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(times(x0, 2ndsneg(z0, z1))) → c70(TIMES(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(times(x0, pi(z0))) → c70(TIMES(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(times(x0, plus(z0, z1))) → c70(TIMES(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(times(x0, times(z0, z1))) → c70(TIMES(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(times(x0, square(z0))) → c70(TIMES(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(times(s(z0), x1)) → c70(TIMES(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(times(posrecip(z0), x1)) → c70(TIMES(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(times(negrecip(z0), x1)) → c70(TIMES(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(times(cons(z0, z1), x1)) → c70(TIMES(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(times(rcons(z0, z1), x1)) → c70(TIMES(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(times(from(z0), x1)) → c70(TIMES(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(times(2ndspos(z0, z1), x1)) → c70(TIMES(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(times(2ndsneg(z0, z1), x1)) → c70(TIMES(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(times(pi(z0), x1)) → c70(TIMES(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(times(plus(z0, z1), x1)) → c70(TIMES(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(times(times(z0, z1), x1)) → c70(TIMES(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(times(square(z0), x1)) → c70(TIMES(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(times(x0, 0)) → c70(TIMES(proper(x0), ok(0)), PROPER(x0))
PROPER(times(x0, nil)) → c70(TIMES(proper(x0), ok(nil)), PROPER(x0))
PROPER(times(x0, rnil)) → c70(TIMES(proper(x0), ok(rnil)), PROPER(x0))
PROPER(times(0, x1)) → c70(TIMES(ok(0), proper(x1)), PROPER(x1))
PROPER(times(nil, x1)) → c70(TIMES(ok(nil), proper(x1)), PROPER(x1))
PROPER(times(rnil, x1)) → c70(TIMES(ok(rnil), proper(x1)), PROPER(x1))
PROPER(square(s(z0))) → c71(SQUARE(s(proper(z0))), PROPER(s(z0)))
PROPER(square(posrecip(z0))) → c71(SQUARE(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(square(negrecip(z0))) → c71(SQUARE(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(square(cons(z0, z1))) → c71(SQUARE(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(square(rcons(z0, z1))) → c71(SQUARE(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(square(from(z0))) → c71(SQUARE(from(proper(z0))), PROPER(from(z0)))
PROPER(square(2ndspos(z0, z1))) → c71(SQUARE(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(square(2ndsneg(z0, z1))) → c71(SQUARE(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(square(pi(z0))) → c71(SQUARE(pi(proper(z0))), PROPER(pi(z0)))
PROPER(square(plus(z0, z1))) → c71(SQUARE(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(square(times(z0, z1))) → c71(SQUARE(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(square(square(z0))) → c71(SQUARE(square(proper(z0))), PROPER(square(z0)))
PROPER(square(0)) → c71(SQUARE(ok(0)))
PROPER(square(nil)) → c71(SQUARE(ok(nil)))
PROPER(square(rnil)) → c71(SQUARE(ok(rnil)))
TOP(mark(s(z0))) → c72(TOP(s(proper(z0))), PROPER(s(z0)))
TOP(mark(posrecip(z0))) → c72(TOP(posrecip(proper(z0))), PROPER(posrecip(z0)))
TOP(mark(negrecip(z0))) → c72(TOP(negrecip(proper(z0))), PROPER(negrecip(z0)))
TOP(mark(cons(z0, z1))) → c72(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
TOP(mark(rcons(z0, z1))) → c72(TOP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
TOP(mark(from(z0))) → c72(TOP(from(proper(z0))), PROPER(from(z0)))
TOP(mark(2ndspos(z0, z1))) → c72(TOP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
TOP(mark(2ndsneg(z0, z1))) → c72(TOP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
TOP(mark(pi(z0))) → c72(TOP(pi(proper(z0))), PROPER(pi(z0)))
TOP(mark(plus(z0, z1))) → c72(TOP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
TOP(mark(times(z0, z1))) → c72(TOP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
TOP(mark(square(z0))) → c72(TOP(square(proper(z0))), PROPER(square(z0)))
TOP(mark(0)) → c72(TOP(ok(0)))
TOP(mark(nil)) → c72(TOP(ok(nil)))
TOP(mark(rnil)) → c72(TOP(ok(rnil)))
TOP(ok(from(z0))) → c73(TOP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
TOP(ok(2ndspos(0, z0))) → c73(TOP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
TOP(ok(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c73(TOP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
TOP(ok(2ndsneg(0, z0))) → c73(TOP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
TOP(ok(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c73(TOP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
TOP(ok(pi(z0))) → c73(TOP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
TOP(ok(plus(0, z0))) → c73(TOP(mark(z0)), ACTIVE(plus(0, z0)))
TOP(ok(plus(s(z0), z1))) → c73(TOP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
TOP(ok(times(0, z0))) → c73(TOP(mark(0)), ACTIVE(times(0, z0)))
TOP(ok(times(s(z0), z1))) → c73(TOP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
TOP(ok(square(z0))) → c73(TOP(mark(times(z0, z0))), ACTIVE(square(z0)))
TOP(ok(s(z0))) → c73(TOP(s(active(z0))), ACTIVE(s(z0)))
TOP(ok(posrecip(z0))) → c73(TOP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
TOP(ok(negrecip(z0))) → c73(TOP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
TOP(ok(cons(z0, z1))) → c73(TOP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
TOP(ok(rcons(z0, z1))) → c73(TOP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
TOP(ok(rcons(z0, z1))) → c73(TOP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
TOP(ok(from(z0))) → c73(TOP(from(active(z0))), ACTIVE(from(z0)))
TOP(ok(2ndspos(z0, z1))) → c73(TOP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
TOP(ok(2ndspos(z0, z1))) → c73(TOP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
TOP(ok(2ndsneg(z0, z1))) → c73(TOP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
TOP(ok(2ndsneg(z0, z1))) → c73(TOP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
TOP(ok(pi(z0))) → c73(TOP(pi(active(z0))), ACTIVE(pi(z0)))
TOP(ok(plus(z0, z1))) → c73(TOP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
TOP(ok(plus(z0, z1))) → c73(TOP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
TOP(ok(times(z0, z1))) → c73(TOP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
TOP(ok(times(z0, z1))) → c73(TOP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
TOP(ok(square(z0))) → c73(TOP(square(active(z0))), ACTIVE(square(z0)))

K tuples:none
Defined Rule Symbols:

active, rcons, posrecip, 2ndsneg, negrecip, 2ndspos, s, cons, from, pi, plus, times, square, proper

Defined Pair Symbols:

ACTIVE, S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP

Compound Symbols:

c10, c15, c16, c18, c19, c20, c21, c23, c24, c25, c26, 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, c, c5, c7, c9, c1, c11, c12, c13, c14, c17, c22, c27, c58, c58, c59, c59, c60, c60, c62, c62, c64, c64, c65, c65, c66, c66, c67, c67, c68, c68, c69, c69, c70, c70, c71, c71, c72, c72, c73

(79) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID) transformation)

Removed 3 trailing nodes:

TOP(mark(rnil)) → c72(TOP(ok(rnil)))
TOP(mark(nil)) → c72(TOP(ok(nil)))
TOP(mark(0)) → c72(TOP(ok(0)))

(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, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(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(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))
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))
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))
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(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)) → c10(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c58(S(ok(0)))
PROPER(s(nil)) → c58(S(ok(nil)))
PROPER(s(rnil)) → c58(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(rcons(x0, s(z0))) → c64(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c64(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c64(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, cons(z0, z1))) → c64(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, rcons(z0, z1))) → c64(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c64(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c64(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c64(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c64(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c64(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c64(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c64(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(s(z0), x1)) → c64(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c64(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c64(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c64(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c64(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c64(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c64(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c64(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c64(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c64(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c64(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c64(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(rcons(x0, 0)) → c64(RCONS(proper(x0), ok(0)), PROPER(x0))
PROPER(rcons(x0, nil)) → c64(RCONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(rcons(x0, rnil)) → c64(RCONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(rcons(0, x1)) → c64(RCONS(ok(0), proper(x1)), PROPER(x1))
PROPER(rcons(nil, x1)) → c64(RCONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c64(RCONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(from(s(z0))) → c65(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(posrecip(z0))) → c65(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(from(negrecip(z0))) → c65(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(from(cons(z0, z1))) → c65(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(rcons(z0, z1))) → c65(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(from(from(z0))) → c65(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(2ndspos(z0, z1))) → c65(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(from(2ndsneg(z0, z1))) → c65(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(from(pi(z0))) → c65(FROM(pi(proper(z0))), PROPER(pi(z0)))
PROPER(from(plus(z0, z1))) → c65(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(from(times(z0, z1))) → c65(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(from(square(z0))) → c65(FROM(square(proper(z0))), PROPER(square(z0)))
PROPER(from(0)) → c65(FROM(ok(0)))
PROPER(from(nil)) → c65(FROM(ok(nil)))
PROPER(from(rnil)) → c65(FROM(ok(rnil)))
PROPER(2ndspos(x0, s(z0))) → c66(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndspos(x0, posrecip(z0))) → c66(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndspos(x0, negrecip(z0))) → c66(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndspos(x0, cons(z0, z1))) → c66(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndspos(x0, rcons(z0, z1))) → c66(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndspos(x0, from(z0))) → c66(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndspos(x0, pi(z0))) → c66(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndspos(x0, plus(z0, z1))) → c66(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndspos(x0, times(z0, z1))) → c66(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndspos(x0, square(z0))) → c66(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndspos(s(z0), x1)) → c66(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndspos(posrecip(z0), x1)) → c66(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndspos(negrecip(z0), x1)) → c66(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndspos(cons(z0, z1), x1)) → c66(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndspos(rcons(z0, z1), x1)) → c66(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndspos(from(z0), x1)) → c66(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c66(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c66(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndspos(pi(z0), x1)) → c66(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndspos(plus(z0, z1), x1)) → c66(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndspos(times(z0, z1), x1)) → c66(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndspos(square(z0), x1)) → c66(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndspos(x0, 0)) → c66(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndspos(x0, nil)) → c66(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndspos(x0, rnil)) → c66(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndspos(0, x1)) → c66(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndspos(nil, x1)) → c66(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndspos(rnil, x1)) → c66(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(x0, s(z0))) → c67(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndsneg(x0, posrecip(z0))) → c67(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndsneg(x0, negrecip(z0))) → c67(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndsneg(x0, cons(z0, z1))) → c67(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndsneg(x0, rcons(z0, z1))) → c67(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndsneg(x0, from(z0))) → c67(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndsneg(x0, pi(z0))) → c67(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndsneg(x0, plus(z0, z1))) → c67(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndsneg(x0, times(z0, z1))) → c67(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndsneg(x0, square(z0))) → c67(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndsneg(s(z0), x1)) → c67(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndsneg(posrecip(z0), x1)) → c67(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndsneg(negrecip(z0), x1)) → c67(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndsneg(cons(z0, z1), x1)) → c67(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(rcons(z0, z1), x1)) → c67(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(from(z0), x1)) → c67(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c67(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c67(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndsneg(pi(z0), x1)) → c67(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndsneg(plus(z0, z1), x1)) → c67(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndsneg(times(z0, z1), x1)) → c67(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndsneg(square(z0), x1)) → c67(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndsneg(x0, 0)) → c67(2NDSNEG(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndsneg(x0, nil)) → c67(2NDSNEG(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndsneg(x0, rnil)) → c67(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndsneg(0, x1)) → c67(2NDSNEG(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndsneg(nil, x1)) → c67(2NDSNEG(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(rnil, x1)) → c67(2NDSNEG(ok(rnil), proper(x1)), PROPER(x1))
PROPER(pi(s(z0))) → c68(PI(s(proper(z0))), PROPER(s(z0)))
PROPER(pi(posrecip(z0))) → c68(PI(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(pi(negrecip(z0))) → c68(PI(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(pi(cons(z0, z1))) → c68(PI(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(pi(rcons(z0, z1))) → c68(PI(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(pi(from(z0))) → c68(PI(from(proper(z0))), PROPER(from(z0)))
PROPER(pi(2ndspos(z0, z1))) → c68(PI(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(pi(2ndsneg(z0, z1))) → c68(PI(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(pi(pi(z0))) → c68(PI(pi(proper(z0))), PROPER(pi(z0)))
PROPER(pi(plus(z0, z1))) → c68(PI(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(pi(times(z0, z1))) → c68(PI(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(pi(square(z0))) → c68(PI(square(proper(z0))), PROPER(square(z0)))
PROPER(pi(0)) → c68(PI(ok(0)))
PROPER(pi(nil)) → c68(PI(ok(nil)))
PROPER(pi(rnil)) → c68(PI(ok(rnil)))
PROPER(plus(x0, s(z0))) → c69(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(plus(x0, posrecip(z0))) → c69(PLUS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(plus(x0, negrecip(z0))) → c69(PLUS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(plus(x0, cons(z0, z1))) → c69(PLUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(plus(x0, rcons(z0, z1))) → c69(PLUS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(plus(x0, from(z0))) → c69(PLUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(plus(x0, 2ndspos(z0, z1))) → c69(PLUS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(plus(x0, 2ndsneg(z0, z1))) → c69(PLUS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(plus(x0, pi(z0))) → c69(PLUS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(plus(x0, plus(z0, z1))) → c69(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(plus(x0, times(z0, z1))) → c69(PLUS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(plus(x0, square(z0))) → c69(PLUS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(plus(s(z0), x1)) → c69(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(plus(posrecip(z0), x1)) → c69(PLUS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(plus(negrecip(z0), x1)) → c69(PLUS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(plus(cons(z0, z1), x1)) → c69(PLUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(plus(rcons(z0, z1), x1)) → c69(PLUS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(plus(from(z0), x1)) → c69(PLUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(plus(2ndspos(z0, z1), x1)) → c69(PLUS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(plus(2ndsneg(z0, z1), x1)) → c69(PLUS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(plus(pi(z0), x1)) → c69(PLUS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(plus(plus(z0, z1), x1)) → c69(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(plus(times(z0, z1), x1)) → c69(PLUS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(plus(square(z0), x1)) → c69(PLUS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(plus(x0, 0)) → c69(PLUS(proper(x0), ok(0)), PROPER(x0))
PROPER(plus(x0, nil)) → c69(PLUS(proper(x0), ok(nil)), PROPER(x0))
PROPER(plus(x0, rnil)) → c69(PLUS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(plus(0, x1)) → c69(PLUS(ok(0), proper(x1)), PROPER(x1))
PROPER(plus(nil, x1)) → c69(PLUS(ok(nil), proper(x1)), PROPER(x1))
PROPER(plus(rnil, x1)) → c69(PLUS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(times(x0, s(z0))) → c70(TIMES(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(times(x0, posrecip(z0))) → c70(TIMES(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(times(x0, negrecip(z0))) → c70(TIMES(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(times(x0, cons(z0, z1))) → c70(TIMES(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(times(x0, rcons(z0, z1))) → c70(TIMES(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(times(x0, from(z0))) → c70(TIMES(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(times(x0, 2ndspos(z0, z1))) → c70(TIMES(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(times(x0, 2ndsneg(z0, z1))) → c70(TIMES(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(times(x0, pi(z0))) → c70(TIMES(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(times(x0, plus(z0, z1))) → c70(TIMES(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(times(x0, times(z0, z1))) → c70(TIMES(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(times(x0, square(z0))) → c70(TIMES(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(times(s(z0), x1)) → c70(TIMES(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(times(posrecip(z0), x1)) → c70(TIMES(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(times(negrecip(z0), x1)) → c70(TIMES(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(times(cons(z0, z1), x1)) → c70(TIMES(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(times(rcons(z0, z1), x1)) → c70(TIMES(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(times(from(z0), x1)) → c70(TIMES(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(times(2ndspos(z0, z1), x1)) → c70(TIMES(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(times(2ndsneg(z0, z1), x1)) → c70(TIMES(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(times(pi(z0), x1)) → c70(TIMES(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(times(plus(z0, z1), x1)) → c70(TIMES(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(times(times(z0, z1), x1)) → c70(TIMES(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(times(square(z0), x1)) → c70(TIMES(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(times(x0, 0)) → c70(TIMES(proper(x0), ok(0)), PROPER(x0))
PROPER(times(x0, nil)) → c70(TIMES(proper(x0), ok(nil)), PROPER(x0))
PROPER(times(x0, rnil)) → c70(TIMES(proper(x0), ok(rnil)), PROPER(x0))
PROPER(times(0, x1)) → c70(TIMES(ok(0), proper(x1)), PROPER(x1))
PROPER(times(nil, x1)) → c70(TIMES(ok(nil), proper(x1)), PROPER(x1))
PROPER(times(rnil, x1)) → c70(TIMES(ok(rnil), proper(x1)), PROPER(x1))
PROPER(square(s(z0))) → c71(SQUARE(s(proper(z0))), PROPER(s(z0)))
PROPER(square(posrecip(z0))) → c71(SQUARE(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(square(negrecip(z0))) → c71(SQUARE(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(square(cons(z0, z1))) → c71(SQUARE(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(square(rcons(z0, z1))) → c71(SQUARE(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(square(from(z0))) → c71(SQUARE(from(proper(z0))), PROPER(from(z0)))
PROPER(square(2ndspos(z0, z1))) → c71(SQUARE(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(square(2ndsneg(z0, z1))) → c71(SQUARE(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(square(pi(z0))) → c71(SQUARE(pi(proper(z0))), PROPER(pi(z0)))
PROPER(square(plus(z0, z1))) → c71(SQUARE(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(square(times(z0, z1))) → c71(SQUARE(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(square(square(z0))) → c71(SQUARE(square(proper(z0))), PROPER(square(z0)))
PROPER(square(0)) → c71(SQUARE(ok(0)))
PROPER(square(nil)) → c71(SQUARE(ok(nil)))
PROPER(square(rnil)) → c71(SQUARE(ok(rnil)))
TOP(mark(s(z0))) → c72(TOP(s(proper(z0))), PROPER(s(z0)))
TOP(mark(posrecip(z0))) → c72(TOP(posrecip(proper(z0))), PROPER(posrecip(z0)))
TOP(mark(negrecip(z0))) → c72(TOP(negrecip(proper(z0))), PROPER(negrecip(z0)))
TOP(mark(cons(z0, z1))) → c72(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
TOP(mark(rcons(z0, z1))) → c72(TOP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
TOP(mark(from(z0))) → c72(TOP(from(proper(z0))), PROPER(from(z0)))
TOP(mark(2ndspos(z0, z1))) → c72(TOP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
TOP(mark(2ndsneg(z0, z1))) → c72(TOP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
TOP(mark(pi(z0))) → c72(TOP(pi(proper(z0))), PROPER(pi(z0)))
TOP(mark(plus(z0, z1))) → c72(TOP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
TOP(mark(times(z0, z1))) → c72(TOP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
TOP(mark(square(z0))) → c72(TOP(square(proper(z0))), PROPER(square(z0)))
TOP(ok(from(z0))) → c73(TOP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
TOP(ok(2ndspos(0, z0))) → c73(TOP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
TOP(ok(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c73(TOP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
TOP(ok(2ndsneg(0, z0))) → c73(TOP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
TOP(ok(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c73(TOP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
TOP(ok(pi(z0))) → c73(TOP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
TOP(ok(plus(0, z0))) → c73(TOP(mark(z0)), ACTIVE(plus(0, z0)))
TOP(ok(plus(s(z0), z1))) → c73(TOP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
TOP(ok(times(0, z0))) → c73(TOP(mark(0)), ACTIVE(times(0, z0)))
TOP(ok(times(s(z0), z1))) → c73(TOP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
TOP(ok(square(z0))) → c73(TOP(mark(times(z0, z0))), ACTIVE(square(z0)))
TOP(ok(s(z0))) → c73(TOP(s(active(z0))), ACTIVE(s(z0)))
TOP(ok(posrecip(z0))) → c73(TOP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
TOP(ok(negrecip(z0))) → c73(TOP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
TOP(ok(cons(z0, z1))) → c73(TOP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
TOP(ok(rcons(z0, z1))) → c73(TOP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
TOP(ok(rcons(z0, z1))) → c73(TOP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
TOP(ok(from(z0))) → c73(TOP(from(active(z0))), ACTIVE(from(z0)))
TOP(ok(2ndspos(z0, z1))) → c73(TOP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
TOP(ok(2ndspos(z0, z1))) → c73(TOP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
TOP(ok(2ndsneg(z0, z1))) → c73(TOP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
TOP(ok(2ndsneg(z0, z1))) → c73(TOP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
TOP(ok(pi(z0))) → c73(TOP(pi(active(z0))), ACTIVE(pi(z0)))
TOP(ok(plus(z0, z1))) → c73(TOP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
TOP(ok(plus(z0, z1))) → c73(TOP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
TOP(ok(times(z0, z1))) → c73(TOP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
TOP(ok(times(z0, z1))) → c73(TOP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
TOP(ok(square(z0))) → c73(TOP(square(active(z0))), ACTIVE(square(z0)))

S tuples:

ACTIVE(square(z0)) → c10(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c58(S(ok(0)))
PROPER(s(nil)) → c58(S(ok(nil)))
PROPER(s(rnil)) → c58(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(rcons(x0, s(z0))) → c64(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c64(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c64(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, cons(z0, z1))) → c64(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, rcons(z0, z1))) → c64(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c64(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c64(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c64(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c64(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c64(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c64(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c64(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(s(z0), x1)) → c64(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c64(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c64(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c64(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c64(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c64(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c64(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c64(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c64(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c64(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c64(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c64(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(rcons(x0, 0)) → c64(RCONS(proper(x0), ok(0)), PROPER(x0))
PROPER(rcons(x0, nil)) → c64(RCONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(rcons(x0, rnil)) → c64(RCONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(rcons(0, x1)) → c64(RCONS(ok(0), proper(x1)), PROPER(x1))
PROPER(rcons(nil, x1)) → c64(RCONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c64(RCONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(from(s(z0))) → c65(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(posrecip(z0))) → c65(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(from(negrecip(z0))) → c65(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(from(cons(z0, z1))) → c65(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(rcons(z0, z1))) → c65(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(from(from(z0))) → c65(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(2ndspos(z0, z1))) → c65(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(from(2ndsneg(z0, z1))) → c65(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(from(pi(z0))) → c65(FROM(pi(proper(z0))), PROPER(pi(z0)))
PROPER(from(plus(z0, z1))) → c65(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(from(times(z0, z1))) → c65(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(from(square(z0))) → c65(FROM(square(proper(z0))), PROPER(square(z0)))
PROPER(from(0)) → c65(FROM(ok(0)))
PROPER(from(nil)) → c65(FROM(ok(nil)))
PROPER(from(rnil)) → c65(FROM(ok(rnil)))
PROPER(2ndspos(x0, s(z0))) → c66(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndspos(x0, posrecip(z0))) → c66(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndspos(x0, negrecip(z0))) → c66(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndspos(x0, cons(z0, z1))) → c66(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndspos(x0, rcons(z0, z1))) → c66(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndspos(x0, from(z0))) → c66(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndspos(x0, pi(z0))) → c66(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndspos(x0, plus(z0, z1))) → c66(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndspos(x0, times(z0, z1))) → c66(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndspos(x0, square(z0))) → c66(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndspos(s(z0), x1)) → c66(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndspos(posrecip(z0), x1)) → c66(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndspos(negrecip(z0), x1)) → c66(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndspos(cons(z0, z1), x1)) → c66(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndspos(rcons(z0, z1), x1)) → c66(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndspos(from(z0), x1)) → c66(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c66(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c66(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndspos(pi(z0), x1)) → c66(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndspos(plus(z0, z1), x1)) → c66(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndspos(times(z0, z1), x1)) → c66(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndspos(square(z0), x1)) → c66(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndspos(x0, 0)) → c66(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndspos(x0, nil)) → c66(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndspos(x0, rnil)) → c66(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndspos(0, x1)) → c66(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndspos(nil, x1)) → c66(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndspos(rnil, x1)) → c66(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(x0, s(z0))) → c67(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndsneg(x0, posrecip(z0))) → c67(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndsneg(x0, negrecip(z0))) → c67(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndsneg(x0, cons(z0, z1))) → c67(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndsneg(x0, rcons(z0, z1))) → c67(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndsneg(x0, from(z0))) → c67(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndsneg(x0, pi(z0))) → c67(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndsneg(x0, plus(z0, z1))) → c67(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndsneg(x0, times(z0, z1))) → c67(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndsneg(x0, square(z0))) → c67(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndsneg(s(z0), x1)) → c67(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndsneg(posrecip(z0), x1)) → c67(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndsneg(negrecip(z0), x1)) → c67(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndsneg(cons(z0, z1), x1)) → c67(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(rcons(z0, z1), x1)) → c67(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(from(z0), x1)) → c67(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c67(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c67(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndsneg(pi(z0), x1)) → c67(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndsneg(plus(z0, z1), x1)) → c67(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndsneg(times(z0, z1), x1)) → c67(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndsneg(square(z0), x1)) → c67(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndsneg(x0, 0)) → c67(2NDSNEG(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndsneg(x0, nil)) → c67(2NDSNEG(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndsneg(x0, rnil)) → c67(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndsneg(0, x1)) → c67(2NDSNEG(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndsneg(nil, x1)) → c67(2NDSNEG(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(rnil, x1)) → c67(2NDSNEG(ok(rnil), proper(x1)), PROPER(x1))
PROPER(pi(s(z0))) → c68(PI(s(proper(z0))), PROPER(s(z0)))
PROPER(pi(posrecip(z0))) → c68(PI(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(pi(negrecip(z0))) → c68(PI(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(pi(cons(z0, z1))) → c68(PI(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(pi(rcons(z0, z1))) → c68(PI(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(pi(from(z0))) → c68(PI(from(proper(z0))), PROPER(from(z0)))
PROPER(pi(2ndspos(z0, z1))) → c68(PI(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(pi(2ndsneg(z0, z1))) → c68(PI(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(pi(pi(z0))) → c68(PI(pi(proper(z0))), PROPER(pi(z0)))
PROPER(pi(plus(z0, z1))) → c68(PI(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(pi(times(z0, z1))) → c68(PI(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(pi(square(z0))) → c68(PI(square(proper(z0))), PROPER(square(z0)))
PROPER(pi(0)) → c68(PI(ok(0)))
PROPER(pi(nil)) → c68(PI(ok(nil)))
PROPER(pi(rnil)) → c68(PI(ok(rnil)))
PROPER(plus(x0, s(z0))) → c69(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(plus(x0, posrecip(z0))) → c69(PLUS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(plus(x0, negrecip(z0))) → c69(PLUS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(plus(x0, cons(z0, z1))) → c69(PLUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(plus(x0, rcons(z0, z1))) → c69(PLUS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(plus(x0, from(z0))) → c69(PLUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(plus(x0, 2ndspos(z0, z1))) → c69(PLUS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(plus(x0, 2ndsneg(z0, z1))) → c69(PLUS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(plus(x0, pi(z0))) → c69(PLUS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(plus(x0, plus(z0, z1))) → c69(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(plus(x0, times(z0, z1))) → c69(PLUS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(plus(x0, square(z0))) → c69(PLUS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(plus(s(z0), x1)) → c69(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(plus(posrecip(z0), x1)) → c69(PLUS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(plus(negrecip(z0), x1)) → c69(PLUS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(plus(cons(z0, z1), x1)) → c69(PLUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(plus(rcons(z0, z1), x1)) → c69(PLUS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(plus(from(z0), x1)) → c69(PLUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(plus(2ndspos(z0, z1), x1)) → c69(PLUS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(plus(2ndsneg(z0, z1), x1)) → c69(PLUS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(plus(pi(z0), x1)) → c69(PLUS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(plus(plus(z0, z1), x1)) → c69(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(plus(times(z0, z1), x1)) → c69(PLUS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(plus(square(z0), x1)) → c69(PLUS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(plus(x0, 0)) → c69(PLUS(proper(x0), ok(0)), PROPER(x0))
PROPER(plus(x0, nil)) → c69(PLUS(proper(x0), ok(nil)), PROPER(x0))
PROPER(plus(x0, rnil)) → c69(PLUS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(plus(0, x1)) → c69(PLUS(ok(0), proper(x1)), PROPER(x1))
PROPER(plus(nil, x1)) → c69(PLUS(ok(nil), proper(x1)), PROPER(x1))
PROPER(plus(rnil, x1)) → c69(PLUS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(times(x0, s(z0))) → c70(TIMES(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(times(x0, posrecip(z0))) → c70(TIMES(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(times(x0, negrecip(z0))) → c70(TIMES(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(times(x0, cons(z0, z1))) → c70(TIMES(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(times(x0, rcons(z0, z1))) → c70(TIMES(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(times(x0, from(z0))) → c70(TIMES(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(times(x0, 2ndspos(z0, z1))) → c70(TIMES(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(times(x0, 2ndsneg(z0, z1))) → c70(TIMES(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(times(x0, pi(z0))) → c70(TIMES(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(times(x0, plus(z0, z1))) → c70(TIMES(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(times(x0, times(z0, z1))) → c70(TIMES(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(times(x0, square(z0))) → c70(TIMES(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(times(s(z0), x1)) → c70(TIMES(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(times(posrecip(z0), x1)) → c70(TIMES(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(times(negrecip(z0), x1)) → c70(TIMES(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(times(cons(z0, z1), x1)) → c70(TIMES(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(times(rcons(z0, z1), x1)) → c70(TIMES(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(times(from(z0), x1)) → c70(TIMES(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(times(2ndspos(z0, z1), x1)) → c70(TIMES(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(times(2ndsneg(z0, z1), x1)) → c70(TIMES(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(times(pi(z0), x1)) → c70(TIMES(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(times(plus(z0, z1), x1)) → c70(TIMES(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(times(times(z0, z1), x1)) → c70(TIMES(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(times(square(z0), x1)) → c70(TIMES(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(times(x0, 0)) → c70(TIMES(proper(x0), ok(0)), PROPER(x0))
PROPER(times(x0, nil)) → c70(TIMES(proper(x0), ok(nil)), PROPER(x0))
PROPER(times(x0, rnil)) → c70(TIMES(proper(x0), ok(rnil)), PROPER(x0))
PROPER(times(0, x1)) → c70(TIMES(ok(0), proper(x1)), PROPER(x1))
PROPER(times(nil, x1)) → c70(TIMES(ok(nil), proper(x1)), PROPER(x1))
PROPER(times(rnil, x1)) → c70(TIMES(ok(rnil), proper(x1)), PROPER(x1))
PROPER(square(s(z0))) → c71(SQUARE(s(proper(z0))), PROPER(s(z0)))
PROPER(square(posrecip(z0))) → c71(SQUARE(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(square(negrecip(z0))) → c71(SQUARE(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(square(cons(z0, z1))) → c71(SQUARE(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(square(rcons(z0, z1))) → c71(SQUARE(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(square(from(z0))) → c71(SQUARE(from(proper(z0))), PROPER(from(z0)))
PROPER(square(2ndspos(z0, z1))) → c71(SQUARE(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(square(2ndsneg(z0, z1))) → c71(SQUARE(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(square(pi(z0))) → c71(SQUARE(pi(proper(z0))), PROPER(pi(z0)))
PROPER(square(plus(z0, z1))) → c71(SQUARE(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(square(times(z0, z1))) → c71(SQUARE(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(square(square(z0))) → c71(SQUARE(square(proper(z0))), PROPER(square(z0)))
PROPER(square(0)) → c71(SQUARE(ok(0)))
PROPER(square(nil)) → c71(SQUARE(ok(nil)))
PROPER(square(rnil)) → c71(SQUARE(ok(rnil)))
TOP(mark(s(z0))) → c72(TOP(s(proper(z0))), PROPER(s(z0)))
TOP(mark(posrecip(z0))) → c72(TOP(posrecip(proper(z0))), PROPER(posrecip(z0)))
TOP(mark(negrecip(z0))) → c72(TOP(negrecip(proper(z0))), PROPER(negrecip(z0)))
TOP(mark(cons(z0, z1))) → c72(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
TOP(mark(rcons(z0, z1))) → c72(TOP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
TOP(mark(from(z0))) → c72(TOP(from(proper(z0))), PROPER(from(z0)))
TOP(mark(2ndspos(z0, z1))) → c72(TOP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
TOP(mark(2ndsneg(z0, z1))) → c72(TOP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
TOP(mark(pi(z0))) → c72(TOP(pi(proper(z0))), PROPER(pi(z0)))
TOP(mark(plus(z0, z1))) → c72(TOP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
TOP(mark(times(z0, z1))) → c72(TOP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
TOP(mark(square(z0))) → c72(TOP(square(proper(z0))), PROPER(square(z0)))
TOP(ok(from(z0))) → c73(TOP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
TOP(ok(2ndspos(0, z0))) → c73(TOP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
TOP(ok(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c73(TOP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
TOP(ok(2ndsneg(0, z0))) → c73(TOP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
TOP(ok(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c73(TOP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
TOP(ok(pi(z0))) → c73(TOP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
TOP(ok(plus(0, z0))) → c73(TOP(mark(z0)), ACTIVE(plus(0, z0)))
TOP(ok(plus(s(z0), z1))) → c73(TOP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
TOP(ok(times(0, z0))) → c73(TOP(mark(0)), ACTIVE(times(0, z0)))
TOP(ok(times(s(z0), z1))) → c73(TOP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
TOP(ok(square(z0))) → c73(TOP(mark(times(z0, z0))), ACTIVE(square(z0)))
TOP(ok(s(z0))) → c73(TOP(s(active(z0))), ACTIVE(s(z0)))
TOP(ok(posrecip(z0))) → c73(TOP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
TOP(ok(negrecip(z0))) → c73(TOP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
TOP(ok(cons(z0, z1))) → c73(TOP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
TOP(ok(rcons(z0, z1))) → c73(TOP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
TOP(ok(rcons(z0, z1))) → c73(TOP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
TOP(ok(from(z0))) → c73(TOP(from(active(z0))), ACTIVE(from(z0)))
TOP(ok(2ndspos(z0, z1))) → c73(TOP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
TOP(ok(2ndspos(z0, z1))) → c73(TOP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
TOP(ok(2ndsneg(z0, z1))) → c73(TOP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
TOP(ok(2ndsneg(z0, z1))) → c73(TOP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
TOP(ok(pi(z0))) → c73(TOP(pi(active(z0))), ACTIVE(pi(z0)))
TOP(ok(plus(z0, z1))) → c73(TOP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
TOP(ok(plus(z0, z1))) → c73(TOP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
TOP(ok(times(z0, z1))) → c73(TOP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
TOP(ok(times(z0, z1))) → c73(TOP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
TOP(ok(square(z0))) → c73(TOP(square(active(z0))), ACTIVE(square(z0)))

K tuples:none
Defined Rule Symbols:

active, rcons, posrecip, 2ndsneg, negrecip, 2ndspos, s, cons, from, pi, plus, times, square, proper

Defined Pair Symbols:

ACTIVE, S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE, PROPER, TOP

Compound Symbols:

c10, c15, c16, c18, c19, c20, c21, c23, c24, c25, c26, 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, c, c5, c7, c9, c1, c11, c12, c13, c14, c17, c22, c27, c58, c58, c59, c59, c60, c60, c62, c62, c64, c64, c65, c65, c66, c66, c67, c67, c68, c68, c69, c69, c70, c70, c71, c71, c72, c73

(81) CdtUnreachableProof (EQUIVALENT transformation)

The following tuples could be removed as they are not reachable from basic start terms:

ACTIVE(square(z0)) → c10(TIMES(z0, z0))
ACTIVE(rcons(z0, z1)) → c15(RCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(rcons(z0, z1)) → c16(RCONS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndspos(z0, z1)) → c18(2NDSPOS(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndspos(z0, z1)) → c19(2NDSPOS(z0, active(z1)), ACTIVE(z1))
ACTIVE(2ndsneg(z0, z1)) → c20(2NDSNEG(active(z0), z1), ACTIVE(z0))
ACTIVE(2ndsneg(z0, z1)) → c21(2NDSNEG(z0, active(z1)), ACTIVE(z1))
ACTIVE(plus(z0, z1)) → c23(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c24(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(times(z0, z1)) → c25(TIMES(active(z0), z1), ACTIVE(z0))
ACTIVE(times(z0, z1)) → c26(TIMES(z0, active(z1)), ACTIVE(z1))
ACTIVE(from(z0)) → c(S(z0))
ACTIVE(pi(z0)) → c5(2NDSPOS(z0, from(0)))
ACTIVE(plus(s(z0), z1)) → c7(PLUS(z0, z1))
ACTIVE(times(s(z0), z1)) → c9(TIMES(z0, z1))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(posrecip(z2), 2ndsneg(z0, z3)))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(POSRECIP(z2))
ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSNEG(z0, z3))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(RCONS(negrecip(z2), 2ndspos(z0, z3)))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(NEGRECIP(z2))
ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))) → c1(2NDSPOS(z0, z3))
ACTIVE(s(from(z0))) → c11(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(s(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(2ndsneg(0, z0))) → c11(S(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(s(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c11(S(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(s(pi(z0))) → c11(S(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(s(plus(0, z0))) → c11(S(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(s(plus(s(z0), z1))) → c11(S(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(s(times(0, z0))) → c11(S(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(s(times(s(z0), z1))) → c11(S(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(s(square(z0))) → c11(S(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(posrecip(z0))) → c11(S(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(s(negrecip(z0))) → c11(S(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(s(rcons(z0, z1))) → c11(S(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(s(from(z0))) → c11(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndspos(z0, z1))) → c11(S(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(2ndsneg(z0, z1))) → c11(S(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(s(pi(z0))) → c11(S(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c11(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(s(times(z0, z1))) → c11(S(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(s(square(z0))) → c11(S(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(posrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(2ndsneg(0, z0))) → c12(POSRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(posrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c12(POSRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(0, z0))) → c12(POSRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(posrecip(plus(s(z0), z1))) → c12(POSRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(posrecip(times(0, z0))) → c12(POSRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(posrecip(times(s(z0), z1))) → c12(POSRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(posrecip(s(z0))) → c12(POSRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(posrecip(posrecip(z0))) → c12(POSRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(posrecip(negrecip(z0))) → c12(POSRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(posrecip(cons(z0, z1))) → c12(POSRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(rcons(z0, z1))) → c12(POSRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(posrecip(from(z0))) → c12(POSRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndspos(z0, z1))) → c12(POSRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(2ndsneg(z0, z1))) → c12(POSRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(posrecip(pi(z0))) → c12(POSRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(plus(z0, z1))) → c12(POSRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(times(z0, z1))) → c12(POSRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(posrecip(square(z0))) → c12(POSRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(negrecip(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(2ndsneg(0, z0))) → c13(NEGRECIP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(negrecip(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c13(NEGRECIP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(0, z0))) → c13(NEGRECIP(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(negrecip(plus(s(z0), z1))) → c13(NEGRECIP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(negrecip(times(0, z0))) → c13(NEGRECIP(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(negrecip(times(s(z0), z1))) → c13(NEGRECIP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(negrecip(s(z0))) → c13(NEGRECIP(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(negrecip(posrecip(z0))) → c13(NEGRECIP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(negrecip(negrecip(z0))) → c13(NEGRECIP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(negrecip(cons(z0, z1))) → c13(NEGRECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(rcons(z0, z1))) → c13(NEGRECIP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(negrecip(from(z0))) → c13(NEGRECIP(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndspos(z0, z1))) → c13(NEGRECIP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(2ndsneg(z0, z1))) → c13(NEGRECIP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(negrecip(pi(z0))) → c13(NEGRECIP(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(plus(z0, z1))) → c13(NEGRECIP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(times(z0, z1))) → c13(NEGRECIP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(negrecip(square(z0))) → c13(NEGRECIP(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndspos(0, z0)))
ACTIVE(cons(2ndspos(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(posrecip(z2), 2ndsneg(z0, z3))), x1), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(2ndsneg(0, z0), x1)) → c14(CONS(mark(rnil), x1), ACTIVE(2ndsneg(0, z0)))
ACTIVE(cons(2ndsneg(s(z0), cons(z1, cons(z2, z3))), x1)) → c14(CONS(mark(rcons(negrecip(z2), 2ndspos(z0, z3))), x1), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(mark(2ndspos(z0, from(0))), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(0, z0), x1)) → c14(CONS(mark(z0), x1), ACTIVE(plus(0, z0)))
ACTIVE(cons(plus(s(z0), z1), x1)) → c14(CONS(mark(s(plus(z0, z1))), x1), ACTIVE(plus(s(z0), z1)))
ACTIVE(cons(times(0, z0), x1)) → c14(CONS(mark(0), x1), ACTIVE(times(0, z0)))
ACTIVE(cons(times(s(z0), z1), x1)) → c14(CONS(mark(plus(z1, times(z0, z1))), x1), ACTIVE(times(s(z0), z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(mark(times(z0, z0)), x1), ACTIVE(square(z0)))
ACTIVE(cons(s(z0), x1)) → c14(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(posrecip(z0), x1)) → c14(CONS(posrecip(active(z0)), x1), ACTIVE(posrecip(z0)))
ACTIVE(cons(negrecip(z0), x1)) → c14(CONS(negrecip(active(z0)), x1), ACTIVE(negrecip(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c14(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(active(z0), z1), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(rcons(z0, z1), x1)) → c14(CONS(rcons(z0, active(z1)), x1), ACTIVE(rcons(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c14(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(active(z0), z1), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndspos(z0, z1), x1)) → c14(CONS(2ndspos(z0, active(z1)), x1), ACTIVE(2ndspos(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(active(z0), z1), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(2ndsneg(z0, z1), x1)) → c14(CONS(2ndsneg(z0, active(z1)), x1), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(cons(pi(z0), x1)) → c14(CONS(pi(active(z0)), x1), ACTIVE(pi(z0)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(plus(z0, z1), x1)) → c14(CONS(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(active(z0), z1), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(times(z0, z1), x1)) → c14(CONS(times(z0, active(z1)), x1), ACTIVE(times(z0, z1)))
ACTIVE(cons(square(z0), x1)) → c14(CONS(square(active(z0)), x1), ACTIVE(square(z0)))
ACTIVE(from(from(z0))) → c17(FROM(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(from(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(2ndsneg(0, z0))) → c17(FROM(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(from(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c17(FROM(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(from(pi(z0))) → c17(FROM(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(from(plus(0, z0))) → c17(FROM(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(from(plus(s(z0), z1))) → c17(FROM(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(from(times(0, z0))) → c17(FROM(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(from(times(s(z0), z1))) → c17(FROM(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(from(square(z0))) → c17(FROM(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(from(s(z0))) → c17(FROM(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(from(posrecip(z0))) → c17(FROM(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(from(negrecip(z0))) → c17(FROM(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(from(cons(z0, z1))) → c17(FROM(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(from(rcons(z0, z1))) → c17(FROM(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(from(from(z0))) → c17(FROM(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndspos(z0, z1))) → c17(FROM(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(2ndsneg(z0, z1))) → c17(FROM(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(from(pi(z0))) → c17(FROM(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(from(plus(z0, z1))) → c17(FROM(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(from(times(z0, z1))) → c17(FROM(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(from(square(z0))) → c17(FROM(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(pi(from(z0))) → c22(PI(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(pi(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(2ndsneg(0, z0))) → c22(PI(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(pi(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c22(PI(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(pi(pi(z0))) → c22(PI(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(0, z0))) → c22(PI(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(pi(plus(s(z0), z1))) → c22(PI(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(pi(times(0, z0))) → c22(PI(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(pi(times(s(z0), z1))) → c22(PI(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(pi(square(z0))) → c22(PI(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(pi(s(z0))) → c22(PI(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(pi(posrecip(z0))) → c22(PI(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(pi(negrecip(z0))) → c22(PI(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(pi(cons(z0, z1))) → c22(PI(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(rcons(z0, z1))) → c22(PI(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(pi(from(z0))) → c22(PI(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndspos(z0, z1))) → c22(PI(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(2ndsneg(z0, z1))) → c22(PI(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(pi(pi(z0))) → c22(PI(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(pi(plus(z0, z1))) → c22(PI(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(pi(times(z0, z1))) → c22(PI(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(pi(square(z0))) → c22(PI(square(active(z0))), ACTIVE(square(z0)))
ACTIVE(square(from(z0))) → c27(SQUARE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndspos(0, z0)))
ACTIVE(square(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(2ndsneg(0, z0))) → c27(SQUARE(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
ACTIVE(square(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c27(SQUARE(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
ACTIVE(square(pi(z0))) → c27(SQUARE(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
ACTIVE(square(plus(0, z0))) → c27(SQUARE(mark(z0)), ACTIVE(plus(0, z0)))
ACTIVE(square(plus(s(z0), z1))) → c27(SQUARE(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
ACTIVE(square(times(0, z0))) → c27(SQUARE(mark(0)), ACTIVE(times(0, z0)))
ACTIVE(square(times(s(z0), z1))) → c27(SQUARE(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(mark(times(z0, z0))), ACTIVE(square(z0)))
ACTIVE(square(s(z0))) → c27(SQUARE(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(square(posrecip(z0))) → c27(SQUARE(posrecip(active(z0))), ACTIVE(posrecip(z0)))
ACTIVE(square(negrecip(z0))) → c27(SQUARE(negrecip(active(z0))), ACTIVE(negrecip(z0)))
ACTIVE(square(cons(z0, z1))) → c27(SQUARE(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
ACTIVE(square(rcons(z0, z1))) → c27(SQUARE(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
ACTIVE(square(from(z0))) → c27(SQUARE(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndspos(z0, z1))) → c27(SQUARE(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(2ndsneg(z0, z1))) → c27(SQUARE(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
ACTIVE(square(pi(z0))) → c27(SQUARE(pi(active(z0))), ACTIVE(pi(z0)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(square(plus(z0, z1))) → c27(SQUARE(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(active(z0), z1)), ACTIVE(times(z0, z1)))
ACTIVE(square(times(z0, z1))) → c27(SQUARE(times(z0, active(z1))), ACTIVE(times(z0, z1)))
ACTIVE(square(square(z0))) → c27(SQUARE(square(active(z0))), ACTIVE(square(z0)))
PROPER(s(s(z0))) → c58(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(posrecip(z0))) → c58(S(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(s(negrecip(z0))) → c58(S(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(s(cons(z0, z1))) → c58(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(rcons(z0, z1))) → c58(S(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(s(from(z0))) → c58(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(2ndspos(z0, z1))) → c58(S(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(s(2ndsneg(z0, z1))) → c58(S(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(s(pi(z0))) → c58(S(pi(proper(z0))), PROPER(pi(z0)))
PROPER(s(plus(z0, z1))) → c58(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(times(z0, z1))) → c58(S(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(s(square(z0))) → c58(S(square(proper(z0))), PROPER(square(z0)))
PROPER(s(0)) → c58(S(ok(0)))
PROPER(s(nil)) → c58(S(ok(nil)))
PROPER(s(rnil)) → c58(S(ok(rnil)))
PROPER(posrecip(s(z0))) → c59(POSRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(posrecip(posrecip(z0))) → c59(POSRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(posrecip(negrecip(z0))) → c59(POSRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(posrecip(cons(z0, z1))) → c59(POSRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(posrecip(rcons(z0, z1))) → c59(POSRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(posrecip(from(z0))) → c59(POSRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(posrecip(2ndspos(z0, z1))) → c59(POSRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(posrecip(2ndsneg(z0, z1))) → c59(POSRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(posrecip(pi(z0))) → c59(POSRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(posrecip(plus(z0, z1))) → c59(POSRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(posrecip(times(z0, z1))) → c59(POSRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(posrecip(square(z0))) → c59(POSRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(posrecip(0)) → c59(POSRECIP(ok(0)))
PROPER(posrecip(nil)) → c59(POSRECIP(ok(nil)))
PROPER(posrecip(rnil)) → c59(POSRECIP(ok(rnil)))
PROPER(negrecip(s(z0))) → c60(NEGRECIP(s(proper(z0))), PROPER(s(z0)))
PROPER(negrecip(posrecip(z0))) → c60(NEGRECIP(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(negrecip(negrecip(z0))) → c60(NEGRECIP(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(negrecip(cons(z0, z1))) → c60(NEGRECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(negrecip(rcons(z0, z1))) → c60(NEGRECIP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(negrecip(from(z0))) → c60(NEGRECIP(from(proper(z0))), PROPER(from(z0)))
PROPER(negrecip(2ndspos(z0, z1))) → c60(NEGRECIP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(negrecip(2ndsneg(z0, z1))) → c60(NEGRECIP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(negrecip(pi(z0))) → c60(NEGRECIP(pi(proper(z0))), PROPER(pi(z0)))
PROPER(negrecip(plus(z0, z1))) → c60(NEGRECIP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(negrecip(times(z0, z1))) → c60(NEGRECIP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(negrecip(square(z0))) → c60(NEGRECIP(square(proper(z0))), PROPER(square(z0)))
PROPER(negrecip(0)) → c60(NEGRECIP(ok(0)))
PROPER(negrecip(nil)) → c60(NEGRECIP(ok(nil)))
PROPER(negrecip(rnil)) → c60(NEGRECIP(ok(rnil)))
PROPER(cons(x0, s(z0))) → c62(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, posrecip(z0))) → c62(CONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(cons(x0, negrecip(z0))) → c62(CONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(cons(x0, cons(z0, z1))) → c62(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, rcons(z0, z1))) → c62(CONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(cons(x0, from(z0))) → c62(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, 2ndspos(z0, z1))) → c62(CONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(cons(x0, 2ndsneg(z0, z1))) → c62(CONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(cons(x0, pi(z0))) → c62(CONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(cons(x0, plus(z0, z1))) → c62(CONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(cons(x0, times(z0, z1))) → c62(CONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(cons(x0, square(z0))) → c62(CONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(cons(s(z0), x1)) → c62(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(posrecip(z0), x1)) → c62(CONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(cons(negrecip(z0), x1)) → c62(CONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c62(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(rcons(z0, z1), x1)) → c62(CONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c62(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(2ndspos(z0, z1), x1)) → c62(CONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(cons(2ndsneg(z0, z1), x1)) → c62(CONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(cons(pi(z0), x1)) → c62(CONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(cons(plus(z0, z1), x1)) → c62(CONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(cons(times(z0, z1), x1)) → c62(CONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(cons(square(z0), x1)) → c62(CONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c62(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c62(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, rnil)) → c62(CONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(cons(0, x1)) → c62(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c62(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(rnil, x1)) → c62(CONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(rcons(x0, s(z0))) → c64(RCONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(rcons(x0, posrecip(z0))) → c64(RCONS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(rcons(x0, negrecip(z0))) → c64(RCONS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(rcons(x0, cons(z0, z1))) → c64(RCONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(rcons(x0, rcons(z0, z1))) → c64(RCONS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(rcons(x0, from(z0))) → c64(RCONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(rcons(x0, 2ndspos(z0, z1))) → c64(RCONS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(rcons(x0, 2ndsneg(z0, z1))) → c64(RCONS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(rcons(x0, pi(z0))) → c64(RCONS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(rcons(x0, plus(z0, z1))) → c64(RCONS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(rcons(x0, times(z0, z1))) → c64(RCONS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(rcons(x0, square(z0))) → c64(RCONS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(rcons(s(z0), x1)) → c64(RCONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(rcons(posrecip(z0), x1)) → c64(RCONS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(rcons(negrecip(z0), x1)) → c64(RCONS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(rcons(cons(z0, z1), x1)) → c64(RCONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(rcons(rcons(z0, z1), x1)) → c64(RCONS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(rcons(from(z0), x1)) → c64(RCONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(rcons(2ndspos(z0, z1), x1)) → c64(RCONS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(rcons(2ndsneg(z0, z1), x1)) → c64(RCONS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(rcons(pi(z0), x1)) → c64(RCONS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(rcons(plus(z0, z1), x1)) → c64(RCONS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(rcons(times(z0, z1), x1)) → c64(RCONS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(rcons(square(z0), x1)) → c64(RCONS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(rcons(x0, 0)) → c64(RCONS(proper(x0), ok(0)), PROPER(x0))
PROPER(rcons(x0, nil)) → c64(RCONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(rcons(x0, rnil)) → c64(RCONS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(rcons(0, x1)) → c64(RCONS(ok(0), proper(x1)), PROPER(x1))
PROPER(rcons(nil, x1)) → c64(RCONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(rcons(rnil, x1)) → c64(RCONS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(from(s(z0))) → c65(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(posrecip(z0))) → c65(FROM(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(from(negrecip(z0))) → c65(FROM(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(from(cons(z0, z1))) → c65(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(rcons(z0, z1))) → c65(FROM(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(from(from(z0))) → c65(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(2ndspos(z0, z1))) → c65(FROM(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(from(2ndsneg(z0, z1))) → c65(FROM(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(from(pi(z0))) → c65(FROM(pi(proper(z0))), PROPER(pi(z0)))
PROPER(from(plus(z0, z1))) → c65(FROM(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(from(times(z0, z1))) → c65(FROM(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(from(square(z0))) → c65(FROM(square(proper(z0))), PROPER(square(z0)))
PROPER(from(0)) → c65(FROM(ok(0)))
PROPER(from(nil)) → c65(FROM(ok(nil)))
PROPER(from(rnil)) → c65(FROM(ok(rnil)))
PROPER(2ndspos(x0, s(z0))) → c66(2NDSPOS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndspos(x0, posrecip(z0))) → c66(2NDSPOS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndspos(x0, negrecip(z0))) → c66(2NDSPOS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndspos(x0, cons(z0, z1))) → c66(2NDSPOS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndspos(x0, rcons(z0, z1))) → c66(2NDSPOS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndspos(x0, from(z0))) → c66(2NDSPOS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndspos(x0, 2ndspos(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndspos(x0, 2ndsneg(z0, z1))) → c66(2NDSPOS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndspos(x0, pi(z0))) → c66(2NDSPOS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndspos(x0, plus(z0, z1))) → c66(2NDSPOS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndspos(x0, times(z0, z1))) → c66(2NDSPOS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndspos(x0, square(z0))) → c66(2NDSPOS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndspos(s(z0), x1)) → c66(2NDSPOS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndspos(posrecip(z0), x1)) → c66(2NDSPOS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndspos(negrecip(z0), x1)) → c66(2NDSPOS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndspos(cons(z0, z1), x1)) → c66(2NDSPOS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndspos(rcons(z0, z1), x1)) → c66(2NDSPOS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndspos(from(z0), x1)) → c66(2NDSPOS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndspos(2ndspos(z0, z1), x1)) → c66(2NDSPOS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndspos(2ndsneg(z0, z1), x1)) → c66(2NDSPOS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndspos(pi(z0), x1)) → c66(2NDSPOS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndspos(plus(z0, z1), x1)) → c66(2NDSPOS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndspos(times(z0, z1), x1)) → c66(2NDSPOS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndspos(square(z0), x1)) → c66(2NDSPOS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndspos(x0, 0)) → c66(2NDSPOS(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndspos(x0, nil)) → c66(2NDSPOS(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndspos(x0, rnil)) → c66(2NDSPOS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndspos(0, x1)) → c66(2NDSPOS(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndspos(nil, x1)) → c66(2NDSPOS(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndspos(rnil, x1)) → c66(2NDSPOS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(x0, s(z0))) → c67(2NDSNEG(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(2ndsneg(x0, posrecip(z0))) → c67(2NDSNEG(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(2ndsneg(x0, negrecip(z0))) → c67(2NDSNEG(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(2ndsneg(x0, cons(z0, z1))) → c67(2NDSNEG(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(2ndsneg(x0, rcons(z0, z1))) → c67(2NDSNEG(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(2ndsneg(x0, from(z0))) → c67(2NDSNEG(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(2ndsneg(x0, 2ndspos(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(2ndsneg(x0, 2ndsneg(z0, z1))) → c67(2NDSNEG(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(2ndsneg(x0, pi(z0))) → c67(2NDSNEG(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(2ndsneg(x0, plus(z0, z1))) → c67(2NDSNEG(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(2ndsneg(x0, times(z0, z1))) → c67(2NDSNEG(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(2ndsneg(x0, square(z0))) → c67(2NDSNEG(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(2ndsneg(s(z0), x1)) → c67(2NDSNEG(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(2ndsneg(posrecip(z0), x1)) → c67(2NDSNEG(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(2ndsneg(negrecip(z0), x1)) → c67(2NDSNEG(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(2ndsneg(cons(z0, z1), x1)) → c67(2NDSNEG(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(rcons(z0, z1), x1)) → c67(2NDSNEG(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(2ndsneg(from(z0), x1)) → c67(2NDSNEG(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(2ndsneg(2ndspos(z0, z1), x1)) → c67(2NDSNEG(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(2ndsneg(2ndsneg(z0, z1), x1)) → c67(2NDSNEG(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(2ndsneg(pi(z0), x1)) → c67(2NDSNEG(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(2ndsneg(plus(z0, z1), x1)) → c67(2NDSNEG(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(2ndsneg(times(z0, z1), x1)) → c67(2NDSNEG(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(2ndsneg(square(z0), x1)) → c67(2NDSNEG(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(2ndsneg(x0, 0)) → c67(2NDSNEG(proper(x0), ok(0)), PROPER(x0))
PROPER(2ndsneg(x0, nil)) → c67(2NDSNEG(proper(x0), ok(nil)), PROPER(x0))
PROPER(2ndsneg(x0, rnil)) → c67(2NDSNEG(proper(x0), ok(rnil)), PROPER(x0))
PROPER(2ndsneg(0, x1)) → c67(2NDSNEG(ok(0), proper(x1)), PROPER(x1))
PROPER(2ndsneg(nil, x1)) → c67(2NDSNEG(ok(nil), proper(x1)), PROPER(x1))
PROPER(2ndsneg(rnil, x1)) → c67(2NDSNEG(ok(rnil), proper(x1)), PROPER(x1))
PROPER(pi(s(z0))) → c68(PI(s(proper(z0))), PROPER(s(z0)))
PROPER(pi(posrecip(z0))) → c68(PI(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(pi(negrecip(z0))) → c68(PI(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(pi(cons(z0, z1))) → c68(PI(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(pi(rcons(z0, z1))) → c68(PI(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(pi(from(z0))) → c68(PI(from(proper(z0))), PROPER(from(z0)))
PROPER(pi(2ndspos(z0, z1))) → c68(PI(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(pi(2ndsneg(z0, z1))) → c68(PI(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(pi(pi(z0))) → c68(PI(pi(proper(z0))), PROPER(pi(z0)))
PROPER(pi(plus(z0, z1))) → c68(PI(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(pi(times(z0, z1))) → c68(PI(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(pi(square(z0))) → c68(PI(square(proper(z0))), PROPER(square(z0)))
PROPER(pi(0)) → c68(PI(ok(0)))
PROPER(pi(nil)) → c68(PI(ok(nil)))
PROPER(pi(rnil)) → c68(PI(ok(rnil)))
PROPER(plus(x0, s(z0))) → c69(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(plus(x0, posrecip(z0))) → c69(PLUS(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(plus(x0, negrecip(z0))) → c69(PLUS(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(plus(x0, cons(z0, z1))) → c69(PLUS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(plus(x0, rcons(z0, z1))) → c69(PLUS(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(plus(x0, from(z0))) → c69(PLUS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(plus(x0, 2ndspos(z0, z1))) → c69(PLUS(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(plus(x0, 2ndsneg(z0, z1))) → c69(PLUS(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(plus(x0, pi(z0))) → c69(PLUS(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(plus(x0, plus(z0, z1))) → c69(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(plus(x0, times(z0, z1))) → c69(PLUS(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(plus(x0, square(z0))) → c69(PLUS(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(plus(s(z0), x1)) → c69(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(plus(posrecip(z0), x1)) → c69(PLUS(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(plus(negrecip(z0), x1)) → c69(PLUS(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(plus(cons(z0, z1), x1)) → c69(PLUS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(plus(rcons(z0, z1), x1)) → c69(PLUS(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(plus(from(z0), x1)) → c69(PLUS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(plus(2ndspos(z0, z1), x1)) → c69(PLUS(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(plus(2ndsneg(z0, z1), x1)) → c69(PLUS(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(plus(pi(z0), x1)) → c69(PLUS(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(plus(plus(z0, z1), x1)) → c69(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(plus(times(z0, z1), x1)) → c69(PLUS(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(plus(square(z0), x1)) → c69(PLUS(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(plus(x0, 0)) → c69(PLUS(proper(x0), ok(0)), PROPER(x0))
PROPER(plus(x0, nil)) → c69(PLUS(proper(x0), ok(nil)), PROPER(x0))
PROPER(plus(x0, rnil)) → c69(PLUS(proper(x0), ok(rnil)), PROPER(x0))
PROPER(plus(0, x1)) → c69(PLUS(ok(0), proper(x1)), PROPER(x1))
PROPER(plus(nil, x1)) → c69(PLUS(ok(nil), proper(x1)), PROPER(x1))
PROPER(plus(rnil, x1)) → c69(PLUS(ok(rnil), proper(x1)), PROPER(x1))
PROPER(times(x0, s(z0))) → c70(TIMES(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(times(x0, posrecip(z0))) → c70(TIMES(proper(x0), posrecip(proper(z0))), PROPER(x0), PROPER(posrecip(z0)))
PROPER(times(x0, negrecip(z0))) → c70(TIMES(proper(x0), negrecip(proper(z0))), PROPER(x0), PROPER(negrecip(z0)))
PROPER(times(x0, cons(z0, z1))) → c70(TIMES(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(times(x0, rcons(z0, z1))) → c70(TIMES(proper(x0), rcons(proper(z0), proper(z1))), PROPER(x0), PROPER(rcons(z0, z1)))
PROPER(times(x0, from(z0))) → c70(TIMES(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(times(x0, 2ndspos(z0, z1))) → c70(TIMES(proper(x0), 2ndspos(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndspos(z0, z1)))
PROPER(times(x0, 2ndsneg(z0, z1))) → c70(TIMES(proper(x0), 2ndsneg(proper(z0), proper(z1))), PROPER(x0), PROPER(2ndsneg(z0, z1)))
PROPER(times(x0, pi(z0))) → c70(TIMES(proper(x0), pi(proper(z0))), PROPER(x0), PROPER(pi(z0)))
PROPER(times(x0, plus(z0, z1))) → c70(TIMES(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(times(x0, times(z0, z1))) → c70(TIMES(proper(x0), times(proper(z0), proper(z1))), PROPER(x0), PROPER(times(z0, z1)))
PROPER(times(x0, square(z0))) → c70(TIMES(proper(x0), square(proper(z0))), PROPER(x0), PROPER(square(z0)))
PROPER(times(s(z0), x1)) → c70(TIMES(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(times(posrecip(z0), x1)) → c70(TIMES(posrecip(proper(z0)), proper(x1)), PROPER(posrecip(z0)), PROPER(x1))
PROPER(times(negrecip(z0), x1)) → c70(TIMES(negrecip(proper(z0)), proper(x1)), PROPER(negrecip(z0)), PROPER(x1))
PROPER(times(cons(z0, z1), x1)) → c70(TIMES(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(times(rcons(z0, z1), x1)) → c70(TIMES(rcons(proper(z0), proper(z1)), proper(x1)), PROPER(rcons(z0, z1)), PROPER(x1))
PROPER(times(from(z0), x1)) → c70(TIMES(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(times(2ndspos(z0, z1), x1)) → c70(TIMES(2ndspos(proper(z0), proper(z1)), proper(x1)), PROPER(2ndspos(z0, z1)), PROPER(x1))
PROPER(times(2ndsneg(z0, z1), x1)) → c70(TIMES(2ndsneg(proper(z0), proper(z1)), proper(x1)), PROPER(2ndsneg(z0, z1)), PROPER(x1))
PROPER(times(pi(z0), x1)) → c70(TIMES(pi(proper(z0)), proper(x1)), PROPER(pi(z0)), PROPER(x1))
PROPER(times(plus(z0, z1), x1)) → c70(TIMES(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(times(times(z0, z1), x1)) → c70(TIMES(times(proper(z0), proper(z1)), proper(x1)), PROPER(times(z0, z1)), PROPER(x1))
PROPER(times(square(z0), x1)) → c70(TIMES(square(proper(z0)), proper(x1)), PROPER(square(z0)), PROPER(x1))
PROPER(times(x0, 0)) → c70(TIMES(proper(x0), ok(0)), PROPER(x0))
PROPER(times(x0, nil)) → c70(TIMES(proper(x0), ok(nil)), PROPER(x0))
PROPER(times(x0, rnil)) → c70(TIMES(proper(x0), ok(rnil)), PROPER(x0))
PROPER(times(0, x1)) → c70(TIMES(ok(0), proper(x1)), PROPER(x1))
PROPER(times(nil, x1)) → c70(TIMES(ok(nil), proper(x1)), PROPER(x1))
PROPER(times(rnil, x1)) → c70(TIMES(ok(rnil), proper(x1)), PROPER(x1))
PROPER(square(s(z0))) → c71(SQUARE(s(proper(z0))), PROPER(s(z0)))
PROPER(square(posrecip(z0))) → c71(SQUARE(posrecip(proper(z0))), PROPER(posrecip(z0)))
PROPER(square(negrecip(z0))) → c71(SQUARE(negrecip(proper(z0))), PROPER(negrecip(z0)))
PROPER(square(cons(z0, z1))) → c71(SQUARE(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(square(rcons(z0, z1))) → c71(SQUARE(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
PROPER(square(from(z0))) → c71(SQUARE(from(proper(z0))), PROPER(from(z0)))
PROPER(square(2ndspos(z0, z1))) → c71(SQUARE(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
PROPER(square(2ndsneg(z0, z1))) → c71(SQUARE(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
PROPER(square(pi(z0))) → c71(SQUARE(pi(proper(z0))), PROPER(pi(z0)))
PROPER(square(plus(z0, z1))) → c71(SQUARE(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(square(times(z0, z1))) → c71(SQUARE(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
PROPER(square(square(z0))) → c71(SQUARE(square(proper(z0))), PROPER(square(z0)))
PROPER(square(0)) → c71(SQUARE(ok(0)))
PROPER(square(nil)) → c71(SQUARE(ok(nil)))
PROPER(square(rnil)) → c71(SQUARE(ok(rnil)))
TOP(mark(s(z0))) → c72(TOP(s(proper(z0))), PROPER(s(z0)))
TOP(mark(posrecip(z0))) → c72(TOP(posrecip(proper(z0))), PROPER(posrecip(z0)))
TOP(mark(negrecip(z0))) → c72(TOP(negrecip(proper(z0))), PROPER(negrecip(z0)))
TOP(mark(cons(z0, z1))) → c72(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
TOP(mark(rcons(z0, z1))) → c72(TOP(rcons(proper(z0), proper(z1))), PROPER(rcons(z0, z1)))
TOP(mark(from(z0))) → c72(TOP(from(proper(z0))), PROPER(from(z0)))
TOP(mark(2ndspos(z0, z1))) → c72(TOP(2ndspos(proper(z0), proper(z1))), PROPER(2ndspos(z0, z1)))
TOP(mark(2ndsneg(z0, z1))) → c72(TOP(2ndsneg(proper(z0), proper(z1))), PROPER(2ndsneg(z0, z1)))
TOP(mark(pi(z0))) → c72(TOP(pi(proper(z0))), PROPER(pi(z0)))
TOP(mark(plus(z0, z1))) → c72(TOP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
TOP(mark(times(z0, z1))) → c72(TOP(times(proper(z0), proper(z1))), PROPER(times(z0, z1)))
TOP(mark(square(z0))) → c72(TOP(square(proper(z0))), PROPER(square(z0)))
TOP(ok(from(z0))) → c73(TOP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
TOP(ok(2ndspos(0, z0))) → c73(TOP(mark(rnil)), ACTIVE(2ndspos(0, z0)))
TOP(ok(2ndspos(s(z0), cons(z1, cons(z2, z3))))) → c73(TOP(mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))), ACTIVE(2ndspos(s(z0), cons(z1, cons(z2, z3)))))
TOP(ok(2ndsneg(0, z0))) → c73(TOP(mark(rnil)), ACTIVE(2ndsneg(0, z0)))
TOP(ok(2ndsneg(s(z0), cons(z1, cons(z2, z3))))) → c73(TOP(mark(rcons(negrecip(z2), 2ndspos(z0, z3)))), ACTIVE(2ndsneg(s(z0), cons(z1, cons(z2, z3)))))
TOP(ok(pi(z0))) → c73(TOP(mark(2ndspos(z0, from(0)))), ACTIVE(pi(z0)))
TOP(ok(plus(0, z0))) → c73(TOP(mark(z0)), ACTIVE(plus(0, z0)))
TOP(ok(plus(s(z0), z1))) → c73(TOP(mark(s(plus(z0, z1)))), ACTIVE(plus(s(z0), z1)))
TOP(ok(times(0, z0))) → c73(TOP(mark(0)), ACTIVE(times(0, z0)))
TOP(ok(times(s(z0), z1))) → c73(TOP(mark(plus(z1, times(z0, z1)))), ACTIVE(times(s(z0), z1)))
TOP(ok(square(z0))) → c73(TOP(mark(times(z0, z0))), ACTIVE(square(z0)))
TOP(ok(s(z0))) → c73(TOP(s(active(z0))), ACTIVE(s(z0)))
TOP(ok(posrecip(z0))) → c73(TOP(posrecip(active(z0))), ACTIVE(posrecip(z0)))
TOP(ok(negrecip(z0))) → c73(TOP(negrecip(active(z0))), ACTIVE(negrecip(z0)))
TOP(ok(cons(z0, z1))) → c73(TOP(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
TOP(ok(rcons(z0, z1))) → c73(TOP(rcons(active(z0), z1)), ACTIVE(rcons(z0, z1)))
TOP(ok(rcons(z0, z1))) → c73(TOP(rcons(z0, active(z1))), ACTIVE(rcons(z0, z1)))
TOP(ok(from(z0))) → c73(TOP(from(active(z0))), ACTIVE(from(z0)))
TOP(ok(2ndspos(z0, z1))) → c73(TOP(2ndspos(active(z0), z1)), ACTIVE(2ndspos(z0, z1)))
TOP(ok(2ndspos(z0, z1))) → c73(TOP(2ndspos(z0, active(z1))), ACTIVE(2ndspos(z0, z1)))
TOP(ok(2ndsneg(z0, z1))) → c73(TOP(2ndsneg(active(z0), z1)), ACTIVE(2ndsneg(z0, z1)))
TOP(ok(2ndsneg(z0, z1))) → c73(TOP(2ndsneg(z0, active(z1))), ACTIVE(2ndsneg(z0, z1)))
TOP(ok(pi(z0))) → c73(TOP(pi(active(z0))), ACTIVE(pi(z0)))
TOP(ok(plus(z0, z1))) → c73(TOP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
TOP(ok(plus(z0, z1))) → c73(TOP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
TOP(ok(times(z0, z1))) → c73(TOP(times(active(z0), z1)), ACTIVE(times(z0, z1)))
TOP(ok(times(z0, z1))) → c73(TOP(times(z0, active(z1))), ACTIVE(times(z0, z1)))
TOP(ok(square(z0))) → c73(TOP(square(active(z0))), ACTIVE(square(z0)))

(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, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(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(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))
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))
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))
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(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)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))

S tuples:

S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))

K tuples:none
Defined Rule Symbols:

active, rcons, posrecip, 2ndsneg, negrecip, 2ndspos, s, cons, from, pi, plus, times, square, proper

Defined Pair Symbols:

S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE

Compound Symbols:

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

(83) 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, cons(z2, z3)))) → mark(rcons(posrecip(z2), 2ndsneg(z0, z3)))
active(2ndsneg(0, z0)) → mark(rnil)
active(2ndsneg(s(z0), cons(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(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))
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))
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))
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(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))

(84) Obligation:

Complexity Dependency Tuples Problem
Rules:none
Tuples:

S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))

S tuples:

S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))

K tuples:none
Defined Rule Symbols:none

Defined Pair Symbols:

S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE

Compound Symbols:

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

(85) 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) → c36(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))

We considered the (Usable) Rules:none
And the Tuples:

S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))

The order we found is given by the following interpretation:
Polynomial interpretation :

POL(2NDSNEG(x₁, x₂)) = [4]x₁ + x₂
POL(2NDSPOS(x₁, x₂)) = x₂
POL(CONS(x₁, x₂)) = 0
POL(FROM(x₁)) = 0
POL(NEGRECIP(x₁)) = 0
POL(PI(x₁)) = [4]x₁
POL(PLUS(x₁, x₂)) = 0
POL(POSRECIP(x₁)) = 0
POL(RCONS(x₁, x₂)) = x₁
POL(S(x₁)) = 0
POL(SQUARE(x₁)) = 0
POL(TIMES(x₁, x₂)) = 0
POL(c28(x₁)) = x₁
POL(c29(x₁)) = x₁
POL(c30(x₁)) = 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(mark(x₁)) = [1] + x₁
POL(ok(x₁)) = [2] + x₁

(86) Obligation:

Complexity Dependency Tuples Problem
Rules:none
Tuples:

S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))

S tuples:

S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))

K tuples:

RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))

Defined Rule Symbols:none

Defined Pair Symbols:

S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE

Compound Symbols:

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

(87) 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)) → c35(CONS(z0, z1))

We considered the (Usable) Rules:none
And the Tuples:

S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(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(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(c28(x₁)) = x₁
POL(c29(x₁)) = x₁
POL(c30(x₁)) = 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(mark(x₁)) = [2]
POL(ok(x₁)) = [2] + x₁

(88) Obligation:

Complexity Dependency Tuples Problem
Rules:none
Tuples:

S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))

S tuples:

S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))

K tuples:

RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))

Defined Rule Symbols:none

Defined Pair Symbols:

S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE

Compound Symbols:

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

(89) 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)) → c28(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))

We considered the (Usable) Rules:none
And the Tuples:

S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))

The order we found is given by the following interpretation:
Polynomial interpretation :

POL(2NDSNEG(x₁, x₂)) = [3]x₁ + [3]x₂
POL(2NDSPOS(x₁, x₂)) = [4]x₁ + [2]x₂
POL(CONS(x₁, x₂)) = x₁ + [2]x₂
POL(FROM(x₁)) = 0
POL(NEGRECIP(x₁)) = x₁
POL(PI(x₁)) = 0
POL(PLUS(x₁, x₂)) = x₁
POL(POSRECIP(x₁)) = [2]x₁
POL(RCONS(x₁, x₂)) = x₂
POL(S(x₁)) = x₁
POL(SQUARE(x₁)) = 0
POL(TIMES(x₁, x₂)) = 0
POL(c28(x₁)) = x₁
POL(c29(x₁)) = x₁
POL(c30(x₁)) = 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(mark(x₁)) = [1] + x₁
POL(ok(x₁)) = x₁

(90) Obligation:

Complexity Dependency Tuples Problem
Rules:none
Tuples:

S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))

S tuples:

S(ok(z0)) → c29(S(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))

K tuples:

RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
S(mark(z0)) → c28(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))

Defined Rule Symbols:none

Defined Pair Symbols:

S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE

Compound Symbols:

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

(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.

PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))

We considered the (Usable) Rules:none
And the Tuples:

S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(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]x₂
POL(FROM(x₁)) = 0
POL(NEGRECIP(x₁)) = 0
POL(PI(x₁)) = [4]x₁
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(c28(x₁)) = x₁
POL(c29(x₁)) = x₁
POL(c30(x₁)) = 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(mark(x₁)) = [4] + x₁
POL(ok(x₁)) = x₁

(92) Obligation:

Complexity Dependency Tuples Problem
Rules:none
Tuples:

S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))

S tuples:

S(ok(z0)) → c29(S(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))

K tuples:

RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
S(mark(z0)) → c28(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))

Defined Rule Symbols:none

Defined Pair Symbols:

S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE

Compound Symbols:

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

(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.

SQUARE(mark(z0)) → c55(SQUARE(z0))

We considered the (Usable) Rules:none
And the Tuples:

S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))

The order we found is given by the following interpretation:
Polynomial interpretation :

POL(2NDSNEG(x₁, x₂)) = 0
POL(2NDSPOS(x₁, x₂)) = [2]x₂
POL(CONS(x₁, x₂)) = [4]x₁
POL(FROM(x₁)) = 0
POL(NEGRECIP(x₁)) = 0
POL(PI(x₁)) = [4]x₁
POL(PLUS(x₁, x₂)) = 0
POL(POSRECIP(x₁)) = 0
POL(RCONS(x₁, x₂)) = 0
POL(S(x₁)) = 0
POL(SQUARE(x₁)) = x₁
POL(TIMES(x₁, x₂)) = 0
POL(c28(x₁)) = x₁
POL(c29(x₁)) = x₁
POL(c30(x₁)) = 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(mark(x₁)) = [1] + x₁
POL(ok(x₁)) = x₁

(94) Obligation:

Complexity Dependency Tuples Problem
Rules:none
Tuples:

S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))

S tuples:

S(ok(z0)) → c29(S(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(ok(z0)) → c56(SQUARE(z0))

K tuples:

RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
S(mark(z0)) → c28(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))

Defined Rule Symbols:none

Defined Pair Symbols:

S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE

Compound Symbols:

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

(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.

TIMES(mark(z0), z1) → c52(TIMES(z0, z1))

We considered the (Usable) Rules:none
And the Tuples:

S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))

The order we found is given by the following interpretation:
Polynomial interpretation :

POL(2NDSNEG(x₁, x₂)) = [2]x₁
POL(2NDSPOS(x₁, x₂)) = x₁ + [3]x₂
POL(CONS(x₁, x₂)) = [3]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)) = [2]x₂
POL(S(x₁)) = 0
POL(SQUARE(x₁)) = 0
POL(TIMES(x₁, x₂)) = [2]x₁
POL(c28(x₁)) = x₁
POL(c29(x₁)) = x₁
POL(c30(x₁)) = 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(mark(x₁)) = [2] + x₁
POL(ok(x₁)) = x₁

(96) Obligation:

Complexity Dependency Tuples Problem
Rules:none
Tuples:

S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))

S tuples:

S(ok(z0)) → c29(S(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(ok(z0)) → c56(SQUARE(z0))

K tuples:

RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
S(mark(z0)) → c28(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))

Defined Rule Symbols:none

Defined Pair Symbols:

S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE

Compound Symbols:

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

(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.

TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))

We considered the (Usable) Rules:none
And the Tuples:

S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(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 + [3]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)) = [2]x₁
POL(c28(x₁)) = x₁
POL(c29(x₁)) = x₁
POL(c30(x₁)) = 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(mark(x₁)) = [3] + x₁
POL(ok(x₁)) = [1] + x₁

(98) Obligation:

Complexity Dependency Tuples Problem
Rules:none
Tuples:

S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))

S tuples:

S(ok(z0)) → c29(S(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
SQUARE(ok(z0)) → c56(SQUARE(z0))

K tuples:

RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
S(mark(z0)) → c28(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))

Defined Rule Symbols:none

Defined Pair Symbols:

S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE

Compound Symbols:

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

(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.

S(ok(z0)) → c29(S(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))

We considered the (Usable) Rules:none
And the Tuples:

S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(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
POL(FROM(x₁)) = 0
POL(NEGRECIP(x₁)) = [2]x₁
POL(PI(x₁)) = [4]x₁
POL(PLUS(x₁, x₂)) = 0
POL(POSRECIP(x₁)) = x₁
POL(RCONS(x₁, x₂)) = [4]x₁
POL(S(x₁)) = x₁
POL(SQUARE(x₁)) = 0
POL(TIMES(x₁, x₂)) = [2]x₁
POL(c28(x₁)) = x₁
POL(c29(x₁)) = x₁
POL(c30(x₁)) = 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(mark(x₁)) = [2] + x₁
POL(ok(x₁)) = [1] + x₁

(100) Obligation:

Complexity Dependency Tuples Problem
Rules:none
Tuples:

S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))

S tuples:

FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
SQUARE(ok(z0)) → c56(SQUARE(z0))

K tuples:

RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
S(mark(z0)) → c28(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
S(ok(z0)) → c29(S(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))

Defined Rule Symbols:none

Defined Pair Symbols:

S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE

Compound Symbols:

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

(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.

PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))

We considered the (Usable) Rules:none
And the Tuples:

S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))

The order we found is given by the following interpretation:
Polynomial interpretation :

POL(2NDSNEG(x₁, x₂)) = 0
POL(2NDSPOS(x₁, x₂)) = [3]x₂
POL(CONS(x₁, x₂)) = [5]x₂
POL(FROM(x₁)) = 0
POL(NEGRECIP(x₁)) = 0
POL(PI(x₁)) = [4]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)) = 0
POL(c28(x₁)) = x₁
POL(c29(x₁)) = x₁
POL(c30(x₁)) = 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(mark(x₁)) = [3] + x₁
POL(ok(x₁)) = [4] + x₁

(102) Obligation:

Complexity Dependency Tuples Problem
Rules:none
Tuples:

S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))

S tuples:

FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
SQUARE(ok(z0)) → c56(SQUARE(z0))

K tuples:

RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
S(mark(z0)) → c28(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
S(ok(z0)) → c29(S(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))

Defined Rule Symbols:none

Defined Pair Symbols:

S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE

Compound Symbols:

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

(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.

FROM(ok(z0)) → c40(FROM(z0))

We considered the (Usable) Rules:none
And the Tuples:

S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))

The order we found is given by the following interpretation:
Polynomial interpretation :

POL(2NDSNEG(x₁, x₂)) = [4]x₁
POL(2NDSPOS(x₁, x₂)) = [3]x₂
POL(CONS(x₁, x₂)) = [4]x₁ + [2]x₂
POL(FROM(x₁)) = x₁
POL(NEGRECIP(x₁)) = [2]x₁
POL(PI(x₁)) = [4]x₁
POL(PLUS(x₁, x₂)) = 0
POL(POSRECIP(x₁)) = [4]x₁
POL(RCONS(x₁, x₂)) = 0
POL(S(x₁)) = 0
POL(SQUARE(x₁)) = 0
POL(TIMES(x₁, x₂)) = 0
POL(c28(x₁)) = x₁
POL(c29(x₁)) = x₁
POL(c30(x₁)) = 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(mark(x₁)) = x₁
POL(ok(x₁)) = [4] + x₁

(104) Obligation:

Complexity Dependency Tuples Problem
Rules:none
Tuples:

S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))

S tuples:

FROM(mark(z0)) → c39(FROM(z0))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
SQUARE(ok(z0)) → c56(SQUARE(z0))

K tuples:

RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
S(mark(z0)) → c28(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
S(ok(z0)) → c29(S(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
FROM(ok(z0)) → c40(FROM(z0))

Defined Rule Symbols:none

Defined Pair Symbols:

S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE

Compound Symbols:

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

(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.

FROM(mark(z0)) → c39(FROM(z0))

We considered the (Usable) Rules:none
And the Tuples:

S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))

The order we found is given by the following interpretation:
Polynomial interpretation :

POL(2NDSNEG(x₁, x₂)) = [4]x₁
POL(2NDSPOS(x₁, x₂)) = [4]x₁
POL(CONS(x₁, x₂)) = 0
POL(FROM(x₁)) = x₁
POL(NEGRECIP(x₁)) = [3]x₁
POL(PI(x₁)) = [2]x₁
POL(PLUS(x₁, x₂)) = [3]x₁
POL(POSRECIP(x₁)) = 0
POL(RCONS(x₁, x₂)) = [3]x₂
POL(S(x₁)) = [4]x₁
POL(SQUARE(x₁)) = 0
POL(TIMES(x₁, x₂)) = 0
POL(c28(x₁)) = x₁
POL(c29(x₁)) = x₁
POL(c30(x₁)) = 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(mark(x₁)) = [1] + x₁
POL(ok(x₁)) = x₁

(106) Obligation:

Complexity Dependency Tuples Problem
Rules:none
Tuples:

S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))

S tuples:

TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
SQUARE(ok(z0)) → c56(SQUARE(z0))

K tuples:

RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
S(mark(z0)) → c28(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
S(ok(z0)) → c29(S(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
FROM(ok(z0)) → c40(FROM(z0))
FROM(mark(z0)) → c39(FROM(z0))

Defined Rule Symbols:none

Defined Pair Symbols:

S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE

Compound Symbols:

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

(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.

SQUARE(ok(z0)) → c56(SQUARE(z0))

We considered the (Usable) Rules:none
And the Tuples:

S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))

The order we found is given by the following interpretation:
Polynomial interpretation :

POL(2NDSNEG(x₁, x₂)) = [4]x₁ + [4]x₂
POL(2NDSPOS(x₁, x₂)) = [4]x₁
POL(CONS(x₁, x₂)) = [4]x₁ + [4]x₂
POL(FROM(x₁)) = [4]x₁
POL(NEGRECIP(x₁)) = [4]x₁
POL(PI(x₁)) = [4]x₁
POL(PLUS(x₁, x₂)) = 0
POL(POSRECIP(x₁)) = [2]x₁
POL(RCONS(x₁, x₂)) = 0
POL(S(x₁)) = 0
POL(SQUARE(x₁)) = [2]x₁
POL(TIMES(x₁, x₂)) = 0
POL(c28(x₁)) = x₁
POL(c29(x₁)) = x₁
POL(c30(x₁)) = 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(mark(x₁)) = [4] + x₁
POL(ok(x₁)) = [2] + x₁

(108) Obligation:

Complexity Dependency Tuples Problem
Rules:none
Tuples:

S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))

S tuples:

TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))

K tuples:

RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
S(mark(z0)) → c28(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
S(ok(z0)) → c29(S(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
FROM(ok(z0)) → c40(FROM(z0))
FROM(mark(z0)) → c39(FROM(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))

Defined Rule Symbols:none

Defined Pair Symbols:

S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE

Compound Symbols:

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

(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.

TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))

We considered the (Usable) Rules:none
And the Tuples:

S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))

The order we found is given by the following interpretation:
Polynomial interpretation :

POL(2NDSNEG(x₁, x₂)) = [4]x₁ + [4]x₂
POL(2NDSPOS(x₁, x₂)) = [4]x₁ + [2]x₂
POL(CONS(x₁, x₂)) = [4]x₁
POL(FROM(x₁)) = 0
POL(NEGRECIP(x₁)) = 0
POL(PI(x₁)) = [4]x₁
POL(PLUS(x₁, x₂)) = 0
POL(POSRECIP(x₁)) = 0
POL(RCONS(x₁, x₂)) = [3]x₂
POL(S(x₁)) = 0
POL(SQUARE(x₁)) = 0
POL(TIMES(x₁, x₂)) = [4]x₂
POL(c28(x₁)) = x₁
POL(c29(x₁)) = x₁
POL(c30(x₁)) = 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(mark(x₁)) = [1] + x₁
POL(ok(x₁)) = x₁

(110) Obligation:

Complexity Dependency Tuples Problem
Rules:none
Tuples:

S(mark(z0)) → c28(S(z0))
S(ok(z0)) → c29(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
FROM(mark(z0)) → c39(FROM(z0))
FROM(ok(z0)) → c40(FROM(z0))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))

S tuples:none
K tuples:

RCONS(mark(z0), z1) → c36(RCONS(z0, z1))
RCONS(ok(z0), ok(z1)) → c38(RCONS(z0, z1))
2NDSPOS(z0, mark(z1)) → c42(2NDSPOS(z0, z1))
2NDSPOS(ok(z0), ok(z1)) → c43(2NDSPOS(z0, z1))
2NDSNEG(mark(z0), z1) → c44(2NDSNEG(z0, z1))
2NDSNEG(z0, mark(z1)) → c45(2NDSNEG(z0, z1))
2NDSNEG(ok(z0), ok(z1)) → c46(2NDSNEG(z0, z1))
PI(mark(z0)) → c47(PI(z0))
PI(ok(z0)) → c48(PI(z0))
CONS(ok(z0), ok(z1)) → c35(CONS(z0, z1))
S(mark(z0)) → c28(S(z0))
POSRECIP(mark(z0)) → c30(POSRECIP(z0))
NEGRECIP(mark(z0)) → c32(NEGRECIP(z0))
CONS(mark(z0), z1) → c34(CONS(z0, z1))
RCONS(z0, mark(z1)) → c37(RCONS(z0, z1))
2NDSPOS(mark(z0), z1) → c41(2NDSPOS(z0, z1))
PLUS(mark(z0), z1) → c49(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c50(PLUS(z0, z1))
SQUARE(mark(z0)) → c55(SQUARE(z0))
TIMES(mark(z0), z1) → c52(TIMES(z0, z1))
TIMES(ok(z0), ok(z1)) → c54(TIMES(z0, z1))
S(ok(z0)) → c29(S(z0))
POSRECIP(ok(z0)) → c31(POSRECIP(z0))
NEGRECIP(ok(z0)) → c33(NEGRECIP(z0))
PLUS(ok(z0), ok(z1)) → c51(PLUS(z0, z1))
FROM(ok(z0)) → c40(FROM(z0))
FROM(mark(z0)) → c39(FROM(z0))
SQUARE(ok(z0)) → c56(SQUARE(z0))
TIMES(z0, mark(z1)) → c53(TIMES(z0, z1))

Defined Rule Symbols:none

Defined Pair Symbols:

S, POSRECIP, NEGRECIP, CONS, RCONS, FROM, 2NDSPOS, 2NDSNEG, PI, PLUS, TIMES, SQUARE

Compound Symbols:

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

(111) SIsEmptyProof (BOTH BOUNDS(ID, ID) transformation)

The set S is empty