(0) Obligation:
Runtime Complexity TRS:
The TRS R consists of the following rules:
active(dbl(0)) → mark(0)
active(dbl(s(X))) → mark(s(s(dbl(X))))
active(dbls(nil)) → mark(nil)
active(dbls(cons(X, Y))) → mark(cons(dbl(X), dbls(Y)))
active(sel(0, cons(X, Y))) → mark(X)
active(sel(s(X), cons(Y, Z))) → mark(sel(X, Z))
active(indx(nil, X)) → mark(nil)
active(indx(cons(X, Y), Z)) → mark(cons(sel(X, Z), indx(Y, Z)))
active(from(X)) → mark(cons(X, from(s(X))))
active(dbl1(0)) → mark(01)
active(dbl1(s(X))) → mark(s1(s1(dbl1(X))))
active(sel1(0, cons(X, Y))) → mark(X)
active(sel1(s(X), cons(Y, Z))) → mark(sel1(X, Z))
active(quote(0)) → mark(01)
active(quote(s(X))) → mark(s1(quote(X)))
active(quote(dbl(X))) → mark(dbl1(X))
active(quote(sel(X, Y))) → mark(sel1(X, Y))
active(dbl(X)) → dbl(active(X))
active(dbls(X)) → dbls(active(X))
active(sel(X1, X2)) → sel(active(X1), X2)
active(sel(X1, X2)) → sel(X1, active(X2))
active(indx(X1, X2)) → indx(active(X1), X2)
active(dbl1(X)) → dbl1(active(X))
active(s1(X)) → s1(active(X))
active(sel1(X1, X2)) → sel1(active(X1), X2)
active(sel1(X1, X2)) → sel1(X1, active(X2))
active(quote(X)) → quote(active(X))
dbl(mark(X)) → mark(dbl(X))
dbls(mark(X)) → mark(dbls(X))
sel(mark(X1), X2) → mark(sel(X1, X2))
sel(X1, mark(X2)) → mark(sel(X1, X2))
indx(mark(X1), X2) → mark(indx(X1, X2))
dbl1(mark(X)) → mark(dbl1(X))
s1(mark(X)) → mark(s1(X))
sel1(mark(X1), X2) → mark(sel1(X1, X2))
sel1(X1, mark(X2)) → mark(sel1(X1, X2))
quote(mark(X)) → mark(quote(X))
proper(dbl(X)) → dbl(proper(X))
proper(0) → ok(0)
proper(s(X)) → s(proper(X))
proper(dbls(X)) → dbls(proper(X))
proper(nil) → ok(nil)
proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(sel(X1, X2)) → sel(proper(X1), proper(X2))
proper(indx(X1, X2)) → indx(proper(X1), proper(X2))
proper(from(X)) → from(proper(X))
proper(dbl1(X)) → dbl1(proper(X))
proper(01) → ok(01)
proper(s1(X)) → s1(proper(X))
proper(sel1(X1, X2)) → sel1(proper(X1), proper(X2))
proper(quote(X)) → quote(proper(X))
dbl(ok(X)) → ok(dbl(X))
s(ok(X)) → ok(s(X))
dbls(ok(X)) → ok(dbls(X))
cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
sel(ok(X1), ok(X2)) → ok(sel(X1, X2))
indx(ok(X1), ok(X2)) → ok(indx(X1, X2))
from(ok(X)) → ok(from(X))
dbl1(ok(X)) → ok(dbl1(X))
s1(ok(X)) → ok(s1(X))
sel1(ok(X1), ok(X2)) → ok(sel1(X1, X2))
quote(ok(X)) → ok(quote(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(dbl(0)) → mark(0)
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
active(dbls(nil)) → mark(nil)
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1)))
active(sel(0, cons(z0, z1))) → mark(z0)
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
active(indx(nil, z0)) → mark(nil)
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2)))
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(dbl1(0)) → mark(01)
active(dbl1(s(z0))) → mark(s1(s1(dbl1(z0))))
active(sel1(0, cons(z0, z1))) → mark(z0)
active(sel1(s(z0), cons(z1, z2))) → mark(sel1(z0, z2))
active(quote(0)) → mark(01)
active(quote(s(z0))) → mark(s1(quote(z0)))
active(quote(dbl(z0))) → mark(dbl1(z0))
active(quote(sel(z0, z1))) → mark(sel1(z0, z1))
active(dbl(z0)) → dbl(active(z0))
active(dbls(z0)) → dbls(active(z0))
active(sel(z0, z1)) → sel(active(z0), z1)
active(sel(z0, z1)) → sel(z0, active(z1))
active(indx(z0, z1)) → indx(active(z0), z1)
active(dbl1(z0)) → dbl1(active(z0))
active(s1(z0)) → s1(active(z0))
active(sel1(z0, z1)) → sel1(active(z0), z1)
active(sel1(z0, z1)) → sel1(z0, active(z1))
active(quote(z0)) → quote(active(z0))
dbl(mark(z0)) → mark(dbl(z0))
dbl(ok(z0)) → ok(dbl(z0))
dbls(mark(z0)) → mark(dbls(z0))
dbls(ok(z0)) → ok(dbls(z0))
sel(mark(z0), z1) → mark(sel(z0, z1))
sel(z0, mark(z1)) → mark(sel(z0, z1))
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
indx(mark(z0), z1) → mark(indx(z0, z1))
indx(ok(z0), ok(z1)) → ok(indx(z0, z1))
dbl1(mark(z0)) → mark(dbl1(z0))
dbl1(ok(z0)) → ok(dbl1(z0))
s1(mark(z0)) → mark(s1(z0))
s1(ok(z0)) → ok(s1(z0))
sel1(mark(z0), z1) → mark(sel1(z0, z1))
sel1(z0, mark(z1)) → mark(sel1(z0, z1))
sel1(ok(z0), ok(z1)) → ok(sel1(z0, z1))
quote(mark(z0)) → mark(quote(z0))
quote(ok(z0)) → ok(quote(z0))
proper(dbl(z0)) → dbl(proper(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(dbls(z0)) → dbls(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
proper(indx(z0, z1)) → indx(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(dbl1(z0)) → dbl1(proper(z0))
proper(01) → ok(01)
proper(s1(z0)) → s1(proper(z0))
proper(sel1(z0, z1)) → sel1(proper(z0), proper(z1))
proper(quote(z0)) → quote(proper(z0))
s(ok(z0)) → ok(s(z0))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
from(ok(z0)) → ok(from(z0))
top(mark(z0)) → top(proper(z0))
top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(dbl(0)) → c
ACTIVE(dbl(s(z0))) → c1(S(s(dbl(z0))), S(dbl(z0)), DBL(z0))
ACTIVE(dbls(nil)) → c2
ACTIVE(dbls(cons(z0, z1))) → c3(CONS(dbl(z0), dbls(z1)), DBL(z0), DBLS(z1))
ACTIVE(sel(0, cons(z0, z1))) → c4
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(indx(nil, z0)) → c6
ACTIVE(indx(cons(z0, z1), z2)) → c7(CONS(sel(z0, z2), indx(z1, z2)), SEL(z0, z2), INDX(z1, z2))
ACTIVE(from(z0)) → c8(CONS(z0, from(s(z0))), FROM(s(z0)), S(z0))
ACTIVE(dbl1(0)) → c9
ACTIVE(dbl1(s(z0))) → c10(S1(s1(dbl1(z0))), S1(dbl1(z0)), DBL1(z0))
ACTIVE(sel1(0, cons(z0, z1))) → c11
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(0)) → c13
ACTIVE(quote(s(z0))) → c14(S1(quote(z0)), QUOTE(z0))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(dbl(z0)) → c17(DBL(active(z0)), ACTIVE(z0))
ACTIVE(dbls(z0)) → c18(DBLS(active(z0)), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(indx(z0, z1)) → c21(INDX(active(z0), z1), ACTIVE(z0))
ACTIVE(dbl1(z0)) → c22(DBL1(active(z0)), ACTIVE(z0))
ACTIVE(s1(z0)) → c23(S1(active(z0)), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
ACTIVE(quote(z0)) → c26(QUOTE(active(z0)), ACTIVE(z0))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(dbl(z0)) → c45(DBL(proper(z0)), PROPER(z0))
PROPER(0) → c46
PROPER(s(z0)) → c47(S(proper(z0)), PROPER(z0))
PROPER(dbls(z0)) → c48(DBLS(proper(z0)), PROPER(z0))
PROPER(nil) → c49
PROPER(cons(z0, z1)) → c50(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(sel(z0, z1)) → c51(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(indx(z0, z1)) → c52(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c53(FROM(proper(z0)), PROPER(z0))
PROPER(dbl1(z0)) → c54(DBL1(proper(z0)), PROPER(z0))
PROPER(01) → c55
PROPER(s1(z0)) → c56(S1(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c57(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
S tuples:
ACTIVE(dbl(0)) → c
ACTIVE(dbl(s(z0))) → c1(S(s(dbl(z0))), S(dbl(z0)), DBL(z0))
ACTIVE(dbls(nil)) → c2
ACTIVE(dbls(cons(z0, z1))) → c3(CONS(dbl(z0), dbls(z1)), DBL(z0), DBLS(z1))
ACTIVE(sel(0, cons(z0, z1))) → c4
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(indx(nil, z0)) → c6
ACTIVE(indx(cons(z0, z1), z2)) → c7(CONS(sel(z0, z2), indx(z1, z2)), SEL(z0, z2), INDX(z1, z2))
ACTIVE(from(z0)) → c8(CONS(z0, from(s(z0))), FROM(s(z0)), S(z0))
ACTIVE(dbl1(0)) → c9
ACTIVE(dbl1(s(z0))) → c10(S1(s1(dbl1(z0))), S1(dbl1(z0)), DBL1(z0))
ACTIVE(sel1(0, cons(z0, z1))) → c11
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(0)) → c13
ACTIVE(quote(s(z0))) → c14(S1(quote(z0)), QUOTE(z0))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(dbl(z0)) → c17(DBL(active(z0)), ACTIVE(z0))
ACTIVE(dbls(z0)) → c18(DBLS(active(z0)), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(indx(z0, z1)) → c21(INDX(active(z0), z1), ACTIVE(z0))
ACTIVE(dbl1(z0)) → c22(DBL1(active(z0)), ACTIVE(z0))
ACTIVE(s1(z0)) → c23(S1(active(z0)), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
ACTIVE(quote(z0)) → c26(QUOTE(active(z0)), ACTIVE(z0))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(dbl(z0)) → c45(DBL(proper(z0)), PROPER(z0))
PROPER(0) → c46
PROPER(s(z0)) → c47(S(proper(z0)), PROPER(z0))
PROPER(dbls(z0)) → c48(DBLS(proper(z0)), PROPER(z0))
PROPER(nil) → c49
PROPER(cons(z0, z1)) → c50(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(sel(z0, z1)) → c51(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(indx(z0, z1)) → c52(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c53(FROM(proper(z0)), PROPER(z0))
PROPER(dbl1(z0)) → c54(DBL1(proper(z0)), PROPER(z0))
PROPER(01) → c55
PROPER(s1(z0)) → c56(S1(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c57(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
K tuples:none
Defined Rule Symbols:
active, dbl, dbls, sel, indx, dbl1, s1, sel1, quote, proper, s, cons, from, top
Defined Pair Symbols:
ACTIVE, DBL, DBLS, SEL, INDX, DBL1, S1, SEL1, QUOTE, PROPER, S, CONS, FROM, 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
(3) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID) transformation)
Removed 10 trailing nodes:
ACTIVE(sel1(0, cons(z0, z1))) → c11
PROPER(0) → c46
ACTIVE(dbl(0)) → c
PROPER(nil) → c49
ACTIVE(dbls(nil)) → c2
ACTIVE(sel(0, cons(z0, z1))) → c4
ACTIVE(dbl1(0)) → c9
ACTIVE(indx(nil, z0)) → c6
ACTIVE(quote(0)) → c13
PROPER(01) → c55
(4) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(dbl(0)) → mark(0)
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
active(dbls(nil)) → mark(nil)
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1)))
active(sel(0, cons(z0, z1))) → mark(z0)
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
active(indx(nil, z0)) → mark(nil)
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2)))
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(dbl1(0)) → mark(01)
active(dbl1(s(z0))) → mark(s1(s1(dbl1(z0))))
active(sel1(0, cons(z0, z1))) → mark(z0)
active(sel1(s(z0), cons(z1, z2))) → mark(sel1(z0, z2))
active(quote(0)) → mark(01)
active(quote(s(z0))) → mark(s1(quote(z0)))
active(quote(dbl(z0))) → mark(dbl1(z0))
active(quote(sel(z0, z1))) → mark(sel1(z0, z1))
active(dbl(z0)) → dbl(active(z0))
active(dbls(z0)) → dbls(active(z0))
active(sel(z0, z1)) → sel(active(z0), z1)
active(sel(z0, z1)) → sel(z0, active(z1))
active(indx(z0, z1)) → indx(active(z0), z1)
active(dbl1(z0)) → dbl1(active(z0))
active(s1(z0)) → s1(active(z0))
active(sel1(z0, z1)) → sel1(active(z0), z1)
active(sel1(z0, z1)) → sel1(z0, active(z1))
active(quote(z0)) → quote(active(z0))
dbl(mark(z0)) → mark(dbl(z0))
dbl(ok(z0)) → ok(dbl(z0))
dbls(mark(z0)) → mark(dbls(z0))
dbls(ok(z0)) → ok(dbls(z0))
sel(mark(z0), z1) → mark(sel(z0, z1))
sel(z0, mark(z1)) → mark(sel(z0, z1))
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
indx(mark(z0), z1) → mark(indx(z0, z1))
indx(ok(z0), ok(z1)) → ok(indx(z0, z1))
dbl1(mark(z0)) → mark(dbl1(z0))
dbl1(ok(z0)) → ok(dbl1(z0))
s1(mark(z0)) → mark(s1(z0))
s1(ok(z0)) → ok(s1(z0))
sel1(mark(z0), z1) → mark(sel1(z0, z1))
sel1(z0, mark(z1)) → mark(sel1(z0, z1))
sel1(ok(z0), ok(z1)) → ok(sel1(z0, z1))
quote(mark(z0)) → mark(quote(z0))
quote(ok(z0)) → ok(quote(z0))
proper(dbl(z0)) → dbl(proper(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(dbls(z0)) → dbls(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
proper(indx(z0, z1)) → indx(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(dbl1(z0)) → dbl1(proper(z0))
proper(01) → ok(01)
proper(s1(z0)) → s1(proper(z0))
proper(sel1(z0, z1)) → sel1(proper(z0), proper(z1))
proper(quote(z0)) → quote(proper(z0))
s(ok(z0)) → ok(s(z0))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
from(ok(z0)) → ok(from(z0))
top(mark(z0)) → top(proper(z0))
top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(dbl(s(z0))) → c1(S(s(dbl(z0))), S(dbl(z0)), DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c3(CONS(dbl(z0), dbls(z1)), DBL(z0), DBLS(z1))
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c7(CONS(sel(z0, z2), indx(z1, z2)), SEL(z0, z2), INDX(z1, z2))
ACTIVE(from(z0)) → c8(CONS(z0, from(s(z0))), FROM(s(z0)), S(z0))
ACTIVE(dbl1(s(z0))) → c10(S1(s1(dbl1(z0))), S1(dbl1(z0)), DBL1(z0))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(s(z0))) → c14(S1(quote(z0)), QUOTE(z0))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(dbl(z0)) → c17(DBL(active(z0)), ACTIVE(z0))
ACTIVE(dbls(z0)) → c18(DBLS(active(z0)), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(indx(z0, z1)) → c21(INDX(active(z0), z1), ACTIVE(z0))
ACTIVE(dbl1(z0)) → c22(DBL1(active(z0)), ACTIVE(z0))
ACTIVE(s1(z0)) → c23(S1(active(z0)), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
ACTIVE(quote(z0)) → c26(QUOTE(active(z0)), ACTIVE(z0))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(dbl(z0)) → c45(DBL(proper(z0)), PROPER(z0))
PROPER(s(z0)) → c47(S(proper(z0)), PROPER(z0))
PROPER(dbls(z0)) → c48(DBLS(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c50(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(sel(z0, z1)) → c51(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(indx(z0, z1)) → c52(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c53(FROM(proper(z0)), PROPER(z0))
PROPER(dbl1(z0)) → c54(DBL1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c56(S1(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c57(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
S tuples:
ACTIVE(dbl(s(z0))) → c1(S(s(dbl(z0))), S(dbl(z0)), DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c3(CONS(dbl(z0), dbls(z1)), DBL(z0), DBLS(z1))
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c7(CONS(sel(z0, z2), indx(z1, z2)), SEL(z0, z2), INDX(z1, z2))
ACTIVE(from(z0)) → c8(CONS(z0, from(s(z0))), FROM(s(z0)), S(z0))
ACTIVE(dbl1(s(z0))) → c10(S1(s1(dbl1(z0))), S1(dbl1(z0)), DBL1(z0))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(s(z0))) → c14(S1(quote(z0)), QUOTE(z0))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(dbl(z0)) → c17(DBL(active(z0)), ACTIVE(z0))
ACTIVE(dbls(z0)) → c18(DBLS(active(z0)), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(indx(z0, z1)) → c21(INDX(active(z0), z1), ACTIVE(z0))
ACTIVE(dbl1(z0)) → c22(DBL1(active(z0)), ACTIVE(z0))
ACTIVE(s1(z0)) → c23(S1(active(z0)), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
ACTIVE(quote(z0)) → c26(QUOTE(active(z0)), ACTIVE(z0))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(dbl(z0)) → c45(DBL(proper(z0)), PROPER(z0))
PROPER(s(z0)) → c47(S(proper(z0)), PROPER(z0))
PROPER(dbls(z0)) → c48(DBLS(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c50(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(sel(z0, z1)) → c51(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(indx(z0, z1)) → c52(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c53(FROM(proper(z0)), PROPER(z0))
PROPER(dbl1(z0)) → c54(DBL1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c56(S1(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c57(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
K tuples:none
Defined Rule Symbols:
active, dbl, dbls, sel, indx, dbl1, s1, sel1, quote, proper, s, cons, from, top
Defined Pair Symbols:
ACTIVE, DBL, DBLS, SEL, INDX, DBL1, S1, SEL1, QUOTE, PROPER, S, CONS, FROM, TOP
Compound Symbols:
c1, c3, c5, c7, c8, c10, c12, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c47, c48, c50, c51, c52, c53, c54, c56, c57, c58, c59, c60, c61, c62, c63
(5) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 2 trailing tuple parts
(6) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(dbl(0)) → mark(0)
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
active(dbls(nil)) → mark(nil)
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1)))
active(sel(0, cons(z0, z1))) → mark(z0)
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
active(indx(nil, z0)) → mark(nil)
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2)))
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(dbl1(0)) → mark(01)
active(dbl1(s(z0))) → mark(s1(s1(dbl1(z0))))
active(sel1(0, cons(z0, z1))) → mark(z0)
active(sel1(s(z0), cons(z1, z2))) → mark(sel1(z0, z2))
active(quote(0)) → mark(01)
active(quote(s(z0))) → mark(s1(quote(z0)))
active(quote(dbl(z0))) → mark(dbl1(z0))
active(quote(sel(z0, z1))) → mark(sel1(z0, z1))
active(dbl(z0)) → dbl(active(z0))
active(dbls(z0)) → dbls(active(z0))
active(sel(z0, z1)) → sel(active(z0), z1)
active(sel(z0, z1)) → sel(z0, active(z1))
active(indx(z0, z1)) → indx(active(z0), z1)
active(dbl1(z0)) → dbl1(active(z0))
active(s1(z0)) → s1(active(z0))
active(sel1(z0, z1)) → sel1(active(z0), z1)
active(sel1(z0, z1)) → sel1(z0, active(z1))
active(quote(z0)) → quote(active(z0))
dbl(mark(z0)) → mark(dbl(z0))
dbl(ok(z0)) → ok(dbl(z0))
dbls(mark(z0)) → mark(dbls(z0))
dbls(ok(z0)) → ok(dbls(z0))
sel(mark(z0), z1) → mark(sel(z0, z1))
sel(z0, mark(z1)) → mark(sel(z0, z1))
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
indx(mark(z0), z1) → mark(indx(z0, z1))
indx(ok(z0), ok(z1)) → ok(indx(z0, z1))
dbl1(mark(z0)) → mark(dbl1(z0))
dbl1(ok(z0)) → ok(dbl1(z0))
s1(mark(z0)) → mark(s1(z0))
s1(ok(z0)) → ok(s1(z0))
sel1(mark(z0), z1) → mark(sel1(z0, z1))
sel1(z0, mark(z1)) → mark(sel1(z0, z1))
sel1(ok(z0), ok(z1)) → ok(sel1(z0, z1))
quote(mark(z0)) → mark(quote(z0))
quote(ok(z0)) → ok(quote(z0))
proper(dbl(z0)) → dbl(proper(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(dbls(z0)) → dbls(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
proper(indx(z0, z1)) → indx(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(dbl1(z0)) → dbl1(proper(z0))
proper(01) → ok(01)
proper(s1(z0)) → s1(proper(z0))
proper(sel1(z0, z1)) → sel1(proper(z0), proper(z1))
proper(quote(z0)) → quote(proper(z0))
s(ok(z0)) → ok(s(z0))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
from(ok(z0)) → ok(from(z0))
top(mark(z0)) → top(proper(z0))
top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(dbl(s(z0))) → c1(S(s(dbl(z0))), S(dbl(z0)), DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c3(CONS(dbl(z0), dbls(z1)), DBL(z0), DBLS(z1))
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c7(CONS(sel(z0, z2), indx(z1, z2)), SEL(z0, z2), INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c10(S1(s1(dbl1(z0))), S1(dbl1(z0)), DBL1(z0))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(s(z0))) → c14(S1(quote(z0)), QUOTE(z0))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(dbl(z0)) → c17(DBL(active(z0)), ACTIVE(z0))
ACTIVE(dbls(z0)) → c18(DBLS(active(z0)), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(indx(z0, z1)) → c21(INDX(active(z0), z1), ACTIVE(z0))
ACTIVE(dbl1(z0)) → c22(DBL1(active(z0)), ACTIVE(z0))
ACTIVE(s1(z0)) → c23(S1(active(z0)), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
ACTIVE(quote(z0)) → c26(QUOTE(active(z0)), ACTIVE(z0))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(dbl(z0)) → c45(DBL(proper(z0)), PROPER(z0))
PROPER(s(z0)) → c47(S(proper(z0)), PROPER(z0))
PROPER(dbls(z0)) → c48(DBLS(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c50(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(sel(z0, z1)) → c51(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(indx(z0, z1)) → c52(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c53(FROM(proper(z0)), PROPER(z0))
PROPER(dbl1(z0)) → c54(DBL1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c56(S1(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c57(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
S tuples:
ACTIVE(dbl(s(z0))) → c1(S(s(dbl(z0))), S(dbl(z0)), DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c3(CONS(dbl(z0), dbls(z1)), DBL(z0), DBLS(z1))
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c7(CONS(sel(z0, z2), indx(z1, z2)), SEL(z0, z2), INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c10(S1(s1(dbl1(z0))), S1(dbl1(z0)), DBL1(z0))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(s(z0))) → c14(S1(quote(z0)), QUOTE(z0))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(dbl(z0)) → c17(DBL(active(z0)), ACTIVE(z0))
ACTIVE(dbls(z0)) → c18(DBLS(active(z0)), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(indx(z0, z1)) → c21(INDX(active(z0), z1), ACTIVE(z0))
ACTIVE(dbl1(z0)) → c22(DBL1(active(z0)), ACTIVE(z0))
ACTIVE(s1(z0)) → c23(S1(active(z0)), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
ACTIVE(quote(z0)) → c26(QUOTE(active(z0)), ACTIVE(z0))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(dbl(z0)) → c45(DBL(proper(z0)), PROPER(z0))
PROPER(s(z0)) → c47(S(proper(z0)), PROPER(z0))
PROPER(dbls(z0)) → c48(DBLS(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c50(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(sel(z0, z1)) → c51(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(indx(z0, z1)) → c52(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c53(FROM(proper(z0)), PROPER(z0))
PROPER(dbl1(z0)) → c54(DBL1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c56(S1(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c57(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
K tuples:none
Defined Rule Symbols:
active, dbl, dbls, sel, indx, dbl1, s1, sel1, quote, proper, s, cons, from, top
Defined Pair Symbols:
ACTIVE, DBL, DBLS, SEL, INDX, DBL1, S1, SEL1, QUOTE, PROPER, S, CONS, FROM, TOP
Compound Symbols:
c1, c3, c5, c7, c10, c12, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c47, c48, c50, c51, c52, c53, c54, c56, c57, c58, c59, c60, c61, c62, c63, c8
(7) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID) transformation)
Split RHS of tuples not part of any SCC
(8) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(dbl(0)) → mark(0)
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
active(dbls(nil)) → mark(nil)
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1)))
active(sel(0, cons(z0, z1))) → mark(z0)
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
active(indx(nil, z0)) → mark(nil)
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2)))
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(dbl1(0)) → mark(01)
active(dbl1(s(z0))) → mark(s1(s1(dbl1(z0))))
active(sel1(0, cons(z0, z1))) → mark(z0)
active(sel1(s(z0), cons(z1, z2))) → mark(sel1(z0, z2))
active(quote(0)) → mark(01)
active(quote(s(z0))) → mark(s1(quote(z0)))
active(quote(dbl(z0))) → mark(dbl1(z0))
active(quote(sel(z0, z1))) → mark(sel1(z0, z1))
active(dbl(z0)) → dbl(active(z0))
active(dbls(z0)) → dbls(active(z0))
active(sel(z0, z1)) → sel(active(z0), z1)
active(sel(z0, z1)) → sel(z0, active(z1))
active(indx(z0, z1)) → indx(active(z0), z1)
active(dbl1(z0)) → dbl1(active(z0))
active(s1(z0)) → s1(active(z0))
active(sel1(z0, z1)) → sel1(active(z0), z1)
active(sel1(z0, z1)) → sel1(z0, active(z1))
active(quote(z0)) → quote(active(z0))
dbl(mark(z0)) → mark(dbl(z0))
dbl(ok(z0)) → ok(dbl(z0))
dbls(mark(z0)) → mark(dbls(z0))
dbls(ok(z0)) → ok(dbls(z0))
sel(mark(z0), z1) → mark(sel(z0, z1))
sel(z0, mark(z1)) → mark(sel(z0, z1))
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
indx(mark(z0), z1) → mark(indx(z0, z1))
indx(ok(z0), ok(z1)) → ok(indx(z0, z1))
dbl1(mark(z0)) → mark(dbl1(z0))
dbl1(ok(z0)) → ok(dbl1(z0))
s1(mark(z0)) → mark(s1(z0))
s1(ok(z0)) → ok(s1(z0))
sel1(mark(z0), z1) → mark(sel1(z0, z1))
sel1(z0, mark(z1)) → mark(sel1(z0, z1))
sel1(ok(z0), ok(z1)) → ok(sel1(z0, z1))
quote(mark(z0)) → mark(quote(z0))
quote(ok(z0)) → ok(quote(z0))
proper(dbl(z0)) → dbl(proper(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(dbls(z0)) → dbls(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
proper(indx(z0, z1)) → indx(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(dbl1(z0)) → dbl1(proper(z0))
proper(01) → ok(01)
proper(s1(z0)) → s1(proper(z0))
proper(sel1(z0, z1)) → sel1(proper(z0), proper(z1))
proper(quote(z0)) → quote(proper(z0))
s(ok(z0)) → ok(s(z0))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
from(ok(z0)) → ok(from(z0))
top(mark(z0)) → top(proper(z0))
top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(dbl(z0)) → c17(DBL(active(z0)), ACTIVE(z0))
ACTIVE(dbls(z0)) → c18(DBLS(active(z0)), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(indx(z0, z1)) → c21(INDX(active(z0), z1), ACTIVE(z0))
ACTIVE(dbl1(z0)) → c22(DBL1(active(z0)), ACTIVE(z0))
ACTIVE(s1(z0)) → c23(S1(active(z0)), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
ACTIVE(quote(z0)) → c26(QUOTE(active(z0)), ACTIVE(z0))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(dbl(z0)) → c45(DBL(proper(z0)), PROPER(z0))
PROPER(s(z0)) → c47(S(proper(z0)), PROPER(z0))
PROPER(dbls(z0)) → c48(DBLS(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c50(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(sel(z0, z1)) → c51(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(indx(z0, z1)) → c52(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c53(FROM(proper(z0)), PROPER(z0))
PROPER(dbl1(z0)) → c54(DBL1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c56(S1(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c57(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
S tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(dbl(z0)) → c17(DBL(active(z0)), ACTIVE(z0))
ACTIVE(dbls(z0)) → c18(DBLS(active(z0)), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(indx(z0, z1)) → c21(INDX(active(z0), z1), ACTIVE(z0))
ACTIVE(dbl1(z0)) → c22(DBL1(active(z0)), ACTIVE(z0))
ACTIVE(s1(z0)) → c23(S1(active(z0)), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
ACTIVE(quote(z0)) → c26(QUOTE(active(z0)), ACTIVE(z0))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(dbl(z0)) → c45(DBL(proper(z0)), PROPER(z0))
PROPER(s(z0)) → c47(S(proper(z0)), PROPER(z0))
PROPER(dbls(z0)) → c48(DBLS(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c50(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(sel(z0, z1)) → c51(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(indx(z0, z1)) → c52(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c53(FROM(proper(z0)), PROPER(z0))
PROPER(dbl1(z0)) → c54(DBL1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c56(S1(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c57(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
K tuples:none
Defined Rule Symbols:
active, dbl, dbls, sel, indx, dbl1, s1, sel1, quote, proper, s, cons, from, top
Defined Pair Symbols:
ACTIVE, DBL, DBLS, SEL, INDX, DBL1, S1, SEL1, QUOTE, PROPER, S, CONS, FROM, TOP
Compound Symbols:
c5, c12, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c47, c48, c50, c51, c52, c53, c54, c56, c57, c58, c59, c60, c61, c62, c63, c8, c
(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(dbl(0)) → mark(0)
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
active(dbls(nil)) → mark(nil)
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1)))
active(sel(0, cons(z0, z1))) → mark(z0)
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
active(indx(nil, z0)) → mark(nil)
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2)))
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(dbl1(0)) → mark(01)
active(dbl1(s(z0))) → mark(s1(s1(dbl1(z0))))
active(sel1(0, cons(z0, z1))) → mark(z0)
active(sel1(s(z0), cons(z1, z2))) → mark(sel1(z0, z2))
active(quote(0)) → mark(01)
active(quote(s(z0))) → mark(s1(quote(z0)))
active(quote(dbl(z0))) → mark(dbl1(z0))
active(quote(sel(z0, z1))) → mark(sel1(z0, z1))
active(dbl(z0)) → dbl(active(z0))
active(dbls(z0)) → dbls(active(z0))
active(sel(z0, z1)) → sel(active(z0), z1)
active(sel(z0, z1)) → sel(z0, active(z1))
active(indx(z0, z1)) → indx(active(z0), z1)
active(dbl1(z0)) → dbl1(active(z0))
active(s1(z0)) → s1(active(z0))
active(sel1(z0, z1)) → sel1(active(z0), z1)
active(sel1(z0, z1)) → sel1(z0, active(z1))
active(quote(z0)) → quote(active(z0))
s(ok(z0)) → ok(s(z0))
dbl(mark(z0)) → mark(dbl(z0))
dbl(ok(z0)) → ok(dbl(z0))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
dbls(mark(z0)) → mark(dbls(z0))
dbls(ok(z0)) → ok(dbls(z0))
sel(mark(z0), z1) → mark(sel(z0, z1))
sel(z0, mark(z1)) → mark(sel(z0, z1))
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
indx(mark(z0), z1) → mark(indx(z0, z1))
indx(ok(z0), ok(z1)) → ok(indx(z0, z1))
s1(mark(z0)) → mark(s1(z0))
s1(ok(z0)) → ok(s1(z0))
dbl1(mark(z0)) → mark(dbl1(z0))
dbl1(ok(z0)) → ok(dbl1(z0))
sel1(mark(z0), z1) → mark(sel1(z0, z1))
sel1(z0, mark(z1)) → mark(sel1(z0, z1))
sel1(ok(z0), ok(z1)) → ok(sel1(z0, z1))
quote(mark(z0)) → mark(quote(z0))
quote(ok(z0)) → ok(quote(z0))
proper(dbl(z0)) → dbl(proper(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(dbls(z0)) → dbls(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
proper(indx(z0, z1)) → indx(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(dbl1(z0)) → dbl1(proper(z0))
proper(01) → ok(01)
proper(s1(z0)) → s1(proper(z0))
proper(sel1(z0, z1)) → sel1(proper(z0), proper(z1))
proper(quote(z0)) → quote(proper(z0))
from(ok(z0)) → ok(from(z0))
Tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(dbl(z0)) → c17(DBL(active(z0)), ACTIVE(z0))
ACTIVE(dbls(z0)) → c18(DBLS(active(z0)), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(indx(z0, z1)) → c21(INDX(active(z0), z1), ACTIVE(z0))
ACTIVE(dbl1(z0)) → c22(DBL1(active(z0)), ACTIVE(z0))
ACTIVE(s1(z0)) → c23(S1(active(z0)), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
ACTIVE(quote(z0)) → c26(QUOTE(active(z0)), ACTIVE(z0))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(dbl(z0)) → c45(DBL(proper(z0)), PROPER(z0))
PROPER(s(z0)) → c47(S(proper(z0)), PROPER(z0))
PROPER(dbls(z0)) → c48(DBLS(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c50(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(sel(z0, z1)) → c51(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(indx(z0, z1)) → c52(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c53(FROM(proper(z0)), PROPER(z0))
PROPER(dbl1(z0)) → c54(DBL1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c56(S1(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c57(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
S tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(dbl(z0)) → c17(DBL(active(z0)), ACTIVE(z0))
ACTIVE(dbls(z0)) → c18(DBLS(active(z0)), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(indx(z0, z1)) → c21(INDX(active(z0), z1), ACTIVE(z0))
ACTIVE(dbl1(z0)) → c22(DBL1(active(z0)), ACTIVE(z0))
ACTIVE(s1(z0)) → c23(S1(active(z0)), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
ACTIVE(quote(z0)) → c26(QUOTE(active(z0)), ACTIVE(z0))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(dbl(z0)) → c45(DBL(proper(z0)), PROPER(z0))
PROPER(s(z0)) → c47(S(proper(z0)), PROPER(z0))
PROPER(dbls(z0)) → c48(DBLS(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c50(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(sel(z0, z1)) → c51(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(indx(z0, z1)) → c52(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c53(FROM(proper(z0)), PROPER(z0))
PROPER(dbl1(z0)) → c54(DBL1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c56(S1(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c57(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
K tuples:none
Defined Rule Symbols:
active, s, dbl, cons, dbls, sel, indx, s1, dbl1, sel1, quote, proper, from
Defined Pair Symbols:
ACTIVE, DBL, DBLS, SEL, INDX, DBL1, S1, SEL1, QUOTE, PROPER, S, CONS, FROM, TOP
Compound Symbols:
c5, c12, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c47, c48, c50, c51, c52, c53, c54, c56, c57, c58, c59, c60, c61, c62, c63, c8, c
(11) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
ACTIVE(
dbl(
z0)) →
c17(
DBL(
active(
z0)),
ACTIVE(
z0)) by
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)), ACTIVE(dbl(0)))
ACTIVE(dbl(dbl(s(z0)))) → c17(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)), ACTIVE(dbls(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c17(DBL(mark(cons(dbl(z0), dbls(z1)))), ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)), ACTIVE(indx(nil, z0)))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c17(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))), ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl(from(z0))) → c17(DBL(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)), ACTIVE(dbl1(0)))
ACTIVE(dbl(dbl1(s(z0)))) → c17(DBL(mark(s1(s1(dbl1(z0))))), ACTIVE(dbl1(s(z0))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)), ACTIVE(quote(0)))
ACTIVE(dbl(quote(s(z0)))) → c17(DBL(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
(12) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(dbl(0)) → mark(0)
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
active(dbls(nil)) → mark(nil)
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1)))
active(sel(0, cons(z0, z1))) → mark(z0)
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
active(indx(nil, z0)) → mark(nil)
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2)))
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(dbl1(0)) → mark(01)
active(dbl1(s(z0))) → mark(s1(s1(dbl1(z0))))
active(sel1(0, cons(z0, z1))) → mark(z0)
active(sel1(s(z0), cons(z1, z2))) → mark(sel1(z0, z2))
active(quote(0)) → mark(01)
active(quote(s(z0))) → mark(s1(quote(z0)))
active(quote(dbl(z0))) → mark(dbl1(z0))
active(quote(sel(z0, z1))) → mark(sel1(z0, z1))
active(dbl(z0)) → dbl(active(z0))
active(dbls(z0)) → dbls(active(z0))
active(sel(z0, z1)) → sel(active(z0), z1)
active(sel(z0, z1)) → sel(z0, active(z1))
active(indx(z0, z1)) → indx(active(z0), z1)
active(dbl1(z0)) → dbl1(active(z0))
active(s1(z0)) → s1(active(z0))
active(sel1(z0, z1)) → sel1(active(z0), z1)
active(sel1(z0, z1)) → sel1(z0, active(z1))
active(quote(z0)) → quote(active(z0))
s(ok(z0)) → ok(s(z0))
dbl(mark(z0)) → mark(dbl(z0))
dbl(ok(z0)) → ok(dbl(z0))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
dbls(mark(z0)) → mark(dbls(z0))
dbls(ok(z0)) → ok(dbls(z0))
sel(mark(z0), z1) → mark(sel(z0, z1))
sel(z0, mark(z1)) → mark(sel(z0, z1))
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
indx(mark(z0), z1) → mark(indx(z0, z1))
indx(ok(z0), ok(z1)) → ok(indx(z0, z1))
s1(mark(z0)) → mark(s1(z0))
s1(ok(z0)) → ok(s1(z0))
dbl1(mark(z0)) → mark(dbl1(z0))
dbl1(ok(z0)) → ok(dbl1(z0))
sel1(mark(z0), z1) → mark(sel1(z0, z1))
sel1(z0, mark(z1)) → mark(sel1(z0, z1))
sel1(ok(z0), ok(z1)) → ok(sel1(z0, z1))
quote(mark(z0)) → mark(quote(z0))
quote(ok(z0)) → ok(quote(z0))
proper(dbl(z0)) → dbl(proper(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(dbls(z0)) → dbls(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
proper(indx(z0, z1)) → indx(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(dbl1(z0)) → dbl1(proper(z0))
proper(01) → ok(01)
proper(s1(z0)) → s1(proper(z0))
proper(sel1(z0, z1)) → sel1(proper(z0), proper(z1))
proper(quote(z0)) → quote(proper(z0))
from(ok(z0)) → ok(from(z0))
Tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(dbls(z0)) → c18(DBLS(active(z0)), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(indx(z0, z1)) → c21(INDX(active(z0), z1), ACTIVE(z0))
ACTIVE(dbl1(z0)) → c22(DBL1(active(z0)), ACTIVE(z0))
ACTIVE(s1(z0)) → c23(S1(active(z0)), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
ACTIVE(quote(z0)) → c26(QUOTE(active(z0)), ACTIVE(z0))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(dbl(z0)) → c45(DBL(proper(z0)), PROPER(z0))
PROPER(s(z0)) → c47(S(proper(z0)), PROPER(z0))
PROPER(dbls(z0)) → c48(DBLS(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c50(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(sel(z0, z1)) → c51(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(indx(z0, z1)) → c52(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c53(FROM(proper(z0)), PROPER(z0))
PROPER(dbl1(z0)) → c54(DBL1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c56(S1(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c57(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)), ACTIVE(dbl(0)))
ACTIVE(dbl(dbl(s(z0)))) → c17(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)), ACTIVE(dbls(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c17(DBL(mark(cons(dbl(z0), dbls(z1)))), ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)), ACTIVE(indx(nil, z0)))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c17(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))), ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl(from(z0))) → c17(DBL(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)), ACTIVE(dbl1(0)))
ACTIVE(dbl(dbl1(s(z0)))) → c17(DBL(mark(s1(s1(dbl1(z0))))), ACTIVE(dbl1(s(z0))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)), ACTIVE(quote(0)))
ACTIVE(dbl(quote(s(z0)))) → c17(DBL(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
S tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(dbls(z0)) → c18(DBLS(active(z0)), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(indx(z0, z1)) → c21(INDX(active(z0), z1), ACTIVE(z0))
ACTIVE(dbl1(z0)) → c22(DBL1(active(z0)), ACTIVE(z0))
ACTIVE(s1(z0)) → c23(S1(active(z0)), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
ACTIVE(quote(z0)) → c26(QUOTE(active(z0)), ACTIVE(z0))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(dbl(z0)) → c45(DBL(proper(z0)), PROPER(z0))
PROPER(s(z0)) → c47(S(proper(z0)), PROPER(z0))
PROPER(dbls(z0)) → c48(DBLS(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c50(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(sel(z0, z1)) → c51(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(indx(z0, z1)) → c52(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c53(FROM(proper(z0)), PROPER(z0))
PROPER(dbl1(z0)) → c54(DBL1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c56(S1(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c57(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)), ACTIVE(dbl(0)))
ACTIVE(dbl(dbl(s(z0)))) → c17(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)), ACTIVE(dbls(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c17(DBL(mark(cons(dbl(z0), dbls(z1)))), ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)), ACTIVE(indx(nil, z0)))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c17(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))), ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl(from(z0))) → c17(DBL(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)), ACTIVE(dbl1(0)))
ACTIVE(dbl(dbl1(s(z0)))) → c17(DBL(mark(s1(s1(dbl1(z0))))), ACTIVE(dbl1(s(z0))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)), ACTIVE(quote(0)))
ACTIVE(dbl(quote(s(z0)))) → c17(DBL(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
K tuples:none
Defined Rule Symbols:
active, s, dbl, cons, dbls, sel, indx, s1, dbl1, sel1, quote, proper, from
Defined Pair Symbols:
ACTIVE, DBL, DBLS, SEL, INDX, DBL1, S1, SEL1, QUOTE, PROPER, S, CONS, FROM, TOP
Compound Symbols:
c5, c12, 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, c47, c48, c50, c51, c52, c53, c54, c56, c57, c58, c59, c60, c61, c62, c63, c8, c, c17
(13) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 1 trailing tuple parts
(14) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(dbl(0)) → mark(0)
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
active(dbls(nil)) → mark(nil)
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1)))
active(sel(0, cons(z0, z1))) → mark(z0)
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
active(indx(nil, z0)) → mark(nil)
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2)))
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(dbl1(0)) → mark(01)
active(dbl1(s(z0))) → mark(s1(s1(dbl1(z0))))
active(sel1(0, cons(z0, z1))) → mark(z0)
active(sel1(s(z0), cons(z1, z2))) → mark(sel1(z0, z2))
active(quote(0)) → mark(01)
active(quote(s(z0))) → mark(s1(quote(z0)))
active(quote(dbl(z0))) → mark(dbl1(z0))
active(quote(sel(z0, z1))) → mark(sel1(z0, z1))
active(dbl(z0)) → dbl(active(z0))
active(dbls(z0)) → dbls(active(z0))
active(sel(z0, z1)) → sel(active(z0), z1)
active(sel(z0, z1)) → sel(z0, active(z1))
active(indx(z0, z1)) → indx(active(z0), z1)
active(dbl1(z0)) → dbl1(active(z0))
active(s1(z0)) → s1(active(z0))
active(sel1(z0, z1)) → sel1(active(z0), z1)
active(sel1(z0, z1)) → sel1(z0, active(z1))
active(quote(z0)) → quote(active(z0))
s(ok(z0)) → ok(s(z0))
dbl(mark(z0)) → mark(dbl(z0))
dbl(ok(z0)) → ok(dbl(z0))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
dbls(mark(z0)) → mark(dbls(z0))
dbls(ok(z0)) → ok(dbls(z0))
sel(mark(z0), z1) → mark(sel(z0, z1))
sel(z0, mark(z1)) → mark(sel(z0, z1))
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
indx(mark(z0), z1) → mark(indx(z0, z1))
indx(ok(z0), ok(z1)) → ok(indx(z0, z1))
s1(mark(z0)) → mark(s1(z0))
s1(ok(z0)) → ok(s1(z0))
dbl1(mark(z0)) → mark(dbl1(z0))
dbl1(ok(z0)) → ok(dbl1(z0))
sel1(mark(z0), z1) → mark(sel1(z0, z1))
sel1(z0, mark(z1)) → mark(sel1(z0, z1))
sel1(ok(z0), ok(z1)) → ok(sel1(z0, z1))
quote(mark(z0)) → mark(quote(z0))
quote(ok(z0)) → ok(quote(z0))
proper(dbl(z0)) → dbl(proper(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(dbls(z0)) → dbls(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
proper(indx(z0, z1)) → indx(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(dbl1(z0)) → dbl1(proper(z0))
proper(01) → ok(01)
proper(s1(z0)) → s1(proper(z0))
proper(sel1(z0, z1)) → sel1(proper(z0), proper(z1))
proper(quote(z0)) → quote(proper(z0))
from(ok(z0)) → ok(from(z0))
Tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(dbls(z0)) → c18(DBLS(active(z0)), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(indx(z0, z1)) → c21(INDX(active(z0), z1), ACTIVE(z0))
ACTIVE(dbl1(z0)) → c22(DBL1(active(z0)), ACTIVE(z0))
ACTIVE(s1(z0)) → c23(S1(active(z0)), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
ACTIVE(quote(z0)) → c26(QUOTE(active(z0)), ACTIVE(z0))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(dbl(z0)) → c45(DBL(proper(z0)), PROPER(z0))
PROPER(s(z0)) → c47(S(proper(z0)), PROPER(z0))
PROPER(dbls(z0)) → c48(DBLS(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c50(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(sel(z0, z1)) → c51(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(indx(z0, z1)) → c52(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c53(FROM(proper(z0)), PROPER(z0))
PROPER(dbl1(z0)) → c54(DBL1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c56(S1(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c57(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(dbl(s(z0)))) → c17(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)), ACTIVE(dbls(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c17(DBL(mark(cons(dbl(z0), dbls(z1)))), ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)), ACTIVE(indx(nil, z0)))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c17(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))), ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl(from(z0))) → c17(DBL(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)), ACTIVE(dbl1(0)))
ACTIVE(dbl(dbl1(s(z0)))) → c17(DBL(mark(s1(s1(dbl1(z0))))), ACTIVE(dbl1(s(z0))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)), ACTIVE(quote(0)))
ACTIVE(dbl(quote(s(z0)))) → c17(DBL(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
S tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(dbls(z0)) → c18(DBLS(active(z0)), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(indx(z0, z1)) → c21(INDX(active(z0), z1), ACTIVE(z0))
ACTIVE(dbl1(z0)) → c22(DBL1(active(z0)), ACTIVE(z0))
ACTIVE(s1(z0)) → c23(S1(active(z0)), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
ACTIVE(quote(z0)) → c26(QUOTE(active(z0)), ACTIVE(z0))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(dbl(z0)) → c45(DBL(proper(z0)), PROPER(z0))
PROPER(s(z0)) → c47(S(proper(z0)), PROPER(z0))
PROPER(dbls(z0)) → c48(DBLS(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c50(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(sel(z0, z1)) → c51(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(indx(z0, z1)) → c52(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c53(FROM(proper(z0)), PROPER(z0))
PROPER(dbl1(z0)) → c54(DBL1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c56(S1(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c57(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(dbl(s(z0)))) → c17(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)), ACTIVE(dbls(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c17(DBL(mark(cons(dbl(z0), dbls(z1)))), ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)), ACTIVE(indx(nil, z0)))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c17(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))), ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl(from(z0))) → c17(DBL(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)), ACTIVE(dbl1(0)))
ACTIVE(dbl(dbl1(s(z0)))) → c17(DBL(mark(s1(s1(dbl1(z0))))), ACTIVE(dbl1(s(z0))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)), ACTIVE(quote(0)))
ACTIVE(dbl(quote(s(z0)))) → c17(DBL(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
K tuples:none
Defined Rule Symbols:
active, s, dbl, cons, dbls, sel, indx, s1, dbl1, sel1, quote, proper, from
Defined Pair Symbols:
ACTIVE, DBL, DBLS, SEL, INDX, DBL1, S1, SEL1, QUOTE, PROPER, S, CONS, FROM, TOP
Compound Symbols:
c5, c12, 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, c47, c48, c50, c51, c52, c53, c54, c56, c57, c58, c59, c60, c61, c62, c63, c8, c, c17, c17
(15) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID) transformation)
Split RHS of tuples not part of any SCC
(16) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(dbl(0)) → mark(0)
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
active(dbls(nil)) → mark(nil)
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1)))
active(sel(0, cons(z0, z1))) → mark(z0)
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
active(indx(nil, z0)) → mark(nil)
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2)))
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(dbl1(0)) → mark(01)
active(dbl1(s(z0))) → mark(s1(s1(dbl1(z0))))
active(sel1(0, cons(z0, z1))) → mark(z0)
active(sel1(s(z0), cons(z1, z2))) → mark(sel1(z0, z2))
active(quote(0)) → mark(01)
active(quote(s(z0))) → mark(s1(quote(z0)))
active(quote(dbl(z0))) → mark(dbl1(z0))
active(quote(sel(z0, z1))) → mark(sel1(z0, z1))
active(dbl(z0)) → dbl(active(z0))
active(dbls(z0)) → dbls(active(z0))
active(sel(z0, z1)) → sel(active(z0), z1)
active(sel(z0, z1)) → sel(z0, active(z1))
active(indx(z0, z1)) → indx(active(z0), z1)
active(dbl1(z0)) → dbl1(active(z0))
active(s1(z0)) → s1(active(z0))
active(sel1(z0, z1)) → sel1(active(z0), z1)
active(sel1(z0, z1)) → sel1(z0, active(z1))
active(quote(z0)) → quote(active(z0))
s(ok(z0)) → ok(s(z0))
dbl(mark(z0)) → mark(dbl(z0))
dbl(ok(z0)) → ok(dbl(z0))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
dbls(mark(z0)) → mark(dbls(z0))
dbls(ok(z0)) → ok(dbls(z0))
sel(mark(z0), z1) → mark(sel(z0, z1))
sel(z0, mark(z1)) → mark(sel(z0, z1))
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
indx(mark(z0), z1) → mark(indx(z0, z1))
indx(ok(z0), ok(z1)) → ok(indx(z0, z1))
s1(mark(z0)) → mark(s1(z0))
s1(ok(z0)) → ok(s1(z0))
dbl1(mark(z0)) → mark(dbl1(z0))
dbl1(ok(z0)) → ok(dbl1(z0))
sel1(mark(z0), z1) → mark(sel1(z0, z1))
sel1(z0, mark(z1)) → mark(sel1(z0, z1))
sel1(ok(z0), ok(z1)) → ok(sel1(z0, z1))
quote(mark(z0)) → mark(quote(z0))
quote(ok(z0)) → ok(quote(z0))
proper(dbl(z0)) → dbl(proper(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(dbls(z0)) → dbls(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
proper(indx(z0, z1)) → indx(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(dbl1(z0)) → dbl1(proper(z0))
proper(01) → ok(01)
proper(s1(z0)) → s1(proper(z0))
proper(sel1(z0, z1)) → sel1(proper(z0), proper(z1))
proper(quote(z0)) → quote(proper(z0))
from(ok(z0)) → ok(from(z0))
Tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(dbls(z0)) → c18(DBLS(active(z0)), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(indx(z0, z1)) → c21(INDX(active(z0), z1), ACTIVE(z0))
ACTIVE(dbl1(z0)) → c22(DBL1(active(z0)), ACTIVE(z0))
ACTIVE(s1(z0)) → c23(S1(active(z0)), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
ACTIVE(quote(z0)) → c26(QUOTE(active(z0)), ACTIVE(z0))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(dbl(z0)) → c45(DBL(proper(z0)), PROPER(z0))
PROPER(s(z0)) → c47(S(proper(z0)), PROPER(z0))
PROPER(dbls(z0)) → c48(DBLS(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c50(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(sel(z0, z1)) → c51(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(indx(z0, z1)) → c52(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c53(FROM(proper(z0)), PROPER(z0))
PROPER(dbl1(z0)) → c54(DBL1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c56(S1(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c57(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)), ACTIVE(dbls(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c17(DBL(mark(cons(dbl(z0), dbls(z1)))), ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)), ACTIVE(indx(nil, z0)))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c17(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))), ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)), ACTIVE(dbl1(0)))
ACTIVE(dbl(dbl1(s(z0)))) → c17(DBL(mark(s1(s1(dbl1(z0))))), ACTIVE(dbl1(s(z0))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)), ACTIVE(quote(0)))
ACTIVE(dbl(quote(s(z0)))) → c17(DBL(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
S tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(dbls(z0)) → c18(DBLS(active(z0)), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(indx(z0, z1)) → c21(INDX(active(z0), z1), ACTIVE(z0))
ACTIVE(dbl1(z0)) → c22(DBL1(active(z0)), ACTIVE(z0))
ACTIVE(s1(z0)) → c23(S1(active(z0)), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
ACTIVE(quote(z0)) → c26(QUOTE(active(z0)), ACTIVE(z0))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(dbl(z0)) → c45(DBL(proper(z0)), PROPER(z0))
PROPER(s(z0)) → c47(S(proper(z0)), PROPER(z0))
PROPER(dbls(z0)) → c48(DBLS(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c50(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(sel(z0, z1)) → c51(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(indx(z0, z1)) → c52(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c53(FROM(proper(z0)), PROPER(z0))
PROPER(dbl1(z0)) → c54(DBL1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c56(S1(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c57(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)), ACTIVE(dbls(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c17(DBL(mark(cons(dbl(z0), dbls(z1)))), ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)), ACTIVE(indx(nil, z0)))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c17(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))), ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)), ACTIVE(dbl1(0)))
ACTIVE(dbl(dbl1(s(z0)))) → c17(DBL(mark(s1(s1(dbl1(z0))))), ACTIVE(dbl1(s(z0))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)), ACTIVE(quote(0)))
ACTIVE(dbl(quote(s(z0)))) → c17(DBL(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
K tuples:none
Defined Rule Symbols:
active, s, dbl, cons, dbls, sel, indx, s1, dbl1, sel1, quote, proper, from
Defined Pair Symbols:
ACTIVE, DBL, DBLS, SEL, INDX, DBL1, S1, SEL1, QUOTE, PROPER, S, CONS, FROM, TOP
Compound Symbols:
c5, c12, 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, c47, c48, c50, c51, c52, c53, c54, c56, c57, c58, c59, c60, c61, c62, c63, c8, c, c17, c17, c1
(17) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
ACTIVE(
dbls(
z0)) →
c18(
DBLS(
active(
z0)),
ACTIVE(
z0)) by
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)), ACTIVE(dbl(0)))
ACTIVE(dbls(dbl(s(z0)))) → c18(DBLS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)), ACTIVE(dbls(nil)))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c18(DBLS(mark(cons(dbl(z0), dbls(z1)))), ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)), ACTIVE(indx(nil, z0)))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c18(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))), ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(from(z0))) → c18(DBLS(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)), ACTIVE(dbl1(0)))
ACTIVE(dbls(dbl1(s(z0)))) → c18(DBLS(mark(s1(s1(dbl1(z0))))), ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)), ACTIVE(quote(0)))
ACTIVE(dbls(quote(s(z0)))) → c18(DBLS(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
(18) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(dbl(0)) → mark(0)
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
active(dbls(nil)) → mark(nil)
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1)))
active(sel(0, cons(z0, z1))) → mark(z0)
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
active(indx(nil, z0)) → mark(nil)
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2)))
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(dbl1(0)) → mark(01)
active(dbl1(s(z0))) → mark(s1(s1(dbl1(z0))))
active(sel1(0, cons(z0, z1))) → mark(z0)
active(sel1(s(z0), cons(z1, z2))) → mark(sel1(z0, z2))
active(quote(0)) → mark(01)
active(quote(s(z0))) → mark(s1(quote(z0)))
active(quote(dbl(z0))) → mark(dbl1(z0))
active(quote(sel(z0, z1))) → mark(sel1(z0, z1))
active(dbl(z0)) → dbl(active(z0))
active(dbls(z0)) → dbls(active(z0))
active(sel(z0, z1)) → sel(active(z0), z1)
active(sel(z0, z1)) → sel(z0, active(z1))
active(indx(z0, z1)) → indx(active(z0), z1)
active(dbl1(z0)) → dbl1(active(z0))
active(s1(z0)) → s1(active(z0))
active(sel1(z0, z1)) → sel1(active(z0), z1)
active(sel1(z0, z1)) → sel1(z0, active(z1))
active(quote(z0)) → quote(active(z0))
s(ok(z0)) → ok(s(z0))
dbl(mark(z0)) → mark(dbl(z0))
dbl(ok(z0)) → ok(dbl(z0))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
dbls(mark(z0)) → mark(dbls(z0))
dbls(ok(z0)) → ok(dbls(z0))
sel(mark(z0), z1) → mark(sel(z0, z1))
sel(z0, mark(z1)) → mark(sel(z0, z1))
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
indx(mark(z0), z1) → mark(indx(z0, z1))
indx(ok(z0), ok(z1)) → ok(indx(z0, z1))
s1(mark(z0)) → mark(s1(z0))
s1(ok(z0)) → ok(s1(z0))
dbl1(mark(z0)) → mark(dbl1(z0))
dbl1(ok(z0)) → ok(dbl1(z0))
sel1(mark(z0), z1) → mark(sel1(z0, z1))
sel1(z0, mark(z1)) → mark(sel1(z0, z1))
sel1(ok(z0), ok(z1)) → ok(sel1(z0, z1))
quote(mark(z0)) → mark(quote(z0))
quote(ok(z0)) → ok(quote(z0))
proper(dbl(z0)) → dbl(proper(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(dbls(z0)) → dbls(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
proper(indx(z0, z1)) → indx(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(dbl1(z0)) → dbl1(proper(z0))
proper(01) → ok(01)
proper(s1(z0)) → s1(proper(z0))
proper(sel1(z0, z1)) → sel1(proper(z0), proper(z1))
proper(quote(z0)) → quote(proper(z0))
from(ok(z0)) → ok(from(z0))
Tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(indx(z0, z1)) → c21(INDX(active(z0), z1), ACTIVE(z0))
ACTIVE(dbl1(z0)) → c22(DBL1(active(z0)), ACTIVE(z0))
ACTIVE(s1(z0)) → c23(S1(active(z0)), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
ACTIVE(quote(z0)) → c26(QUOTE(active(z0)), ACTIVE(z0))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(dbl(z0)) → c45(DBL(proper(z0)), PROPER(z0))
PROPER(s(z0)) → c47(S(proper(z0)), PROPER(z0))
PROPER(dbls(z0)) → c48(DBLS(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c50(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(sel(z0, z1)) → c51(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(indx(z0, z1)) → c52(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c53(FROM(proper(z0)), PROPER(z0))
PROPER(dbl1(z0)) → c54(DBL1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c56(S1(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c57(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)), ACTIVE(dbls(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c17(DBL(mark(cons(dbl(z0), dbls(z1)))), ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)), ACTIVE(indx(nil, z0)))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c17(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))), ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)), ACTIVE(dbl1(0)))
ACTIVE(dbl(dbl1(s(z0)))) → c17(DBL(mark(s1(s1(dbl1(z0))))), ACTIVE(dbl1(s(z0))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)), ACTIVE(quote(0)))
ACTIVE(dbl(quote(s(z0)))) → c17(DBL(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)), ACTIVE(dbl(0)))
ACTIVE(dbls(dbl(s(z0)))) → c18(DBLS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)), ACTIVE(dbls(nil)))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c18(DBLS(mark(cons(dbl(z0), dbls(z1)))), ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)), ACTIVE(indx(nil, z0)))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c18(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))), ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(from(z0))) → c18(DBLS(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)), ACTIVE(dbl1(0)))
ACTIVE(dbls(dbl1(s(z0)))) → c18(DBLS(mark(s1(s1(dbl1(z0))))), ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)), ACTIVE(quote(0)))
ACTIVE(dbls(quote(s(z0)))) → c18(DBLS(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
S tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(indx(z0, z1)) → c21(INDX(active(z0), z1), ACTIVE(z0))
ACTIVE(dbl1(z0)) → c22(DBL1(active(z0)), ACTIVE(z0))
ACTIVE(s1(z0)) → c23(S1(active(z0)), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
ACTIVE(quote(z0)) → c26(QUOTE(active(z0)), ACTIVE(z0))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(dbl(z0)) → c45(DBL(proper(z0)), PROPER(z0))
PROPER(s(z0)) → c47(S(proper(z0)), PROPER(z0))
PROPER(dbls(z0)) → c48(DBLS(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c50(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(sel(z0, z1)) → c51(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(indx(z0, z1)) → c52(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c53(FROM(proper(z0)), PROPER(z0))
PROPER(dbl1(z0)) → c54(DBL1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c56(S1(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c57(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)), ACTIVE(dbls(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c17(DBL(mark(cons(dbl(z0), dbls(z1)))), ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)), ACTIVE(indx(nil, z0)))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c17(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))), ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)), ACTIVE(dbl1(0)))
ACTIVE(dbl(dbl1(s(z0)))) → c17(DBL(mark(s1(s1(dbl1(z0))))), ACTIVE(dbl1(s(z0))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)), ACTIVE(quote(0)))
ACTIVE(dbl(quote(s(z0)))) → c17(DBL(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)), ACTIVE(dbl(0)))
ACTIVE(dbls(dbl(s(z0)))) → c18(DBLS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)), ACTIVE(dbls(nil)))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c18(DBLS(mark(cons(dbl(z0), dbls(z1)))), ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)), ACTIVE(indx(nil, z0)))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c18(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))), ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(from(z0))) → c18(DBLS(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)), ACTIVE(dbl1(0)))
ACTIVE(dbls(dbl1(s(z0)))) → c18(DBLS(mark(s1(s1(dbl1(z0))))), ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)), ACTIVE(quote(0)))
ACTIVE(dbls(quote(s(z0)))) → c18(DBLS(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
K tuples:none
Defined Rule Symbols:
active, s, dbl, cons, dbls, sel, indx, s1, dbl1, sel1, quote, proper, from
Defined Pair Symbols:
ACTIVE, DBL, DBLS, SEL, INDX, DBL1, S1, SEL1, QUOTE, PROPER, S, CONS, FROM, TOP
Compound Symbols:
c5, c12, c15, c16, 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, c47, c48, c50, c51, c52, c53, c54, c56, c57, c58, c59, c60, c61, c62, c63, c8, c, c17, c17, c1, c18
(19) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 3 trailing tuple parts
(20) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(dbl(0)) → mark(0)
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
active(dbls(nil)) → mark(nil)
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1)))
active(sel(0, cons(z0, z1))) → mark(z0)
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
active(indx(nil, z0)) → mark(nil)
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2)))
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(dbl1(0)) → mark(01)
active(dbl1(s(z0))) → mark(s1(s1(dbl1(z0))))
active(sel1(0, cons(z0, z1))) → mark(z0)
active(sel1(s(z0), cons(z1, z2))) → mark(sel1(z0, z2))
active(quote(0)) → mark(01)
active(quote(s(z0))) → mark(s1(quote(z0)))
active(quote(dbl(z0))) → mark(dbl1(z0))
active(quote(sel(z0, z1))) → mark(sel1(z0, z1))
active(dbl(z0)) → dbl(active(z0))
active(dbls(z0)) → dbls(active(z0))
active(sel(z0, z1)) → sel(active(z0), z1)
active(sel(z0, z1)) → sel(z0, active(z1))
active(indx(z0, z1)) → indx(active(z0), z1)
active(dbl1(z0)) → dbl1(active(z0))
active(s1(z0)) → s1(active(z0))
active(sel1(z0, z1)) → sel1(active(z0), z1)
active(sel1(z0, z1)) → sel1(z0, active(z1))
active(quote(z0)) → quote(active(z0))
s(ok(z0)) → ok(s(z0))
dbl(mark(z0)) → mark(dbl(z0))
dbl(ok(z0)) → ok(dbl(z0))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
dbls(mark(z0)) → mark(dbls(z0))
dbls(ok(z0)) → ok(dbls(z0))
sel(mark(z0), z1) → mark(sel(z0, z1))
sel(z0, mark(z1)) → mark(sel(z0, z1))
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
indx(mark(z0), z1) → mark(indx(z0, z1))
indx(ok(z0), ok(z1)) → ok(indx(z0, z1))
s1(mark(z0)) → mark(s1(z0))
s1(ok(z0)) → ok(s1(z0))
dbl1(mark(z0)) → mark(dbl1(z0))
dbl1(ok(z0)) → ok(dbl1(z0))
sel1(mark(z0), z1) → mark(sel1(z0, z1))
sel1(z0, mark(z1)) → mark(sel1(z0, z1))
sel1(ok(z0), ok(z1)) → ok(sel1(z0, z1))
quote(mark(z0)) → mark(quote(z0))
quote(ok(z0)) → ok(quote(z0))
proper(dbl(z0)) → dbl(proper(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(dbls(z0)) → dbls(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
proper(indx(z0, z1)) → indx(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(dbl1(z0)) → dbl1(proper(z0))
proper(01) → ok(01)
proper(s1(z0)) → s1(proper(z0))
proper(sel1(z0, z1)) → sel1(proper(z0), proper(z1))
proper(quote(z0)) → quote(proper(z0))
from(ok(z0)) → ok(from(z0))
Tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(indx(z0, z1)) → c21(INDX(active(z0), z1), ACTIVE(z0))
ACTIVE(dbl1(z0)) → c22(DBL1(active(z0)), ACTIVE(z0))
ACTIVE(s1(z0)) → c23(S1(active(z0)), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
ACTIVE(quote(z0)) → c26(QUOTE(active(z0)), ACTIVE(z0))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(dbl(z0)) → c45(DBL(proper(z0)), PROPER(z0))
PROPER(s(z0)) → c47(S(proper(z0)), PROPER(z0))
PROPER(dbls(z0)) → c48(DBLS(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c50(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(sel(z0, z1)) → c51(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(indx(z0, z1)) → c52(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c53(FROM(proper(z0)), PROPER(z0))
PROPER(dbl1(z0)) → c54(DBL1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c56(S1(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c57(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c17(DBL(mark(cons(dbl(z0), dbls(z1)))), ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)), ACTIVE(indx(nil, z0)))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c17(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))), ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)), ACTIVE(dbl1(0)))
ACTIVE(dbl(dbl1(s(z0)))) → c17(DBL(mark(s1(s1(dbl1(z0))))), ACTIVE(dbl1(s(z0))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)), ACTIVE(quote(0)))
ACTIVE(dbl(quote(s(z0)))) → c17(DBL(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
ACTIVE(dbls(dbl(s(z0)))) → c18(DBLS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c18(DBLS(mark(cons(dbl(z0), dbls(z1)))), ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)), ACTIVE(indx(nil, z0)))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c18(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))), ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(from(z0))) → c18(DBLS(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)), ACTIVE(dbl1(0)))
ACTIVE(dbls(dbl1(s(z0)))) → c18(DBLS(mark(s1(s1(dbl1(z0))))), ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)), ACTIVE(quote(0)))
ACTIVE(dbls(quote(s(z0)))) → c18(DBLS(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)))
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)))
S tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(indx(z0, z1)) → c21(INDX(active(z0), z1), ACTIVE(z0))
ACTIVE(dbl1(z0)) → c22(DBL1(active(z0)), ACTIVE(z0))
ACTIVE(s1(z0)) → c23(S1(active(z0)), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
ACTIVE(quote(z0)) → c26(QUOTE(active(z0)), ACTIVE(z0))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(dbl(z0)) → c45(DBL(proper(z0)), PROPER(z0))
PROPER(s(z0)) → c47(S(proper(z0)), PROPER(z0))
PROPER(dbls(z0)) → c48(DBLS(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c50(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(sel(z0, z1)) → c51(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(indx(z0, z1)) → c52(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c53(FROM(proper(z0)), PROPER(z0))
PROPER(dbl1(z0)) → c54(DBL1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c56(S1(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c57(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c17(DBL(mark(cons(dbl(z0), dbls(z1)))), ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)), ACTIVE(indx(nil, z0)))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c17(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))), ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)), ACTIVE(dbl1(0)))
ACTIVE(dbl(dbl1(s(z0)))) → c17(DBL(mark(s1(s1(dbl1(z0))))), ACTIVE(dbl1(s(z0))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)), ACTIVE(quote(0)))
ACTIVE(dbl(quote(s(z0)))) → c17(DBL(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
ACTIVE(dbls(dbl(s(z0)))) → c18(DBLS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c18(DBLS(mark(cons(dbl(z0), dbls(z1)))), ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)), ACTIVE(indx(nil, z0)))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c18(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))), ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(from(z0))) → c18(DBLS(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)), ACTIVE(dbl1(0)))
ACTIVE(dbls(dbl1(s(z0)))) → c18(DBLS(mark(s1(s1(dbl1(z0))))), ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)), ACTIVE(quote(0)))
ACTIVE(dbls(quote(s(z0)))) → c18(DBLS(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)))
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)))
K tuples:none
Defined Rule Symbols:
active, s, dbl, cons, dbls, sel, indx, s1, dbl1, sel1, quote, proper, from
Defined Pair Symbols:
ACTIVE, DBL, DBLS, SEL, INDX, DBL1, S1, SEL1, QUOTE, PROPER, S, CONS, FROM, TOP
Compound Symbols:
c5, c12, c15, c16, 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, c47, c48, c50, c51, c52, c53, c54, c56, c57, c58, c59, c60, c61, c62, c63, c8, c, c17, c17, c1, c18, c18
(21) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID) transformation)
Split RHS of tuples not part of any SCC
(22) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(dbl(0)) → mark(0)
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
active(dbls(nil)) → mark(nil)
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1)))
active(sel(0, cons(z0, z1))) → mark(z0)
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
active(indx(nil, z0)) → mark(nil)
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2)))
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(dbl1(0)) → mark(01)
active(dbl1(s(z0))) → mark(s1(s1(dbl1(z0))))
active(sel1(0, cons(z0, z1))) → mark(z0)
active(sel1(s(z0), cons(z1, z2))) → mark(sel1(z0, z2))
active(quote(0)) → mark(01)
active(quote(s(z0))) → mark(s1(quote(z0)))
active(quote(dbl(z0))) → mark(dbl1(z0))
active(quote(sel(z0, z1))) → mark(sel1(z0, z1))
active(dbl(z0)) → dbl(active(z0))
active(dbls(z0)) → dbls(active(z0))
active(sel(z0, z1)) → sel(active(z0), z1)
active(sel(z0, z1)) → sel(z0, active(z1))
active(indx(z0, z1)) → indx(active(z0), z1)
active(dbl1(z0)) → dbl1(active(z0))
active(s1(z0)) → s1(active(z0))
active(sel1(z0, z1)) → sel1(active(z0), z1)
active(sel1(z0, z1)) → sel1(z0, active(z1))
active(quote(z0)) → quote(active(z0))
s(ok(z0)) → ok(s(z0))
dbl(mark(z0)) → mark(dbl(z0))
dbl(ok(z0)) → ok(dbl(z0))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
dbls(mark(z0)) → mark(dbls(z0))
dbls(ok(z0)) → ok(dbls(z0))
sel(mark(z0), z1) → mark(sel(z0, z1))
sel(z0, mark(z1)) → mark(sel(z0, z1))
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
indx(mark(z0), z1) → mark(indx(z0, z1))
indx(ok(z0), ok(z1)) → ok(indx(z0, z1))
s1(mark(z0)) → mark(s1(z0))
s1(ok(z0)) → ok(s1(z0))
dbl1(mark(z0)) → mark(dbl1(z0))
dbl1(ok(z0)) → ok(dbl1(z0))
sel1(mark(z0), z1) → mark(sel1(z0, z1))
sel1(z0, mark(z1)) → mark(sel1(z0, z1))
sel1(ok(z0), ok(z1)) → ok(sel1(z0, z1))
quote(mark(z0)) → mark(quote(z0))
quote(ok(z0)) → ok(quote(z0))
proper(dbl(z0)) → dbl(proper(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(dbls(z0)) → dbls(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
proper(indx(z0, z1)) → indx(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(dbl1(z0)) → dbl1(proper(z0))
proper(01) → ok(01)
proper(s1(z0)) → s1(proper(z0))
proper(sel1(z0, z1)) → sel1(proper(z0), proper(z1))
proper(quote(z0)) → quote(proper(z0))
from(ok(z0)) → ok(from(z0))
Tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(indx(z0, z1)) → c21(INDX(active(z0), z1), ACTIVE(z0))
ACTIVE(dbl1(z0)) → c22(DBL1(active(z0)), ACTIVE(z0))
ACTIVE(s1(z0)) → c23(S1(active(z0)), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
ACTIVE(quote(z0)) → c26(QUOTE(active(z0)), ACTIVE(z0))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(dbl(z0)) → c45(DBL(proper(z0)), PROPER(z0))
PROPER(s(z0)) → c47(S(proper(z0)), PROPER(z0))
PROPER(dbls(z0)) → c48(DBLS(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c50(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(sel(z0, z1)) → c51(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(indx(z0, z1)) → c52(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c53(FROM(proper(z0)), PROPER(z0))
PROPER(dbl1(z0)) → c54(DBL1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c56(S1(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c57(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)), ACTIVE(indx(nil, z0)))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c17(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))), ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)), ACTIVE(dbl1(0)))
ACTIVE(dbl(dbl1(s(z0)))) → c17(DBL(mark(s1(s1(dbl1(z0))))), ACTIVE(dbl1(s(z0))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)), ACTIVE(quote(0)))
ACTIVE(dbl(quote(s(z0)))) → c17(DBL(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)), ACTIVE(indx(nil, z0)))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c18(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))), ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)), ACTIVE(dbl1(0)))
ACTIVE(dbls(dbl1(s(z0)))) → c18(DBLS(mark(s1(s1(dbl1(z0))))), ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)), ACTIVE(quote(0)))
ACTIVE(dbls(quote(s(z0)))) → c18(DBLS(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)))
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0))))))
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0))))))
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0)))
S tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(indx(z0, z1)) → c21(INDX(active(z0), z1), ACTIVE(z0))
ACTIVE(dbl1(z0)) → c22(DBL1(active(z0)), ACTIVE(z0))
ACTIVE(s1(z0)) → c23(S1(active(z0)), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
ACTIVE(quote(z0)) → c26(QUOTE(active(z0)), ACTIVE(z0))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(dbl(z0)) → c45(DBL(proper(z0)), PROPER(z0))
PROPER(s(z0)) → c47(S(proper(z0)), PROPER(z0))
PROPER(dbls(z0)) → c48(DBLS(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c50(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(sel(z0, z1)) → c51(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(indx(z0, z1)) → c52(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c53(FROM(proper(z0)), PROPER(z0))
PROPER(dbl1(z0)) → c54(DBL1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c56(S1(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c57(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)), ACTIVE(indx(nil, z0)))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c17(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))), ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)), ACTIVE(dbl1(0)))
ACTIVE(dbl(dbl1(s(z0)))) → c17(DBL(mark(s1(s1(dbl1(z0))))), ACTIVE(dbl1(s(z0))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)), ACTIVE(quote(0)))
ACTIVE(dbl(quote(s(z0)))) → c17(DBL(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)), ACTIVE(indx(nil, z0)))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c18(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))), ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)), ACTIVE(dbl1(0)))
ACTIVE(dbls(dbl1(s(z0)))) → c18(DBLS(mark(s1(s1(dbl1(z0))))), ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)), ACTIVE(quote(0)))
ACTIVE(dbls(quote(s(z0)))) → c18(DBLS(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)))
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0))))))
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0))))))
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0)))
K tuples:none
Defined Rule Symbols:
active, s, dbl, cons, dbls, sel, indx, s1, dbl1, sel1, quote, proper, from
Defined Pair Symbols:
ACTIVE, DBL, DBLS, SEL, INDX, DBL1, S1, SEL1, QUOTE, PROPER, S, CONS, FROM, TOP
Compound Symbols:
c5, c12, c15, c16, 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, c47, c48, c50, c51, c52, c53, c54, c56, c57, c58, c59, c60, c61, c62, c63, c8, c, c17, c17, c1, c18, c18, c2
(23) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
ACTIVE(
indx(
z0,
z1)) →
c21(
INDX(
active(
z0),
z1),
ACTIVE(
z0)) by
ACTIVE(indx(dbl(0), x1)) → c21(INDX(mark(0), x1), ACTIVE(dbl(0)))
ACTIVE(indx(dbl(s(z0)), x1)) → c21(INDX(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0))))
ACTIVE(indx(dbls(nil), x1)) → c21(INDX(mark(nil), x1), ACTIVE(dbls(nil)))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c21(INDX(mark(cons(dbl(z0), dbls(z1))), x1), ACTIVE(dbls(cons(z0, z1))))
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(indx(indx(nil, z0), x1)) → c21(INDX(mark(nil), x1), ACTIVE(indx(nil, z0)))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c21(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1), ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(from(z0), x1)) → c21(INDX(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(indx(dbl1(0), x1)) → c21(INDX(mark(01), x1), ACTIVE(dbl1(0)))
ACTIVE(indx(dbl1(s(z0)), x1)) → c21(INDX(mark(s1(s1(dbl1(z0)))), x1), ACTIVE(dbl1(s(z0))))
ACTIVE(indx(sel1(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(indx(sel1(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel1(z0, z2)), x1), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(indx(quote(0), x1)) → c21(INDX(mark(01), x1), ACTIVE(quote(0)))
ACTIVE(indx(quote(s(z0)), x1)) → c21(INDX(mark(s1(quote(z0))), x1), ACTIVE(quote(s(z0))))
ACTIVE(indx(quote(dbl(z0)), x1)) → c21(INDX(mark(dbl1(z0)), x1), ACTIVE(quote(dbl(z0))))
ACTIVE(indx(quote(sel(z0, z1)), x1)) → c21(INDX(mark(sel1(z0, z1)), x1), ACTIVE(quote(sel(z0, z1))))
ACTIVE(indx(dbl(z0), x1)) → c21(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
ACTIVE(indx(dbls(z0), x1)) → c21(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(indx(z0, z1), x1)) → c21(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1)))
ACTIVE(indx(dbl1(z0), x1)) → c21(INDX(dbl1(active(z0)), x1), ACTIVE(dbl1(z0)))
ACTIVE(indx(s1(z0), x1)) → c21(INDX(s1(active(z0)), x1), ACTIVE(s1(z0)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(active(z0), z1), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(z0, active(z1)), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(quote(z0), x1)) → c21(INDX(quote(active(z0)), x1), ACTIVE(quote(z0)))
(24) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(dbl(0)) → mark(0)
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
active(dbls(nil)) → mark(nil)
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1)))
active(sel(0, cons(z0, z1))) → mark(z0)
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
active(indx(nil, z0)) → mark(nil)
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2)))
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(dbl1(0)) → mark(01)
active(dbl1(s(z0))) → mark(s1(s1(dbl1(z0))))
active(sel1(0, cons(z0, z1))) → mark(z0)
active(sel1(s(z0), cons(z1, z2))) → mark(sel1(z0, z2))
active(quote(0)) → mark(01)
active(quote(s(z0))) → mark(s1(quote(z0)))
active(quote(dbl(z0))) → mark(dbl1(z0))
active(quote(sel(z0, z1))) → mark(sel1(z0, z1))
active(dbl(z0)) → dbl(active(z0))
active(dbls(z0)) → dbls(active(z0))
active(sel(z0, z1)) → sel(active(z0), z1)
active(sel(z0, z1)) → sel(z0, active(z1))
active(indx(z0, z1)) → indx(active(z0), z1)
active(dbl1(z0)) → dbl1(active(z0))
active(s1(z0)) → s1(active(z0))
active(sel1(z0, z1)) → sel1(active(z0), z1)
active(sel1(z0, z1)) → sel1(z0, active(z1))
active(quote(z0)) → quote(active(z0))
s(ok(z0)) → ok(s(z0))
dbl(mark(z0)) → mark(dbl(z0))
dbl(ok(z0)) → ok(dbl(z0))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
dbls(mark(z0)) → mark(dbls(z0))
dbls(ok(z0)) → ok(dbls(z0))
sel(mark(z0), z1) → mark(sel(z0, z1))
sel(z0, mark(z1)) → mark(sel(z0, z1))
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
indx(mark(z0), z1) → mark(indx(z0, z1))
indx(ok(z0), ok(z1)) → ok(indx(z0, z1))
s1(mark(z0)) → mark(s1(z0))
s1(ok(z0)) → ok(s1(z0))
dbl1(mark(z0)) → mark(dbl1(z0))
dbl1(ok(z0)) → ok(dbl1(z0))
sel1(mark(z0), z1) → mark(sel1(z0, z1))
sel1(z0, mark(z1)) → mark(sel1(z0, z1))
sel1(ok(z0), ok(z1)) → ok(sel1(z0, z1))
quote(mark(z0)) → mark(quote(z0))
quote(ok(z0)) → ok(quote(z0))
proper(dbl(z0)) → dbl(proper(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(dbls(z0)) → dbls(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
proper(indx(z0, z1)) → indx(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(dbl1(z0)) → dbl1(proper(z0))
proper(01) → ok(01)
proper(s1(z0)) → s1(proper(z0))
proper(sel1(z0, z1)) → sel1(proper(z0), proper(z1))
proper(quote(z0)) → quote(proper(z0))
from(ok(z0)) → ok(from(z0))
Tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(dbl1(z0)) → c22(DBL1(active(z0)), ACTIVE(z0))
ACTIVE(s1(z0)) → c23(S1(active(z0)), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
ACTIVE(quote(z0)) → c26(QUOTE(active(z0)), ACTIVE(z0))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(dbl(z0)) → c45(DBL(proper(z0)), PROPER(z0))
PROPER(s(z0)) → c47(S(proper(z0)), PROPER(z0))
PROPER(dbls(z0)) → c48(DBLS(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c50(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(sel(z0, z1)) → c51(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(indx(z0, z1)) → c52(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c53(FROM(proper(z0)), PROPER(z0))
PROPER(dbl1(z0)) → c54(DBL1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c56(S1(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c57(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)), ACTIVE(indx(nil, z0)))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c17(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))), ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)), ACTIVE(dbl1(0)))
ACTIVE(dbl(dbl1(s(z0)))) → c17(DBL(mark(s1(s1(dbl1(z0))))), ACTIVE(dbl1(s(z0))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)), ACTIVE(quote(0)))
ACTIVE(dbl(quote(s(z0)))) → c17(DBL(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)), ACTIVE(indx(nil, z0)))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c18(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))), ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)), ACTIVE(dbl1(0)))
ACTIVE(dbls(dbl1(s(z0)))) → c18(DBLS(mark(s1(s1(dbl1(z0))))), ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)), ACTIVE(quote(0)))
ACTIVE(dbls(quote(s(z0)))) → c18(DBLS(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)))
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0))))))
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0))))))
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0)))
ACTIVE(indx(dbl(0), x1)) → c21(INDX(mark(0), x1), ACTIVE(dbl(0)))
ACTIVE(indx(dbl(s(z0)), x1)) → c21(INDX(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0))))
ACTIVE(indx(dbls(nil), x1)) → c21(INDX(mark(nil), x1), ACTIVE(dbls(nil)))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c21(INDX(mark(cons(dbl(z0), dbls(z1))), x1), ACTIVE(dbls(cons(z0, z1))))
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(indx(indx(nil, z0), x1)) → c21(INDX(mark(nil), x1), ACTIVE(indx(nil, z0)))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c21(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1), ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(from(z0), x1)) → c21(INDX(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(indx(dbl1(0), x1)) → c21(INDX(mark(01), x1), ACTIVE(dbl1(0)))
ACTIVE(indx(dbl1(s(z0)), x1)) → c21(INDX(mark(s1(s1(dbl1(z0)))), x1), ACTIVE(dbl1(s(z0))))
ACTIVE(indx(sel1(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(indx(sel1(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel1(z0, z2)), x1), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(indx(quote(0), x1)) → c21(INDX(mark(01), x1), ACTIVE(quote(0)))
ACTIVE(indx(quote(s(z0)), x1)) → c21(INDX(mark(s1(quote(z0))), x1), ACTIVE(quote(s(z0))))
ACTIVE(indx(quote(dbl(z0)), x1)) → c21(INDX(mark(dbl1(z0)), x1), ACTIVE(quote(dbl(z0))))
ACTIVE(indx(quote(sel(z0, z1)), x1)) → c21(INDX(mark(sel1(z0, z1)), x1), ACTIVE(quote(sel(z0, z1))))
ACTIVE(indx(dbl(z0), x1)) → c21(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
ACTIVE(indx(dbls(z0), x1)) → c21(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(indx(z0, z1), x1)) → c21(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1)))
ACTIVE(indx(dbl1(z0), x1)) → c21(INDX(dbl1(active(z0)), x1), ACTIVE(dbl1(z0)))
ACTIVE(indx(s1(z0), x1)) → c21(INDX(s1(active(z0)), x1), ACTIVE(s1(z0)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(active(z0), z1), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(z0, active(z1)), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(quote(z0), x1)) → c21(INDX(quote(active(z0)), x1), ACTIVE(quote(z0)))
S tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(dbl1(z0)) → c22(DBL1(active(z0)), ACTIVE(z0))
ACTIVE(s1(z0)) → c23(S1(active(z0)), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
ACTIVE(quote(z0)) → c26(QUOTE(active(z0)), ACTIVE(z0))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(dbl(z0)) → c45(DBL(proper(z0)), PROPER(z0))
PROPER(s(z0)) → c47(S(proper(z0)), PROPER(z0))
PROPER(dbls(z0)) → c48(DBLS(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c50(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(sel(z0, z1)) → c51(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(indx(z0, z1)) → c52(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c53(FROM(proper(z0)), PROPER(z0))
PROPER(dbl1(z0)) → c54(DBL1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c56(S1(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c57(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)), ACTIVE(indx(nil, z0)))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c17(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))), ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)), ACTIVE(dbl1(0)))
ACTIVE(dbl(dbl1(s(z0)))) → c17(DBL(mark(s1(s1(dbl1(z0))))), ACTIVE(dbl1(s(z0))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)), ACTIVE(quote(0)))
ACTIVE(dbl(quote(s(z0)))) → c17(DBL(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)), ACTIVE(indx(nil, z0)))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c18(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))), ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)), ACTIVE(dbl1(0)))
ACTIVE(dbls(dbl1(s(z0)))) → c18(DBLS(mark(s1(s1(dbl1(z0))))), ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)), ACTIVE(quote(0)))
ACTIVE(dbls(quote(s(z0)))) → c18(DBLS(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)))
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0))))))
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0))))))
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0)))
ACTIVE(indx(dbl(0), x1)) → c21(INDX(mark(0), x1), ACTIVE(dbl(0)))
ACTIVE(indx(dbl(s(z0)), x1)) → c21(INDX(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0))))
ACTIVE(indx(dbls(nil), x1)) → c21(INDX(mark(nil), x1), ACTIVE(dbls(nil)))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c21(INDX(mark(cons(dbl(z0), dbls(z1))), x1), ACTIVE(dbls(cons(z0, z1))))
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(indx(indx(nil, z0), x1)) → c21(INDX(mark(nil), x1), ACTIVE(indx(nil, z0)))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c21(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1), ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(from(z0), x1)) → c21(INDX(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(indx(dbl1(0), x1)) → c21(INDX(mark(01), x1), ACTIVE(dbl1(0)))
ACTIVE(indx(dbl1(s(z0)), x1)) → c21(INDX(mark(s1(s1(dbl1(z0)))), x1), ACTIVE(dbl1(s(z0))))
ACTIVE(indx(sel1(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(indx(sel1(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel1(z0, z2)), x1), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(indx(quote(0), x1)) → c21(INDX(mark(01), x1), ACTIVE(quote(0)))
ACTIVE(indx(quote(s(z0)), x1)) → c21(INDX(mark(s1(quote(z0))), x1), ACTIVE(quote(s(z0))))
ACTIVE(indx(quote(dbl(z0)), x1)) → c21(INDX(mark(dbl1(z0)), x1), ACTIVE(quote(dbl(z0))))
ACTIVE(indx(quote(sel(z0, z1)), x1)) → c21(INDX(mark(sel1(z0, z1)), x1), ACTIVE(quote(sel(z0, z1))))
ACTIVE(indx(dbl(z0), x1)) → c21(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
ACTIVE(indx(dbls(z0), x1)) → c21(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(indx(z0, z1), x1)) → c21(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1)))
ACTIVE(indx(dbl1(z0), x1)) → c21(INDX(dbl1(active(z0)), x1), ACTIVE(dbl1(z0)))
ACTIVE(indx(s1(z0), x1)) → c21(INDX(s1(active(z0)), x1), ACTIVE(s1(z0)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(active(z0), z1), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(z0, active(z1)), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(quote(z0), x1)) → c21(INDX(quote(active(z0)), x1), ACTIVE(quote(z0)))
K tuples:none
Defined Rule Symbols:
active, s, dbl, cons, dbls, sel, indx, s1, dbl1, sel1, quote, proper, from
Defined Pair Symbols:
ACTIVE, DBL, DBLS, SEL, INDX, DBL1, S1, SEL1, QUOTE, PROPER, S, CONS, FROM, TOP
Compound Symbols:
c5, c12, c15, c16, c19, c20, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c47, c48, c50, c51, c52, c53, c54, c56, c57, c58, c59, c60, c61, c62, c63, c8, c, c17, c17, c1, c18, c18, c2, c21
(25) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 5 trailing tuple parts
(26) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(dbl(0)) → mark(0)
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
active(dbls(nil)) → mark(nil)
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1)))
active(sel(0, cons(z0, z1))) → mark(z0)
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
active(indx(nil, z0)) → mark(nil)
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2)))
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(dbl1(0)) → mark(01)
active(dbl1(s(z0))) → mark(s1(s1(dbl1(z0))))
active(sel1(0, cons(z0, z1))) → mark(z0)
active(sel1(s(z0), cons(z1, z2))) → mark(sel1(z0, z2))
active(quote(0)) → mark(01)
active(quote(s(z0))) → mark(s1(quote(z0)))
active(quote(dbl(z0))) → mark(dbl1(z0))
active(quote(sel(z0, z1))) → mark(sel1(z0, z1))
active(dbl(z0)) → dbl(active(z0))
active(dbls(z0)) → dbls(active(z0))
active(sel(z0, z1)) → sel(active(z0), z1)
active(sel(z0, z1)) → sel(z0, active(z1))
active(indx(z0, z1)) → indx(active(z0), z1)
active(dbl1(z0)) → dbl1(active(z0))
active(s1(z0)) → s1(active(z0))
active(sel1(z0, z1)) → sel1(active(z0), z1)
active(sel1(z0, z1)) → sel1(z0, active(z1))
active(quote(z0)) → quote(active(z0))
s(ok(z0)) → ok(s(z0))
dbl(mark(z0)) → mark(dbl(z0))
dbl(ok(z0)) → ok(dbl(z0))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
dbls(mark(z0)) → mark(dbls(z0))
dbls(ok(z0)) → ok(dbls(z0))
sel(mark(z0), z1) → mark(sel(z0, z1))
sel(z0, mark(z1)) → mark(sel(z0, z1))
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
indx(mark(z0), z1) → mark(indx(z0, z1))
indx(ok(z0), ok(z1)) → ok(indx(z0, z1))
s1(mark(z0)) → mark(s1(z0))
s1(ok(z0)) → ok(s1(z0))
dbl1(mark(z0)) → mark(dbl1(z0))
dbl1(ok(z0)) → ok(dbl1(z0))
sel1(mark(z0), z1) → mark(sel1(z0, z1))
sel1(z0, mark(z1)) → mark(sel1(z0, z1))
sel1(ok(z0), ok(z1)) → ok(sel1(z0, z1))
quote(mark(z0)) → mark(quote(z0))
quote(ok(z0)) → ok(quote(z0))
proper(dbl(z0)) → dbl(proper(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(dbls(z0)) → dbls(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
proper(indx(z0, z1)) → indx(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(dbl1(z0)) → dbl1(proper(z0))
proper(01) → ok(01)
proper(s1(z0)) → s1(proper(z0))
proper(sel1(z0, z1)) → sel1(proper(z0), proper(z1))
proper(quote(z0)) → quote(proper(z0))
from(ok(z0)) → ok(from(z0))
Tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(dbl1(z0)) → c22(DBL1(active(z0)), ACTIVE(z0))
ACTIVE(s1(z0)) → c23(S1(active(z0)), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
ACTIVE(quote(z0)) → c26(QUOTE(active(z0)), ACTIVE(z0))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(dbl(z0)) → c45(DBL(proper(z0)), PROPER(z0))
PROPER(s(z0)) → c47(S(proper(z0)), PROPER(z0))
PROPER(dbls(z0)) → c48(DBLS(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c50(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(sel(z0, z1)) → c51(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(indx(z0, z1)) → c52(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c53(FROM(proper(z0)), PROPER(z0))
PROPER(dbl1(z0)) → c54(DBL1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c56(S1(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c57(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c17(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))), ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)), ACTIVE(dbl1(0)))
ACTIVE(dbl(dbl1(s(z0)))) → c17(DBL(mark(s1(s1(dbl1(z0))))), ACTIVE(dbl1(s(z0))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)), ACTIVE(quote(0)))
ACTIVE(dbl(quote(s(z0)))) → c17(DBL(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c18(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))), ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)), ACTIVE(dbl1(0)))
ACTIVE(dbls(dbl1(s(z0)))) → c18(DBLS(mark(s1(s1(dbl1(z0))))), ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)), ACTIVE(quote(0)))
ACTIVE(dbls(quote(s(z0)))) → c18(DBLS(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)))
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0))))))
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0))))))
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0)))
ACTIVE(indx(dbl(s(z0)), x1)) → c21(INDX(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0))))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c21(INDX(mark(cons(dbl(z0), dbls(z1))), x1), ACTIVE(dbls(cons(z0, z1))))
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c21(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1), ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(from(z0), x1)) → c21(INDX(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(indx(dbl1(0), x1)) → c21(INDX(mark(01), x1), ACTIVE(dbl1(0)))
ACTIVE(indx(dbl1(s(z0)), x1)) → c21(INDX(mark(s1(s1(dbl1(z0)))), x1), ACTIVE(dbl1(s(z0))))
ACTIVE(indx(sel1(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(indx(sel1(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel1(z0, z2)), x1), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(indx(quote(0), x1)) → c21(INDX(mark(01), x1), ACTIVE(quote(0)))
ACTIVE(indx(quote(s(z0)), x1)) → c21(INDX(mark(s1(quote(z0))), x1), ACTIVE(quote(s(z0))))
ACTIVE(indx(quote(dbl(z0)), x1)) → c21(INDX(mark(dbl1(z0)), x1), ACTIVE(quote(dbl(z0))))
ACTIVE(indx(quote(sel(z0, z1)), x1)) → c21(INDX(mark(sel1(z0, z1)), x1), ACTIVE(quote(sel(z0, z1))))
ACTIVE(indx(dbl(z0), x1)) → c21(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
ACTIVE(indx(dbls(z0), x1)) → c21(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(indx(z0, z1), x1)) → c21(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1)))
ACTIVE(indx(dbl1(z0), x1)) → c21(INDX(dbl1(active(z0)), x1), ACTIVE(dbl1(z0)))
ACTIVE(indx(s1(z0), x1)) → c21(INDX(s1(active(z0)), x1), ACTIVE(s1(z0)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(active(z0), z1), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(z0, active(z1)), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(quote(z0), x1)) → c21(INDX(quote(active(z0)), x1), ACTIVE(quote(z0)))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)))
ACTIVE(indx(dbl(0), x1)) → c21(INDX(mark(0), x1))
ACTIVE(indx(dbls(nil), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(indx(indx(nil, z0), x1)) → c21(INDX(mark(nil), x1))
S tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(dbl1(z0)) → c22(DBL1(active(z0)), ACTIVE(z0))
ACTIVE(s1(z0)) → c23(S1(active(z0)), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
ACTIVE(quote(z0)) → c26(QUOTE(active(z0)), ACTIVE(z0))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(dbl(z0)) → c45(DBL(proper(z0)), PROPER(z0))
PROPER(s(z0)) → c47(S(proper(z0)), PROPER(z0))
PROPER(dbls(z0)) → c48(DBLS(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c50(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(sel(z0, z1)) → c51(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(indx(z0, z1)) → c52(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c53(FROM(proper(z0)), PROPER(z0))
PROPER(dbl1(z0)) → c54(DBL1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c56(S1(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c57(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c17(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))), ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)), ACTIVE(dbl1(0)))
ACTIVE(dbl(dbl1(s(z0)))) → c17(DBL(mark(s1(s1(dbl1(z0))))), ACTIVE(dbl1(s(z0))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)), ACTIVE(quote(0)))
ACTIVE(dbl(quote(s(z0)))) → c17(DBL(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c18(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))), ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)), ACTIVE(dbl1(0)))
ACTIVE(dbls(dbl1(s(z0)))) → c18(DBLS(mark(s1(s1(dbl1(z0))))), ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)), ACTIVE(quote(0)))
ACTIVE(dbls(quote(s(z0)))) → c18(DBLS(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)))
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0))))))
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0))))))
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0)))
ACTIVE(indx(dbl(s(z0)), x1)) → c21(INDX(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0))))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c21(INDX(mark(cons(dbl(z0), dbls(z1))), x1), ACTIVE(dbls(cons(z0, z1))))
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c21(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1), ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(from(z0), x1)) → c21(INDX(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(indx(dbl1(0), x1)) → c21(INDX(mark(01), x1), ACTIVE(dbl1(0)))
ACTIVE(indx(dbl1(s(z0)), x1)) → c21(INDX(mark(s1(s1(dbl1(z0)))), x1), ACTIVE(dbl1(s(z0))))
ACTIVE(indx(sel1(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(indx(sel1(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel1(z0, z2)), x1), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(indx(quote(0), x1)) → c21(INDX(mark(01), x1), ACTIVE(quote(0)))
ACTIVE(indx(quote(s(z0)), x1)) → c21(INDX(mark(s1(quote(z0))), x1), ACTIVE(quote(s(z0))))
ACTIVE(indx(quote(dbl(z0)), x1)) → c21(INDX(mark(dbl1(z0)), x1), ACTIVE(quote(dbl(z0))))
ACTIVE(indx(quote(sel(z0, z1)), x1)) → c21(INDX(mark(sel1(z0, z1)), x1), ACTIVE(quote(sel(z0, z1))))
ACTIVE(indx(dbl(z0), x1)) → c21(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
ACTIVE(indx(dbls(z0), x1)) → c21(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(indx(z0, z1), x1)) → c21(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1)))
ACTIVE(indx(dbl1(z0), x1)) → c21(INDX(dbl1(active(z0)), x1), ACTIVE(dbl1(z0)))
ACTIVE(indx(s1(z0), x1)) → c21(INDX(s1(active(z0)), x1), ACTIVE(s1(z0)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(active(z0), z1), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(z0, active(z1)), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(quote(z0), x1)) → c21(INDX(quote(active(z0)), x1), ACTIVE(quote(z0)))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)))
ACTIVE(indx(dbl(0), x1)) → c21(INDX(mark(0), x1))
ACTIVE(indx(dbls(nil), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(indx(indx(nil, z0), x1)) → c21(INDX(mark(nil), x1))
K tuples:none
Defined Rule Symbols:
active, s, dbl, cons, dbls, sel, indx, s1, dbl1, sel1, quote, proper, from
Defined Pair Symbols:
ACTIVE, DBL, DBLS, SEL, INDX, DBL1, S1, SEL1, QUOTE, PROPER, S, CONS, FROM, TOP
Compound Symbols:
c5, c12, c15, c16, c19, c20, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c47, c48, c50, c51, c52, c53, c54, c56, c57, c58, c59, c60, c61, c62, c63, c8, c, c17, c17, c1, c18, c18, c2, c21, c21
(27) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID) transformation)
Split RHS of tuples not part of any SCC
(28) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(dbl(0)) → mark(0)
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
active(dbls(nil)) → mark(nil)
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1)))
active(sel(0, cons(z0, z1))) → mark(z0)
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
active(indx(nil, z0)) → mark(nil)
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2)))
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(dbl1(0)) → mark(01)
active(dbl1(s(z0))) → mark(s1(s1(dbl1(z0))))
active(sel1(0, cons(z0, z1))) → mark(z0)
active(sel1(s(z0), cons(z1, z2))) → mark(sel1(z0, z2))
active(quote(0)) → mark(01)
active(quote(s(z0))) → mark(s1(quote(z0)))
active(quote(dbl(z0))) → mark(dbl1(z0))
active(quote(sel(z0, z1))) → mark(sel1(z0, z1))
active(dbl(z0)) → dbl(active(z0))
active(dbls(z0)) → dbls(active(z0))
active(sel(z0, z1)) → sel(active(z0), z1)
active(sel(z0, z1)) → sel(z0, active(z1))
active(indx(z0, z1)) → indx(active(z0), z1)
active(dbl1(z0)) → dbl1(active(z0))
active(s1(z0)) → s1(active(z0))
active(sel1(z0, z1)) → sel1(active(z0), z1)
active(sel1(z0, z1)) → sel1(z0, active(z1))
active(quote(z0)) → quote(active(z0))
s(ok(z0)) → ok(s(z0))
dbl(mark(z0)) → mark(dbl(z0))
dbl(ok(z0)) → ok(dbl(z0))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
dbls(mark(z0)) → mark(dbls(z0))
dbls(ok(z0)) → ok(dbls(z0))
sel(mark(z0), z1) → mark(sel(z0, z1))
sel(z0, mark(z1)) → mark(sel(z0, z1))
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
indx(mark(z0), z1) → mark(indx(z0, z1))
indx(ok(z0), ok(z1)) → ok(indx(z0, z1))
s1(mark(z0)) → mark(s1(z0))
s1(ok(z0)) → ok(s1(z0))
dbl1(mark(z0)) → mark(dbl1(z0))
dbl1(ok(z0)) → ok(dbl1(z0))
sel1(mark(z0), z1) → mark(sel1(z0, z1))
sel1(z0, mark(z1)) → mark(sel1(z0, z1))
sel1(ok(z0), ok(z1)) → ok(sel1(z0, z1))
quote(mark(z0)) → mark(quote(z0))
quote(ok(z0)) → ok(quote(z0))
proper(dbl(z0)) → dbl(proper(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(dbls(z0)) → dbls(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
proper(indx(z0, z1)) → indx(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(dbl1(z0)) → dbl1(proper(z0))
proper(01) → ok(01)
proper(s1(z0)) → s1(proper(z0))
proper(sel1(z0, z1)) → sel1(proper(z0), proper(z1))
proper(quote(z0)) → quote(proper(z0))
from(ok(z0)) → ok(from(z0))
Tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(dbl1(z0)) → c22(DBL1(active(z0)), ACTIVE(z0))
ACTIVE(s1(z0)) → c23(S1(active(z0)), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
ACTIVE(quote(z0)) → c26(QUOTE(active(z0)), ACTIVE(z0))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(dbl(z0)) → c45(DBL(proper(z0)), PROPER(z0))
PROPER(s(z0)) → c47(S(proper(z0)), PROPER(z0))
PROPER(dbls(z0)) → c48(DBLS(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c50(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(sel(z0, z1)) → c51(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(indx(z0, z1)) → c52(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c53(FROM(proper(z0)), PROPER(z0))
PROPER(dbl1(z0)) → c54(DBL1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c56(S1(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c57(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)), ACTIVE(dbl1(0)))
ACTIVE(dbl(dbl1(s(z0)))) → c17(DBL(mark(s1(s1(dbl1(z0))))), ACTIVE(dbl1(s(z0))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)), ACTIVE(quote(0)))
ACTIVE(dbl(quote(s(z0)))) → c17(DBL(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)), ACTIVE(dbl1(0)))
ACTIVE(dbls(dbl1(s(z0)))) → c18(DBLS(mark(s1(s1(dbl1(z0))))), ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)), ACTIVE(quote(0)))
ACTIVE(dbls(quote(s(z0)))) → c18(DBLS(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)))
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0))))))
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0))))))
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0)))
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(indx(dbl1(0), x1)) → c21(INDX(mark(01), x1), ACTIVE(dbl1(0)))
ACTIVE(indx(dbl1(s(z0)), x1)) → c21(INDX(mark(s1(s1(dbl1(z0)))), x1), ACTIVE(dbl1(s(z0))))
ACTIVE(indx(sel1(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(indx(sel1(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel1(z0, z2)), x1), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(indx(quote(0), x1)) → c21(INDX(mark(01), x1), ACTIVE(quote(0)))
ACTIVE(indx(quote(s(z0)), x1)) → c21(INDX(mark(s1(quote(z0))), x1), ACTIVE(quote(s(z0))))
ACTIVE(indx(quote(dbl(z0)), x1)) → c21(INDX(mark(dbl1(z0)), x1), ACTIVE(quote(dbl(z0))))
ACTIVE(indx(quote(sel(z0, z1)), x1)) → c21(INDX(mark(sel1(z0, z1)), x1), ACTIVE(quote(sel(z0, z1))))
ACTIVE(indx(dbl(z0), x1)) → c21(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
ACTIVE(indx(dbls(z0), x1)) → c21(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(indx(z0, z1), x1)) → c21(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1)))
ACTIVE(indx(dbl1(z0), x1)) → c21(INDX(dbl1(active(z0)), x1), ACTIVE(dbl1(z0)))
ACTIVE(indx(s1(z0), x1)) → c21(INDX(s1(active(z0)), x1), ACTIVE(s1(z0)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(active(z0), z1), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(z0, active(z1)), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(quote(z0), x1)) → c21(INDX(quote(active(z0)), x1), ACTIVE(quote(z0)))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)))
ACTIVE(indx(dbl(0), x1)) → c21(INDX(mark(0), x1))
ACTIVE(indx(dbls(nil), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(indx(indx(nil, z0), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0))))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1))
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0)))
S tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(dbl1(z0)) → c22(DBL1(active(z0)), ACTIVE(z0))
ACTIVE(s1(z0)) → c23(S1(active(z0)), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
ACTIVE(quote(z0)) → c26(QUOTE(active(z0)), ACTIVE(z0))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(dbl(z0)) → c45(DBL(proper(z0)), PROPER(z0))
PROPER(s(z0)) → c47(S(proper(z0)), PROPER(z0))
PROPER(dbls(z0)) → c48(DBLS(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c50(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(sel(z0, z1)) → c51(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(indx(z0, z1)) → c52(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c53(FROM(proper(z0)), PROPER(z0))
PROPER(dbl1(z0)) → c54(DBL1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c56(S1(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c57(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)), ACTIVE(dbl1(0)))
ACTIVE(dbl(dbl1(s(z0)))) → c17(DBL(mark(s1(s1(dbl1(z0))))), ACTIVE(dbl1(s(z0))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)), ACTIVE(quote(0)))
ACTIVE(dbl(quote(s(z0)))) → c17(DBL(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)), ACTIVE(dbl1(0)))
ACTIVE(dbls(dbl1(s(z0)))) → c18(DBLS(mark(s1(s1(dbl1(z0))))), ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)), ACTIVE(quote(0)))
ACTIVE(dbls(quote(s(z0)))) → c18(DBLS(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)))
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0))))))
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0))))))
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0)))
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(indx(dbl1(0), x1)) → c21(INDX(mark(01), x1), ACTIVE(dbl1(0)))
ACTIVE(indx(dbl1(s(z0)), x1)) → c21(INDX(mark(s1(s1(dbl1(z0)))), x1), ACTIVE(dbl1(s(z0))))
ACTIVE(indx(sel1(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(indx(sel1(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel1(z0, z2)), x1), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(indx(quote(0), x1)) → c21(INDX(mark(01), x1), ACTIVE(quote(0)))
ACTIVE(indx(quote(s(z0)), x1)) → c21(INDX(mark(s1(quote(z0))), x1), ACTIVE(quote(s(z0))))
ACTIVE(indx(quote(dbl(z0)), x1)) → c21(INDX(mark(dbl1(z0)), x1), ACTIVE(quote(dbl(z0))))
ACTIVE(indx(quote(sel(z0, z1)), x1)) → c21(INDX(mark(sel1(z0, z1)), x1), ACTIVE(quote(sel(z0, z1))))
ACTIVE(indx(dbl(z0), x1)) → c21(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
ACTIVE(indx(dbls(z0), x1)) → c21(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(indx(z0, z1), x1)) → c21(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1)))
ACTIVE(indx(dbl1(z0), x1)) → c21(INDX(dbl1(active(z0)), x1), ACTIVE(dbl1(z0)))
ACTIVE(indx(s1(z0), x1)) → c21(INDX(s1(active(z0)), x1), ACTIVE(s1(z0)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(active(z0), z1), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(z0, active(z1)), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(quote(z0), x1)) → c21(INDX(quote(active(z0)), x1), ACTIVE(quote(z0)))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)))
ACTIVE(indx(dbl(0), x1)) → c21(INDX(mark(0), x1))
ACTIVE(indx(dbls(nil), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(indx(indx(nil, z0), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0))))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1))
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0)))
K tuples:none
Defined Rule Symbols:
active, s, dbl, cons, dbls, sel, indx, s1, dbl1, sel1, quote, proper, from
Defined Pair Symbols:
ACTIVE, DBL, DBLS, SEL, INDX, DBL1, S1, SEL1, QUOTE, PROPER, S, CONS, FROM, TOP
Compound Symbols:
c5, c12, c15, c16, c19, c20, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c47, c48, c50, c51, c52, c53, c54, c56, c57, c58, c59, c60, c61, c62, c63, c8, c, c17, c17, c1, c18, c18, c2, c21, c21, c3
(29) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
ACTIVE(
dbl1(
z0)) →
c22(
DBL1(
active(
z0)),
ACTIVE(
z0)) by
ACTIVE(dbl1(dbl(0))) → c22(DBL1(mark(0)), ACTIVE(dbl(0)))
ACTIVE(dbl1(dbl(s(z0)))) → c22(DBL1(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
ACTIVE(dbl1(dbls(nil))) → c22(DBL1(mark(nil)), ACTIVE(dbls(nil)))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c22(DBL1(mark(cons(dbl(z0), dbls(z1)))), ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbl1(sel(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl1(sel(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl1(indx(nil, z0))) → c22(DBL1(mark(nil)), ACTIVE(indx(nil, z0)))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c22(DBL1(mark(cons(sel(z0, z2), indx(z1, z2)))), ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl1(from(z0))) → c22(DBL1(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(dbl1(dbl1(0))) → c22(DBL1(mark(01)), ACTIVE(dbl1(0)))
ACTIVE(dbl1(dbl1(s(z0)))) → c22(DBL1(mark(s1(s1(dbl1(z0))))), ACTIVE(dbl1(s(z0))))
ACTIVE(dbl1(sel1(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl1(sel1(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl1(quote(0))) → c22(DBL1(mark(01)), ACTIVE(quote(0)))
ACTIVE(dbl1(quote(s(z0)))) → c22(DBL1(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(dbl1(quote(dbl(z0)))) → c22(DBL1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl1(quote(sel(z0, z1)))) → c22(DBL1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl1(dbl(z0))) → c22(DBL1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl1(dbls(z0))) → c22(DBL1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(indx(z0, z1))) → c22(DBL1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl1(dbl1(z0))) → c22(DBL1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl1(s1(z0))) → c22(DBL1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(quote(z0))) → c22(DBL1(quote(active(z0))), ACTIVE(quote(z0)))
(30) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(dbl(0)) → mark(0)
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
active(dbls(nil)) → mark(nil)
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1)))
active(sel(0, cons(z0, z1))) → mark(z0)
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
active(indx(nil, z0)) → mark(nil)
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2)))
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(dbl1(0)) → mark(01)
active(dbl1(s(z0))) → mark(s1(s1(dbl1(z0))))
active(sel1(0, cons(z0, z1))) → mark(z0)
active(sel1(s(z0), cons(z1, z2))) → mark(sel1(z0, z2))
active(quote(0)) → mark(01)
active(quote(s(z0))) → mark(s1(quote(z0)))
active(quote(dbl(z0))) → mark(dbl1(z0))
active(quote(sel(z0, z1))) → mark(sel1(z0, z1))
active(dbl(z0)) → dbl(active(z0))
active(dbls(z0)) → dbls(active(z0))
active(sel(z0, z1)) → sel(active(z0), z1)
active(sel(z0, z1)) → sel(z0, active(z1))
active(indx(z0, z1)) → indx(active(z0), z1)
active(dbl1(z0)) → dbl1(active(z0))
active(s1(z0)) → s1(active(z0))
active(sel1(z0, z1)) → sel1(active(z0), z1)
active(sel1(z0, z1)) → sel1(z0, active(z1))
active(quote(z0)) → quote(active(z0))
s(ok(z0)) → ok(s(z0))
dbl(mark(z0)) → mark(dbl(z0))
dbl(ok(z0)) → ok(dbl(z0))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
dbls(mark(z0)) → mark(dbls(z0))
dbls(ok(z0)) → ok(dbls(z0))
sel(mark(z0), z1) → mark(sel(z0, z1))
sel(z0, mark(z1)) → mark(sel(z0, z1))
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
indx(mark(z0), z1) → mark(indx(z0, z1))
indx(ok(z0), ok(z1)) → ok(indx(z0, z1))
s1(mark(z0)) → mark(s1(z0))
s1(ok(z0)) → ok(s1(z0))
dbl1(mark(z0)) → mark(dbl1(z0))
dbl1(ok(z0)) → ok(dbl1(z0))
sel1(mark(z0), z1) → mark(sel1(z0, z1))
sel1(z0, mark(z1)) → mark(sel1(z0, z1))
sel1(ok(z0), ok(z1)) → ok(sel1(z0, z1))
quote(mark(z0)) → mark(quote(z0))
quote(ok(z0)) → ok(quote(z0))
proper(dbl(z0)) → dbl(proper(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(dbls(z0)) → dbls(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
proper(indx(z0, z1)) → indx(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(dbl1(z0)) → dbl1(proper(z0))
proper(01) → ok(01)
proper(s1(z0)) → s1(proper(z0))
proper(sel1(z0, z1)) → sel1(proper(z0), proper(z1))
proper(quote(z0)) → quote(proper(z0))
from(ok(z0)) → ok(from(z0))
Tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(s1(z0)) → c23(S1(active(z0)), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
ACTIVE(quote(z0)) → c26(QUOTE(active(z0)), ACTIVE(z0))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(dbl(z0)) → c45(DBL(proper(z0)), PROPER(z0))
PROPER(s(z0)) → c47(S(proper(z0)), PROPER(z0))
PROPER(dbls(z0)) → c48(DBLS(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c50(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(sel(z0, z1)) → c51(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(indx(z0, z1)) → c52(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c53(FROM(proper(z0)), PROPER(z0))
PROPER(dbl1(z0)) → c54(DBL1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c56(S1(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c57(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)), ACTIVE(dbl1(0)))
ACTIVE(dbl(dbl1(s(z0)))) → c17(DBL(mark(s1(s1(dbl1(z0))))), ACTIVE(dbl1(s(z0))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)), ACTIVE(quote(0)))
ACTIVE(dbl(quote(s(z0)))) → c17(DBL(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)), ACTIVE(dbl1(0)))
ACTIVE(dbls(dbl1(s(z0)))) → c18(DBLS(mark(s1(s1(dbl1(z0))))), ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)), ACTIVE(quote(0)))
ACTIVE(dbls(quote(s(z0)))) → c18(DBLS(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)))
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0))))))
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0))))))
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0)))
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(indx(dbl1(0), x1)) → c21(INDX(mark(01), x1), ACTIVE(dbl1(0)))
ACTIVE(indx(dbl1(s(z0)), x1)) → c21(INDX(mark(s1(s1(dbl1(z0)))), x1), ACTIVE(dbl1(s(z0))))
ACTIVE(indx(sel1(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(indx(sel1(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel1(z0, z2)), x1), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(indx(quote(0), x1)) → c21(INDX(mark(01), x1), ACTIVE(quote(0)))
ACTIVE(indx(quote(s(z0)), x1)) → c21(INDX(mark(s1(quote(z0))), x1), ACTIVE(quote(s(z0))))
ACTIVE(indx(quote(dbl(z0)), x1)) → c21(INDX(mark(dbl1(z0)), x1), ACTIVE(quote(dbl(z0))))
ACTIVE(indx(quote(sel(z0, z1)), x1)) → c21(INDX(mark(sel1(z0, z1)), x1), ACTIVE(quote(sel(z0, z1))))
ACTIVE(indx(dbl(z0), x1)) → c21(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
ACTIVE(indx(dbls(z0), x1)) → c21(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(indx(z0, z1), x1)) → c21(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1)))
ACTIVE(indx(dbl1(z0), x1)) → c21(INDX(dbl1(active(z0)), x1), ACTIVE(dbl1(z0)))
ACTIVE(indx(s1(z0), x1)) → c21(INDX(s1(active(z0)), x1), ACTIVE(s1(z0)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(active(z0), z1), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(z0, active(z1)), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(quote(z0), x1)) → c21(INDX(quote(active(z0)), x1), ACTIVE(quote(z0)))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)))
ACTIVE(indx(dbl(0), x1)) → c21(INDX(mark(0), x1))
ACTIVE(indx(dbls(nil), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(indx(indx(nil, z0), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0))))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1))
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0)))
ACTIVE(dbl1(dbl(0))) → c22(DBL1(mark(0)), ACTIVE(dbl(0)))
ACTIVE(dbl1(dbl(s(z0)))) → c22(DBL1(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
ACTIVE(dbl1(dbls(nil))) → c22(DBL1(mark(nil)), ACTIVE(dbls(nil)))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c22(DBL1(mark(cons(dbl(z0), dbls(z1)))), ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbl1(sel(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl1(sel(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl1(indx(nil, z0))) → c22(DBL1(mark(nil)), ACTIVE(indx(nil, z0)))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c22(DBL1(mark(cons(sel(z0, z2), indx(z1, z2)))), ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl1(from(z0))) → c22(DBL1(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(dbl1(dbl1(0))) → c22(DBL1(mark(01)), ACTIVE(dbl1(0)))
ACTIVE(dbl1(dbl1(s(z0)))) → c22(DBL1(mark(s1(s1(dbl1(z0))))), ACTIVE(dbl1(s(z0))))
ACTIVE(dbl1(sel1(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl1(sel1(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl1(quote(0))) → c22(DBL1(mark(01)), ACTIVE(quote(0)))
ACTIVE(dbl1(quote(s(z0)))) → c22(DBL1(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(dbl1(quote(dbl(z0)))) → c22(DBL1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl1(quote(sel(z0, z1)))) → c22(DBL1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl1(dbl(z0))) → c22(DBL1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl1(dbls(z0))) → c22(DBL1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(indx(z0, z1))) → c22(DBL1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl1(dbl1(z0))) → c22(DBL1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl1(s1(z0))) → c22(DBL1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(quote(z0))) → c22(DBL1(quote(active(z0))), ACTIVE(quote(z0)))
S tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(s1(z0)) → c23(S1(active(z0)), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
ACTIVE(quote(z0)) → c26(QUOTE(active(z0)), ACTIVE(z0))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(dbl(z0)) → c45(DBL(proper(z0)), PROPER(z0))
PROPER(s(z0)) → c47(S(proper(z0)), PROPER(z0))
PROPER(dbls(z0)) → c48(DBLS(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c50(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(sel(z0, z1)) → c51(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(indx(z0, z1)) → c52(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c53(FROM(proper(z0)), PROPER(z0))
PROPER(dbl1(z0)) → c54(DBL1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c56(S1(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c57(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)), ACTIVE(dbl1(0)))
ACTIVE(dbl(dbl1(s(z0)))) → c17(DBL(mark(s1(s1(dbl1(z0))))), ACTIVE(dbl1(s(z0))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)), ACTIVE(quote(0)))
ACTIVE(dbl(quote(s(z0)))) → c17(DBL(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)), ACTIVE(dbl1(0)))
ACTIVE(dbls(dbl1(s(z0)))) → c18(DBLS(mark(s1(s1(dbl1(z0))))), ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)), ACTIVE(quote(0)))
ACTIVE(dbls(quote(s(z0)))) → c18(DBLS(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)))
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0))))))
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0))))))
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0)))
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(indx(dbl1(0), x1)) → c21(INDX(mark(01), x1), ACTIVE(dbl1(0)))
ACTIVE(indx(dbl1(s(z0)), x1)) → c21(INDX(mark(s1(s1(dbl1(z0)))), x1), ACTIVE(dbl1(s(z0))))
ACTIVE(indx(sel1(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(indx(sel1(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel1(z0, z2)), x1), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(indx(quote(0), x1)) → c21(INDX(mark(01), x1), ACTIVE(quote(0)))
ACTIVE(indx(quote(s(z0)), x1)) → c21(INDX(mark(s1(quote(z0))), x1), ACTIVE(quote(s(z0))))
ACTIVE(indx(quote(dbl(z0)), x1)) → c21(INDX(mark(dbl1(z0)), x1), ACTIVE(quote(dbl(z0))))
ACTIVE(indx(quote(sel(z0, z1)), x1)) → c21(INDX(mark(sel1(z0, z1)), x1), ACTIVE(quote(sel(z0, z1))))
ACTIVE(indx(dbl(z0), x1)) → c21(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
ACTIVE(indx(dbls(z0), x1)) → c21(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(indx(z0, z1), x1)) → c21(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1)))
ACTIVE(indx(dbl1(z0), x1)) → c21(INDX(dbl1(active(z0)), x1), ACTIVE(dbl1(z0)))
ACTIVE(indx(s1(z0), x1)) → c21(INDX(s1(active(z0)), x1), ACTIVE(s1(z0)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(active(z0), z1), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(z0, active(z1)), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(quote(z0), x1)) → c21(INDX(quote(active(z0)), x1), ACTIVE(quote(z0)))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)))
ACTIVE(indx(dbl(0), x1)) → c21(INDX(mark(0), x1))
ACTIVE(indx(dbls(nil), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(indx(indx(nil, z0), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0))))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1))
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0)))
ACTIVE(dbl1(dbl(0))) → c22(DBL1(mark(0)), ACTIVE(dbl(0)))
ACTIVE(dbl1(dbl(s(z0)))) → c22(DBL1(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
ACTIVE(dbl1(dbls(nil))) → c22(DBL1(mark(nil)), ACTIVE(dbls(nil)))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c22(DBL1(mark(cons(dbl(z0), dbls(z1)))), ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbl1(sel(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl1(sel(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl1(indx(nil, z0))) → c22(DBL1(mark(nil)), ACTIVE(indx(nil, z0)))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c22(DBL1(mark(cons(sel(z0, z2), indx(z1, z2)))), ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl1(from(z0))) → c22(DBL1(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(dbl1(dbl1(0))) → c22(DBL1(mark(01)), ACTIVE(dbl1(0)))
ACTIVE(dbl1(dbl1(s(z0)))) → c22(DBL1(mark(s1(s1(dbl1(z0))))), ACTIVE(dbl1(s(z0))))
ACTIVE(dbl1(sel1(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl1(sel1(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl1(quote(0))) → c22(DBL1(mark(01)), ACTIVE(quote(0)))
ACTIVE(dbl1(quote(s(z0)))) → c22(DBL1(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(dbl1(quote(dbl(z0)))) → c22(DBL1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl1(quote(sel(z0, z1)))) → c22(DBL1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl1(dbl(z0))) → c22(DBL1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl1(dbls(z0))) → c22(DBL1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(indx(z0, z1))) → c22(DBL1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl1(dbl1(z0))) → c22(DBL1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl1(s1(z0))) → c22(DBL1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(quote(z0))) → c22(DBL1(quote(active(z0))), ACTIVE(quote(z0)))
K tuples:none
Defined Rule Symbols:
active, s, dbl, cons, dbls, sel, indx, s1, dbl1, sel1, quote, proper, from
Defined Pair Symbols:
ACTIVE, DBL, DBLS, SEL, INDX, DBL1, S1, SEL1, QUOTE, PROPER, S, CONS, FROM, TOP
Compound Symbols:
c5, c12, c15, c16, c19, c20, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c47, c48, c50, c51, c52, c53, c54, c56, c57, c58, c59, c60, c61, c62, c63, c8, c, c17, c17, c1, c18, c18, c2, c21, c21, c3, c22
(31) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 7 trailing tuple parts
(32) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(dbl(0)) → mark(0)
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
active(dbls(nil)) → mark(nil)
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1)))
active(sel(0, cons(z0, z1))) → mark(z0)
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
active(indx(nil, z0)) → mark(nil)
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2)))
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(dbl1(0)) → mark(01)
active(dbl1(s(z0))) → mark(s1(s1(dbl1(z0))))
active(sel1(0, cons(z0, z1))) → mark(z0)
active(sel1(s(z0), cons(z1, z2))) → mark(sel1(z0, z2))
active(quote(0)) → mark(01)
active(quote(s(z0))) → mark(s1(quote(z0)))
active(quote(dbl(z0))) → mark(dbl1(z0))
active(quote(sel(z0, z1))) → mark(sel1(z0, z1))
active(dbl(z0)) → dbl(active(z0))
active(dbls(z0)) → dbls(active(z0))
active(sel(z0, z1)) → sel(active(z0), z1)
active(sel(z0, z1)) → sel(z0, active(z1))
active(indx(z0, z1)) → indx(active(z0), z1)
active(dbl1(z0)) → dbl1(active(z0))
active(s1(z0)) → s1(active(z0))
active(sel1(z0, z1)) → sel1(active(z0), z1)
active(sel1(z0, z1)) → sel1(z0, active(z1))
active(quote(z0)) → quote(active(z0))
s(ok(z0)) → ok(s(z0))
dbl(mark(z0)) → mark(dbl(z0))
dbl(ok(z0)) → ok(dbl(z0))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
dbls(mark(z0)) → mark(dbls(z0))
dbls(ok(z0)) → ok(dbls(z0))
sel(mark(z0), z1) → mark(sel(z0, z1))
sel(z0, mark(z1)) → mark(sel(z0, z1))
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
indx(mark(z0), z1) → mark(indx(z0, z1))
indx(ok(z0), ok(z1)) → ok(indx(z0, z1))
s1(mark(z0)) → mark(s1(z0))
s1(ok(z0)) → ok(s1(z0))
dbl1(mark(z0)) → mark(dbl1(z0))
dbl1(ok(z0)) → ok(dbl1(z0))
sel1(mark(z0), z1) → mark(sel1(z0, z1))
sel1(z0, mark(z1)) → mark(sel1(z0, z1))
sel1(ok(z0), ok(z1)) → ok(sel1(z0, z1))
quote(mark(z0)) → mark(quote(z0))
quote(ok(z0)) → ok(quote(z0))
proper(dbl(z0)) → dbl(proper(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(dbls(z0)) → dbls(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
proper(indx(z0, z1)) → indx(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(dbl1(z0)) → dbl1(proper(z0))
proper(01) → ok(01)
proper(s1(z0)) → s1(proper(z0))
proper(sel1(z0, z1)) → sel1(proper(z0), proper(z1))
proper(quote(z0)) → quote(proper(z0))
from(ok(z0)) → ok(from(z0))
Tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(s1(z0)) → c23(S1(active(z0)), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
ACTIVE(quote(z0)) → c26(QUOTE(active(z0)), ACTIVE(z0))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(dbl(z0)) → c45(DBL(proper(z0)), PROPER(z0))
PROPER(s(z0)) → c47(S(proper(z0)), PROPER(z0))
PROPER(dbls(z0)) → c48(DBLS(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c50(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(sel(z0, z1)) → c51(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(indx(z0, z1)) → c52(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c53(FROM(proper(z0)), PROPER(z0))
PROPER(dbl1(z0)) → c54(DBL1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c56(S1(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c57(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(dbl1(s(z0)))) → c17(DBL(mark(s1(s1(dbl1(z0))))), ACTIVE(dbl1(s(z0))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)), ACTIVE(quote(0)))
ACTIVE(dbl(quote(s(z0)))) → c17(DBL(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(dbl1(s(z0)))) → c18(DBLS(mark(s1(s1(dbl1(z0))))), ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)), ACTIVE(quote(0)))
ACTIVE(dbls(quote(s(z0)))) → c18(DBLS(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)))
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0))))))
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0))))))
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0)))
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(indx(dbl1(s(z0)), x1)) → c21(INDX(mark(s1(s1(dbl1(z0)))), x1), ACTIVE(dbl1(s(z0))))
ACTIVE(indx(sel1(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(indx(sel1(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel1(z0, z2)), x1), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(indx(quote(0), x1)) → c21(INDX(mark(01), x1), ACTIVE(quote(0)))
ACTIVE(indx(quote(s(z0)), x1)) → c21(INDX(mark(s1(quote(z0))), x1), ACTIVE(quote(s(z0))))
ACTIVE(indx(quote(dbl(z0)), x1)) → c21(INDX(mark(dbl1(z0)), x1), ACTIVE(quote(dbl(z0))))
ACTIVE(indx(quote(sel(z0, z1)), x1)) → c21(INDX(mark(sel1(z0, z1)), x1), ACTIVE(quote(sel(z0, z1))))
ACTIVE(indx(dbl(z0), x1)) → c21(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
ACTIVE(indx(dbls(z0), x1)) → c21(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(indx(z0, z1), x1)) → c21(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1)))
ACTIVE(indx(dbl1(z0), x1)) → c21(INDX(dbl1(active(z0)), x1), ACTIVE(dbl1(z0)))
ACTIVE(indx(s1(z0), x1)) → c21(INDX(s1(active(z0)), x1), ACTIVE(s1(z0)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(active(z0), z1), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(z0, active(z1)), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(quote(z0), x1)) → c21(INDX(quote(active(z0)), x1), ACTIVE(quote(z0)))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)))
ACTIVE(indx(dbl(0), x1)) → c21(INDX(mark(0), x1))
ACTIVE(indx(dbls(nil), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(indx(indx(nil, z0), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0))))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1))
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0)))
ACTIVE(dbl1(dbl(s(z0)))) → c22(DBL1(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c22(DBL1(mark(cons(dbl(z0), dbls(z1)))), ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbl1(sel(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl1(sel(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c22(DBL1(mark(cons(sel(z0, z2), indx(z1, z2)))), ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl1(from(z0))) → c22(DBL1(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(dbl1(dbl1(s(z0)))) → c22(DBL1(mark(s1(s1(dbl1(z0))))), ACTIVE(dbl1(s(z0))))
ACTIVE(dbl1(sel1(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl1(sel1(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl1(quote(0))) → c22(DBL1(mark(01)), ACTIVE(quote(0)))
ACTIVE(dbl1(quote(s(z0)))) → c22(DBL1(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(dbl1(quote(dbl(z0)))) → c22(DBL1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl1(quote(sel(z0, z1)))) → c22(DBL1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl1(dbl(z0))) → c22(DBL1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl1(dbls(z0))) → c22(DBL1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(indx(z0, z1))) → c22(DBL1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl1(dbl1(z0))) → c22(DBL1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl1(s1(z0))) → c22(DBL1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(quote(z0))) → c22(DBL1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(dbl1(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(dbl(0))) → c22(DBL1(mark(0)))
ACTIVE(dbl1(dbls(nil))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(indx(nil, z0))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(dbl1(0))) → c22(DBL1(mark(01)))
S tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(s1(z0)) → c23(S1(active(z0)), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
ACTIVE(quote(z0)) → c26(QUOTE(active(z0)), ACTIVE(z0))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(dbl(z0)) → c45(DBL(proper(z0)), PROPER(z0))
PROPER(s(z0)) → c47(S(proper(z0)), PROPER(z0))
PROPER(dbls(z0)) → c48(DBLS(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c50(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(sel(z0, z1)) → c51(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(indx(z0, z1)) → c52(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c53(FROM(proper(z0)), PROPER(z0))
PROPER(dbl1(z0)) → c54(DBL1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c56(S1(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c57(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(dbl1(s(z0)))) → c17(DBL(mark(s1(s1(dbl1(z0))))), ACTIVE(dbl1(s(z0))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)), ACTIVE(quote(0)))
ACTIVE(dbl(quote(s(z0)))) → c17(DBL(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(dbl1(s(z0)))) → c18(DBLS(mark(s1(s1(dbl1(z0))))), ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)), ACTIVE(quote(0)))
ACTIVE(dbls(quote(s(z0)))) → c18(DBLS(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)))
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0))))))
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0))))))
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0)))
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(indx(dbl1(s(z0)), x1)) → c21(INDX(mark(s1(s1(dbl1(z0)))), x1), ACTIVE(dbl1(s(z0))))
ACTIVE(indx(sel1(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(indx(sel1(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel1(z0, z2)), x1), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(indx(quote(0), x1)) → c21(INDX(mark(01), x1), ACTIVE(quote(0)))
ACTIVE(indx(quote(s(z0)), x1)) → c21(INDX(mark(s1(quote(z0))), x1), ACTIVE(quote(s(z0))))
ACTIVE(indx(quote(dbl(z0)), x1)) → c21(INDX(mark(dbl1(z0)), x1), ACTIVE(quote(dbl(z0))))
ACTIVE(indx(quote(sel(z0, z1)), x1)) → c21(INDX(mark(sel1(z0, z1)), x1), ACTIVE(quote(sel(z0, z1))))
ACTIVE(indx(dbl(z0), x1)) → c21(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
ACTIVE(indx(dbls(z0), x1)) → c21(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(indx(z0, z1), x1)) → c21(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1)))
ACTIVE(indx(dbl1(z0), x1)) → c21(INDX(dbl1(active(z0)), x1), ACTIVE(dbl1(z0)))
ACTIVE(indx(s1(z0), x1)) → c21(INDX(s1(active(z0)), x1), ACTIVE(s1(z0)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(active(z0), z1), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(z0, active(z1)), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(quote(z0), x1)) → c21(INDX(quote(active(z0)), x1), ACTIVE(quote(z0)))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)))
ACTIVE(indx(dbl(0), x1)) → c21(INDX(mark(0), x1))
ACTIVE(indx(dbls(nil), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(indx(indx(nil, z0), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0))))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1))
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0)))
ACTIVE(dbl1(dbl(s(z0)))) → c22(DBL1(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c22(DBL1(mark(cons(dbl(z0), dbls(z1)))), ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbl1(sel(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl1(sel(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c22(DBL1(mark(cons(sel(z0, z2), indx(z1, z2)))), ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl1(from(z0))) → c22(DBL1(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(dbl1(dbl1(s(z0)))) → c22(DBL1(mark(s1(s1(dbl1(z0))))), ACTIVE(dbl1(s(z0))))
ACTIVE(dbl1(sel1(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl1(sel1(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl1(quote(0))) → c22(DBL1(mark(01)), ACTIVE(quote(0)))
ACTIVE(dbl1(quote(s(z0)))) → c22(DBL1(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(dbl1(quote(dbl(z0)))) → c22(DBL1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl1(quote(sel(z0, z1)))) → c22(DBL1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl1(dbl(z0))) → c22(DBL1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl1(dbls(z0))) → c22(DBL1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(indx(z0, z1))) → c22(DBL1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl1(dbl1(z0))) → c22(DBL1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl1(s1(z0))) → c22(DBL1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(quote(z0))) → c22(DBL1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(dbl1(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(dbl(0))) → c22(DBL1(mark(0)))
ACTIVE(dbl1(dbls(nil))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(indx(nil, z0))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(dbl1(0))) → c22(DBL1(mark(01)))
K tuples:none
Defined Rule Symbols:
active, s, dbl, cons, dbls, sel, indx, s1, dbl1, sel1, quote, proper, from
Defined Pair Symbols:
ACTIVE, DBL, DBLS, SEL, INDX, DBL1, S1, SEL1, QUOTE, PROPER, S, CONS, FROM, TOP
Compound Symbols:
c5, c12, c15, c16, c19, c20, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c47, c48, c50, c51, c52, c53, c54, c56, c57, c58, c59, c60, c61, c62, c63, c8, c, c17, c17, c1, c18, c18, c2, c21, c21, c3, c22, c22
(33) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID) transformation)
Split RHS of tuples not part of any SCC
(34) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(dbl(0)) → mark(0)
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
active(dbls(nil)) → mark(nil)
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1)))
active(sel(0, cons(z0, z1))) → mark(z0)
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
active(indx(nil, z0)) → mark(nil)
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2)))
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(dbl1(0)) → mark(01)
active(dbl1(s(z0))) → mark(s1(s1(dbl1(z0))))
active(sel1(0, cons(z0, z1))) → mark(z0)
active(sel1(s(z0), cons(z1, z2))) → mark(sel1(z0, z2))
active(quote(0)) → mark(01)
active(quote(s(z0))) → mark(s1(quote(z0)))
active(quote(dbl(z0))) → mark(dbl1(z0))
active(quote(sel(z0, z1))) → mark(sel1(z0, z1))
active(dbl(z0)) → dbl(active(z0))
active(dbls(z0)) → dbls(active(z0))
active(sel(z0, z1)) → sel(active(z0), z1)
active(sel(z0, z1)) → sel(z0, active(z1))
active(indx(z0, z1)) → indx(active(z0), z1)
active(dbl1(z0)) → dbl1(active(z0))
active(s1(z0)) → s1(active(z0))
active(sel1(z0, z1)) → sel1(active(z0), z1)
active(sel1(z0, z1)) → sel1(z0, active(z1))
active(quote(z0)) → quote(active(z0))
s(ok(z0)) → ok(s(z0))
dbl(mark(z0)) → mark(dbl(z0))
dbl(ok(z0)) → ok(dbl(z0))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
dbls(mark(z0)) → mark(dbls(z0))
dbls(ok(z0)) → ok(dbls(z0))
sel(mark(z0), z1) → mark(sel(z0, z1))
sel(z0, mark(z1)) → mark(sel(z0, z1))
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
indx(mark(z0), z1) → mark(indx(z0, z1))
indx(ok(z0), ok(z1)) → ok(indx(z0, z1))
s1(mark(z0)) → mark(s1(z0))
s1(ok(z0)) → ok(s1(z0))
dbl1(mark(z0)) → mark(dbl1(z0))
dbl1(ok(z0)) → ok(dbl1(z0))
sel1(mark(z0), z1) → mark(sel1(z0, z1))
sel1(z0, mark(z1)) → mark(sel1(z0, z1))
sel1(ok(z0), ok(z1)) → ok(sel1(z0, z1))
quote(mark(z0)) → mark(quote(z0))
quote(ok(z0)) → ok(quote(z0))
proper(dbl(z0)) → dbl(proper(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(dbls(z0)) → dbls(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
proper(indx(z0, z1)) → indx(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(dbl1(z0)) → dbl1(proper(z0))
proper(01) → ok(01)
proper(s1(z0)) → s1(proper(z0))
proper(sel1(z0, z1)) → sel1(proper(z0), proper(z1))
proper(quote(z0)) → quote(proper(z0))
from(ok(z0)) → ok(from(z0))
Tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(s1(z0)) → c23(S1(active(z0)), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
ACTIVE(quote(z0)) → c26(QUOTE(active(z0)), ACTIVE(z0))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(dbl(z0)) → c45(DBL(proper(z0)), PROPER(z0))
PROPER(s(z0)) → c47(S(proper(z0)), PROPER(z0))
PROPER(dbls(z0)) → c48(DBLS(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c50(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(sel(z0, z1)) → c51(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(indx(z0, z1)) → c52(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c53(FROM(proper(z0)), PROPER(z0))
PROPER(dbl1(z0)) → c54(DBL1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c56(S1(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c57(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)), ACTIVE(quote(0)))
ACTIVE(dbl(quote(s(z0)))) → c17(DBL(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)), ACTIVE(quote(0)))
ACTIVE(dbls(quote(s(z0)))) → c18(DBLS(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)))
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0))))))
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0))))))
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0)))
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(indx(sel1(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(indx(sel1(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel1(z0, z2)), x1), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(indx(quote(0), x1)) → c21(INDX(mark(01), x1), ACTIVE(quote(0)))
ACTIVE(indx(quote(s(z0)), x1)) → c21(INDX(mark(s1(quote(z0))), x1), ACTIVE(quote(s(z0))))
ACTIVE(indx(quote(dbl(z0)), x1)) → c21(INDX(mark(dbl1(z0)), x1), ACTIVE(quote(dbl(z0))))
ACTIVE(indx(quote(sel(z0, z1)), x1)) → c21(INDX(mark(sel1(z0, z1)), x1), ACTIVE(quote(sel(z0, z1))))
ACTIVE(indx(dbl(z0), x1)) → c21(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
ACTIVE(indx(dbls(z0), x1)) → c21(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(indx(z0, z1), x1)) → c21(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1)))
ACTIVE(indx(dbl1(z0), x1)) → c21(INDX(dbl1(active(z0)), x1), ACTIVE(dbl1(z0)))
ACTIVE(indx(s1(z0), x1)) → c21(INDX(s1(active(z0)), x1), ACTIVE(s1(z0)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(active(z0), z1), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(z0, active(z1)), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(quote(z0), x1)) → c21(INDX(quote(active(z0)), x1), ACTIVE(quote(z0)))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)))
ACTIVE(indx(dbl(0), x1)) → c21(INDX(mark(0), x1))
ACTIVE(indx(dbls(nil), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(indx(indx(nil, z0), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0))))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1))
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0)))
ACTIVE(dbl1(sel(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl1(sel(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl1(sel1(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl1(sel1(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl1(quote(0))) → c22(DBL1(mark(01)), ACTIVE(quote(0)))
ACTIVE(dbl1(quote(s(z0)))) → c22(DBL1(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(dbl1(quote(dbl(z0)))) → c22(DBL1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl1(quote(sel(z0, z1)))) → c22(DBL1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl1(dbl(z0))) → c22(DBL1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl1(dbls(z0))) → c22(DBL1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(indx(z0, z1))) → c22(DBL1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl1(dbl1(z0))) → c22(DBL1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl1(s1(z0))) → c22(DBL1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(quote(z0))) → c22(DBL1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(dbl1(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(dbl(0))) → c22(DBL1(mark(0)))
ACTIVE(dbl1(dbls(nil))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(indx(nil, z0))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(dbl1(0))) → c22(DBL1(mark(01)))
ACTIVE(dbl(dbl1(s(z0)))) → c4(DBL(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(DBLS(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(INDX(mark(s1(s1(dbl1(z0)))), x1))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(DBL1(mark(s(s(dbl(z0))))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(ACTIVE(dbl(s(z0))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(DBL1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(DBL1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl1(from(z0))) → c4(DBL1(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl1(from(z0))) → c4(ACTIVE(from(z0)))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(DBL1(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
S tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(s1(z0)) → c23(S1(active(z0)), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
ACTIVE(quote(z0)) → c26(QUOTE(active(z0)), ACTIVE(z0))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(dbl(z0)) → c45(DBL(proper(z0)), PROPER(z0))
PROPER(s(z0)) → c47(S(proper(z0)), PROPER(z0))
PROPER(dbls(z0)) → c48(DBLS(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c50(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(sel(z0, z1)) → c51(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(indx(z0, z1)) → c52(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c53(FROM(proper(z0)), PROPER(z0))
PROPER(dbl1(z0)) → c54(DBL1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c56(S1(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c57(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)), ACTIVE(quote(0)))
ACTIVE(dbl(quote(s(z0)))) → c17(DBL(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)), ACTIVE(quote(0)))
ACTIVE(dbls(quote(s(z0)))) → c18(DBLS(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)))
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0))))))
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0))))))
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0)))
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(indx(sel1(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(indx(sel1(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel1(z0, z2)), x1), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(indx(quote(0), x1)) → c21(INDX(mark(01), x1), ACTIVE(quote(0)))
ACTIVE(indx(quote(s(z0)), x1)) → c21(INDX(mark(s1(quote(z0))), x1), ACTIVE(quote(s(z0))))
ACTIVE(indx(quote(dbl(z0)), x1)) → c21(INDX(mark(dbl1(z0)), x1), ACTIVE(quote(dbl(z0))))
ACTIVE(indx(quote(sel(z0, z1)), x1)) → c21(INDX(mark(sel1(z0, z1)), x1), ACTIVE(quote(sel(z0, z1))))
ACTIVE(indx(dbl(z0), x1)) → c21(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
ACTIVE(indx(dbls(z0), x1)) → c21(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(indx(z0, z1), x1)) → c21(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1)))
ACTIVE(indx(dbl1(z0), x1)) → c21(INDX(dbl1(active(z0)), x1), ACTIVE(dbl1(z0)))
ACTIVE(indx(s1(z0), x1)) → c21(INDX(s1(active(z0)), x1), ACTIVE(s1(z0)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(active(z0), z1), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(z0, active(z1)), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(quote(z0), x1)) → c21(INDX(quote(active(z0)), x1), ACTIVE(quote(z0)))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)))
ACTIVE(indx(dbl(0), x1)) → c21(INDX(mark(0), x1))
ACTIVE(indx(dbls(nil), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(indx(indx(nil, z0), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0))))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1))
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0)))
ACTIVE(dbl1(sel(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl1(sel(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl1(sel1(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl1(sel1(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl1(quote(0))) → c22(DBL1(mark(01)), ACTIVE(quote(0)))
ACTIVE(dbl1(quote(s(z0)))) → c22(DBL1(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(dbl1(quote(dbl(z0)))) → c22(DBL1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl1(quote(sel(z0, z1)))) → c22(DBL1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl1(dbl(z0))) → c22(DBL1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl1(dbls(z0))) → c22(DBL1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(indx(z0, z1))) → c22(DBL1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl1(dbl1(z0))) → c22(DBL1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl1(s1(z0))) → c22(DBL1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(quote(z0))) → c22(DBL1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(dbl1(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(dbl(0))) → c22(DBL1(mark(0)))
ACTIVE(dbl1(dbls(nil))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(indx(nil, z0))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(dbl1(0))) → c22(DBL1(mark(01)))
ACTIVE(dbl(dbl1(s(z0)))) → c4(DBL(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(DBLS(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(INDX(mark(s1(s1(dbl1(z0)))), x1))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(DBL1(mark(s(s(dbl(z0))))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(ACTIVE(dbl(s(z0))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(DBL1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(DBL1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl1(from(z0))) → c4(DBL1(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl1(from(z0))) → c4(ACTIVE(from(z0)))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(DBL1(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
K tuples:none
Defined Rule Symbols:
active, s, dbl, cons, dbls, sel, indx, s1, dbl1, sel1, quote, proper, from
Defined Pair Symbols:
ACTIVE, DBL, DBLS, SEL, INDX, DBL1, S1, SEL1, QUOTE, PROPER, S, CONS, FROM, TOP
Compound Symbols:
c5, c12, c15, c16, c19, c20, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c47, c48, c50, c51, c52, c53, c54, c56, c57, c58, c59, c60, c61, c62, c63, c8, c, c17, c17, c1, c18, c18, c2, c21, c21, c3, c22, c22, c4
(35) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
ACTIVE(
s1(
z0)) →
c23(
S1(
active(
z0)),
ACTIVE(
z0)) by
ACTIVE(s1(dbl(0))) → c23(S1(mark(0)), ACTIVE(dbl(0)))
ACTIVE(s1(dbl(s(z0)))) → c23(S1(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
ACTIVE(s1(dbls(nil))) → c23(S1(mark(nil)), ACTIVE(dbls(nil)))
ACTIVE(s1(dbls(cons(z0, z1)))) → c23(S1(mark(cons(dbl(z0), dbls(z1)))), ACTIVE(dbls(cons(z0, z1))))
ACTIVE(s1(sel(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(s1(sel(s(z0), cons(z1, z2)))) → c23(S1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(s1(indx(nil, z0))) → c23(S1(mark(nil)), ACTIVE(indx(nil, z0)))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c23(S1(mark(cons(sel(z0, z2), indx(z1, z2)))), ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(s1(from(z0))) → c23(S1(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s1(dbl1(0))) → c23(S1(mark(01)), ACTIVE(dbl1(0)))
ACTIVE(s1(dbl1(s(z0)))) → c23(S1(mark(s1(s1(dbl1(z0))))), ACTIVE(dbl1(s(z0))))
ACTIVE(s1(sel1(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(s1(sel1(s(z0), cons(z1, z2)))) → c23(S1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(s1(quote(0))) → c23(S1(mark(01)), ACTIVE(quote(0)))
ACTIVE(s1(quote(s(z0)))) → c23(S1(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(s1(quote(dbl(z0)))) → c23(S1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(s1(quote(sel(z0, z1)))) → c23(S1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(s1(dbl(z0))) → c23(S1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(s1(dbls(z0))) → c23(S1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(s1(indx(z0, z1))) → c23(S1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(s1(dbl1(z0))) → c23(S1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(s1(s1(z0))) → c23(S1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(quote(z0))) → c23(S1(quote(active(z0))), ACTIVE(quote(z0)))
(36) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(dbl(0)) → mark(0)
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
active(dbls(nil)) → mark(nil)
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1)))
active(sel(0, cons(z0, z1))) → mark(z0)
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
active(indx(nil, z0)) → mark(nil)
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2)))
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(dbl1(0)) → mark(01)
active(dbl1(s(z0))) → mark(s1(s1(dbl1(z0))))
active(sel1(0, cons(z0, z1))) → mark(z0)
active(sel1(s(z0), cons(z1, z2))) → mark(sel1(z0, z2))
active(quote(0)) → mark(01)
active(quote(s(z0))) → mark(s1(quote(z0)))
active(quote(dbl(z0))) → mark(dbl1(z0))
active(quote(sel(z0, z1))) → mark(sel1(z0, z1))
active(dbl(z0)) → dbl(active(z0))
active(dbls(z0)) → dbls(active(z0))
active(sel(z0, z1)) → sel(active(z0), z1)
active(sel(z0, z1)) → sel(z0, active(z1))
active(indx(z0, z1)) → indx(active(z0), z1)
active(dbl1(z0)) → dbl1(active(z0))
active(s1(z0)) → s1(active(z0))
active(sel1(z0, z1)) → sel1(active(z0), z1)
active(sel1(z0, z1)) → sel1(z0, active(z1))
active(quote(z0)) → quote(active(z0))
s(ok(z0)) → ok(s(z0))
dbl(mark(z0)) → mark(dbl(z0))
dbl(ok(z0)) → ok(dbl(z0))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
dbls(mark(z0)) → mark(dbls(z0))
dbls(ok(z0)) → ok(dbls(z0))
sel(mark(z0), z1) → mark(sel(z0, z1))
sel(z0, mark(z1)) → mark(sel(z0, z1))
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
indx(mark(z0), z1) → mark(indx(z0, z1))
indx(ok(z0), ok(z1)) → ok(indx(z0, z1))
s1(mark(z0)) → mark(s1(z0))
s1(ok(z0)) → ok(s1(z0))
dbl1(mark(z0)) → mark(dbl1(z0))
dbl1(ok(z0)) → ok(dbl1(z0))
sel1(mark(z0), z1) → mark(sel1(z0, z1))
sel1(z0, mark(z1)) → mark(sel1(z0, z1))
sel1(ok(z0), ok(z1)) → ok(sel1(z0, z1))
quote(mark(z0)) → mark(quote(z0))
quote(ok(z0)) → ok(quote(z0))
proper(dbl(z0)) → dbl(proper(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(dbls(z0)) → dbls(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
proper(indx(z0, z1)) → indx(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(dbl1(z0)) → dbl1(proper(z0))
proper(01) → ok(01)
proper(s1(z0)) → s1(proper(z0))
proper(sel1(z0, z1)) → sel1(proper(z0), proper(z1))
proper(quote(z0)) → quote(proper(z0))
from(ok(z0)) → ok(from(z0))
Tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
ACTIVE(quote(z0)) → c26(QUOTE(active(z0)), ACTIVE(z0))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(dbl(z0)) → c45(DBL(proper(z0)), PROPER(z0))
PROPER(s(z0)) → c47(S(proper(z0)), PROPER(z0))
PROPER(dbls(z0)) → c48(DBLS(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c50(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(sel(z0, z1)) → c51(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(indx(z0, z1)) → c52(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c53(FROM(proper(z0)), PROPER(z0))
PROPER(dbl1(z0)) → c54(DBL1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c56(S1(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c57(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)), ACTIVE(quote(0)))
ACTIVE(dbl(quote(s(z0)))) → c17(DBL(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)), ACTIVE(quote(0)))
ACTIVE(dbls(quote(s(z0)))) → c18(DBLS(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)))
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0))))))
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0))))))
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0)))
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(indx(sel1(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(indx(sel1(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel1(z0, z2)), x1), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(indx(quote(0), x1)) → c21(INDX(mark(01), x1), ACTIVE(quote(0)))
ACTIVE(indx(quote(s(z0)), x1)) → c21(INDX(mark(s1(quote(z0))), x1), ACTIVE(quote(s(z0))))
ACTIVE(indx(quote(dbl(z0)), x1)) → c21(INDX(mark(dbl1(z0)), x1), ACTIVE(quote(dbl(z0))))
ACTIVE(indx(quote(sel(z0, z1)), x1)) → c21(INDX(mark(sel1(z0, z1)), x1), ACTIVE(quote(sel(z0, z1))))
ACTIVE(indx(dbl(z0), x1)) → c21(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
ACTIVE(indx(dbls(z0), x1)) → c21(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(indx(z0, z1), x1)) → c21(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1)))
ACTIVE(indx(dbl1(z0), x1)) → c21(INDX(dbl1(active(z0)), x1), ACTIVE(dbl1(z0)))
ACTIVE(indx(s1(z0), x1)) → c21(INDX(s1(active(z0)), x1), ACTIVE(s1(z0)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(active(z0), z1), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(z0, active(z1)), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(quote(z0), x1)) → c21(INDX(quote(active(z0)), x1), ACTIVE(quote(z0)))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)))
ACTIVE(indx(dbl(0), x1)) → c21(INDX(mark(0), x1))
ACTIVE(indx(dbls(nil), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(indx(indx(nil, z0), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0))))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1))
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0)))
ACTIVE(dbl1(sel(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl1(sel(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl1(sel1(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl1(sel1(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl1(quote(0))) → c22(DBL1(mark(01)), ACTIVE(quote(0)))
ACTIVE(dbl1(quote(s(z0)))) → c22(DBL1(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(dbl1(quote(dbl(z0)))) → c22(DBL1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl1(quote(sel(z0, z1)))) → c22(DBL1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl1(dbl(z0))) → c22(DBL1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl1(dbls(z0))) → c22(DBL1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(indx(z0, z1))) → c22(DBL1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl1(dbl1(z0))) → c22(DBL1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl1(s1(z0))) → c22(DBL1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(quote(z0))) → c22(DBL1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(dbl1(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(dbl(0))) → c22(DBL1(mark(0)))
ACTIVE(dbl1(dbls(nil))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(indx(nil, z0))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(dbl1(0))) → c22(DBL1(mark(01)))
ACTIVE(dbl(dbl1(s(z0)))) → c4(DBL(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(DBLS(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(INDX(mark(s1(s1(dbl1(z0)))), x1))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(DBL1(mark(s(s(dbl(z0))))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(ACTIVE(dbl(s(z0))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(DBL1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(DBL1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl1(from(z0))) → c4(DBL1(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl1(from(z0))) → c4(ACTIVE(from(z0)))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(DBL1(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(s1(dbl(0))) → c23(S1(mark(0)), ACTIVE(dbl(0)))
ACTIVE(s1(dbl(s(z0)))) → c23(S1(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
ACTIVE(s1(dbls(nil))) → c23(S1(mark(nil)), ACTIVE(dbls(nil)))
ACTIVE(s1(dbls(cons(z0, z1)))) → c23(S1(mark(cons(dbl(z0), dbls(z1)))), ACTIVE(dbls(cons(z0, z1))))
ACTIVE(s1(sel(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(s1(sel(s(z0), cons(z1, z2)))) → c23(S1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(s1(indx(nil, z0))) → c23(S1(mark(nil)), ACTIVE(indx(nil, z0)))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c23(S1(mark(cons(sel(z0, z2), indx(z1, z2)))), ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(s1(from(z0))) → c23(S1(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s1(dbl1(0))) → c23(S1(mark(01)), ACTIVE(dbl1(0)))
ACTIVE(s1(dbl1(s(z0)))) → c23(S1(mark(s1(s1(dbl1(z0))))), ACTIVE(dbl1(s(z0))))
ACTIVE(s1(sel1(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(s1(sel1(s(z0), cons(z1, z2)))) → c23(S1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(s1(quote(0))) → c23(S1(mark(01)), ACTIVE(quote(0)))
ACTIVE(s1(quote(s(z0)))) → c23(S1(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(s1(quote(dbl(z0)))) → c23(S1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(s1(quote(sel(z0, z1)))) → c23(S1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(s1(dbl(z0))) → c23(S1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(s1(dbls(z0))) → c23(S1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(s1(indx(z0, z1))) → c23(S1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(s1(dbl1(z0))) → c23(S1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(s1(s1(z0))) → c23(S1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(quote(z0))) → c23(S1(quote(active(z0))), ACTIVE(quote(z0)))
S tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
ACTIVE(quote(z0)) → c26(QUOTE(active(z0)), ACTIVE(z0))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(dbl(z0)) → c45(DBL(proper(z0)), PROPER(z0))
PROPER(s(z0)) → c47(S(proper(z0)), PROPER(z0))
PROPER(dbls(z0)) → c48(DBLS(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c50(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(sel(z0, z1)) → c51(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(indx(z0, z1)) → c52(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c53(FROM(proper(z0)), PROPER(z0))
PROPER(dbl1(z0)) → c54(DBL1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c56(S1(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c57(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)), ACTIVE(quote(0)))
ACTIVE(dbl(quote(s(z0)))) → c17(DBL(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)), ACTIVE(quote(0)))
ACTIVE(dbls(quote(s(z0)))) → c18(DBLS(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)))
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0))))))
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0))))))
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0)))
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(indx(sel1(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(indx(sel1(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel1(z0, z2)), x1), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(indx(quote(0), x1)) → c21(INDX(mark(01), x1), ACTIVE(quote(0)))
ACTIVE(indx(quote(s(z0)), x1)) → c21(INDX(mark(s1(quote(z0))), x1), ACTIVE(quote(s(z0))))
ACTIVE(indx(quote(dbl(z0)), x1)) → c21(INDX(mark(dbl1(z0)), x1), ACTIVE(quote(dbl(z0))))
ACTIVE(indx(quote(sel(z0, z1)), x1)) → c21(INDX(mark(sel1(z0, z1)), x1), ACTIVE(quote(sel(z0, z1))))
ACTIVE(indx(dbl(z0), x1)) → c21(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
ACTIVE(indx(dbls(z0), x1)) → c21(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(indx(z0, z1), x1)) → c21(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1)))
ACTIVE(indx(dbl1(z0), x1)) → c21(INDX(dbl1(active(z0)), x1), ACTIVE(dbl1(z0)))
ACTIVE(indx(s1(z0), x1)) → c21(INDX(s1(active(z0)), x1), ACTIVE(s1(z0)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(active(z0), z1), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(z0, active(z1)), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(quote(z0), x1)) → c21(INDX(quote(active(z0)), x1), ACTIVE(quote(z0)))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)))
ACTIVE(indx(dbl(0), x1)) → c21(INDX(mark(0), x1))
ACTIVE(indx(dbls(nil), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(indx(indx(nil, z0), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0))))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1))
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0)))
ACTIVE(dbl1(sel(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl1(sel(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl1(sel1(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl1(sel1(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl1(quote(0))) → c22(DBL1(mark(01)), ACTIVE(quote(0)))
ACTIVE(dbl1(quote(s(z0)))) → c22(DBL1(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(dbl1(quote(dbl(z0)))) → c22(DBL1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl1(quote(sel(z0, z1)))) → c22(DBL1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl1(dbl(z0))) → c22(DBL1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl1(dbls(z0))) → c22(DBL1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(indx(z0, z1))) → c22(DBL1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl1(dbl1(z0))) → c22(DBL1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl1(s1(z0))) → c22(DBL1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(quote(z0))) → c22(DBL1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(dbl1(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(dbl(0))) → c22(DBL1(mark(0)))
ACTIVE(dbl1(dbls(nil))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(indx(nil, z0))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(dbl1(0))) → c22(DBL1(mark(01)))
ACTIVE(dbl(dbl1(s(z0)))) → c4(DBL(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(DBLS(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(INDX(mark(s1(s1(dbl1(z0)))), x1))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(DBL1(mark(s(s(dbl(z0))))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(ACTIVE(dbl(s(z0))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(DBL1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(DBL1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl1(from(z0))) → c4(DBL1(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl1(from(z0))) → c4(ACTIVE(from(z0)))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(DBL1(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(s1(dbl(0))) → c23(S1(mark(0)), ACTIVE(dbl(0)))
ACTIVE(s1(dbl(s(z0)))) → c23(S1(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
ACTIVE(s1(dbls(nil))) → c23(S1(mark(nil)), ACTIVE(dbls(nil)))
ACTIVE(s1(dbls(cons(z0, z1)))) → c23(S1(mark(cons(dbl(z0), dbls(z1)))), ACTIVE(dbls(cons(z0, z1))))
ACTIVE(s1(sel(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(s1(sel(s(z0), cons(z1, z2)))) → c23(S1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(s1(indx(nil, z0))) → c23(S1(mark(nil)), ACTIVE(indx(nil, z0)))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c23(S1(mark(cons(sel(z0, z2), indx(z1, z2)))), ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(s1(from(z0))) → c23(S1(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s1(dbl1(0))) → c23(S1(mark(01)), ACTIVE(dbl1(0)))
ACTIVE(s1(dbl1(s(z0)))) → c23(S1(mark(s1(s1(dbl1(z0))))), ACTIVE(dbl1(s(z0))))
ACTIVE(s1(sel1(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(s1(sel1(s(z0), cons(z1, z2)))) → c23(S1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(s1(quote(0))) → c23(S1(mark(01)), ACTIVE(quote(0)))
ACTIVE(s1(quote(s(z0)))) → c23(S1(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(s1(quote(dbl(z0)))) → c23(S1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(s1(quote(sel(z0, z1)))) → c23(S1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(s1(dbl(z0))) → c23(S1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(s1(dbls(z0))) → c23(S1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(s1(indx(z0, z1))) → c23(S1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(s1(dbl1(z0))) → c23(S1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(s1(s1(z0))) → c23(S1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(quote(z0))) → c23(S1(quote(active(z0))), ACTIVE(quote(z0)))
K tuples:none
Defined Rule Symbols:
active, s, dbl, cons, dbls, sel, indx, s1, dbl1, sel1, quote, proper, from
Defined Pair Symbols:
ACTIVE, DBL, DBLS, SEL, INDX, DBL1, S1, SEL1, QUOTE, PROPER, S, CONS, FROM, TOP
Compound Symbols:
c5, c12, c15, c16, c19, c20, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c47, c48, c50, c51, c52, c53, c54, c56, c57, c58, c59, c60, c61, c62, c63, c8, c, c17, c17, c1, c18, c18, c2, c21, c21, c3, c22, c22, c4, c23
(37) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 4 trailing tuple parts
(38) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(dbl(0)) → mark(0)
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
active(dbls(nil)) → mark(nil)
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1)))
active(sel(0, cons(z0, z1))) → mark(z0)
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
active(indx(nil, z0)) → mark(nil)
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2)))
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(dbl1(0)) → mark(01)
active(dbl1(s(z0))) → mark(s1(s1(dbl1(z0))))
active(sel1(0, cons(z0, z1))) → mark(z0)
active(sel1(s(z0), cons(z1, z2))) → mark(sel1(z0, z2))
active(quote(0)) → mark(01)
active(quote(s(z0))) → mark(s1(quote(z0)))
active(quote(dbl(z0))) → mark(dbl1(z0))
active(quote(sel(z0, z1))) → mark(sel1(z0, z1))
active(dbl(z0)) → dbl(active(z0))
active(dbls(z0)) → dbls(active(z0))
active(sel(z0, z1)) → sel(active(z0), z1)
active(sel(z0, z1)) → sel(z0, active(z1))
active(indx(z0, z1)) → indx(active(z0), z1)
active(dbl1(z0)) → dbl1(active(z0))
active(s1(z0)) → s1(active(z0))
active(sel1(z0, z1)) → sel1(active(z0), z1)
active(sel1(z0, z1)) → sel1(z0, active(z1))
active(quote(z0)) → quote(active(z0))
s(ok(z0)) → ok(s(z0))
dbl(mark(z0)) → mark(dbl(z0))
dbl(ok(z0)) → ok(dbl(z0))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
dbls(mark(z0)) → mark(dbls(z0))
dbls(ok(z0)) → ok(dbls(z0))
sel(mark(z0), z1) → mark(sel(z0, z1))
sel(z0, mark(z1)) → mark(sel(z0, z1))
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
indx(mark(z0), z1) → mark(indx(z0, z1))
indx(ok(z0), ok(z1)) → ok(indx(z0, z1))
s1(mark(z0)) → mark(s1(z0))
s1(ok(z0)) → ok(s1(z0))
dbl1(mark(z0)) → mark(dbl1(z0))
dbl1(ok(z0)) → ok(dbl1(z0))
sel1(mark(z0), z1) → mark(sel1(z0, z1))
sel1(z0, mark(z1)) → mark(sel1(z0, z1))
sel1(ok(z0), ok(z1)) → ok(sel1(z0, z1))
quote(mark(z0)) → mark(quote(z0))
quote(ok(z0)) → ok(quote(z0))
proper(dbl(z0)) → dbl(proper(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(dbls(z0)) → dbls(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
proper(indx(z0, z1)) → indx(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(dbl1(z0)) → dbl1(proper(z0))
proper(01) → ok(01)
proper(s1(z0)) → s1(proper(z0))
proper(sel1(z0, z1)) → sel1(proper(z0), proper(z1))
proper(quote(z0)) → quote(proper(z0))
from(ok(z0)) → ok(from(z0))
Tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
ACTIVE(quote(z0)) → c26(QUOTE(active(z0)), ACTIVE(z0))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(dbl(z0)) → c45(DBL(proper(z0)), PROPER(z0))
PROPER(s(z0)) → c47(S(proper(z0)), PROPER(z0))
PROPER(dbls(z0)) → c48(DBLS(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c50(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(sel(z0, z1)) → c51(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(indx(z0, z1)) → c52(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c53(FROM(proper(z0)), PROPER(z0))
PROPER(dbl1(z0)) → c54(DBL1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c56(S1(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c57(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)), ACTIVE(quote(0)))
ACTIVE(dbl(quote(s(z0)))) → c17(DBL(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)), ACTIVE(quote(0)))
ACTIVE(dbls(quote(s(z0)))) → c18(DBLS(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)))
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0))))))
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0))))))
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0)))
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(indx(sel1(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(indx(sel1(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel1(z0, z2)), x1), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(indx(quote(0), x1)) → c21(INDX(mark(01), x1), ACTIVE(quote(0)))
ACTIVE(indx(quote(s(z0)), x1)) → c21(INDX(mark(s1(quote(z0))), x1), ACTIVE(quote(s(z0))))
ACTIVE(indx(quote(dbl(z0)), x1)) → c21(INDX(mark(dbl1(z0)), x1), ACTIVE(quote(dbl(z0))))
ACTIVE(indx(quote(sel(z0, z1)), x1)) → c21(INDX(mark(sel1(z0, z1)), x1), ACTIVE(quote(sel(z0, z1))))
ACTIVE(indx(dbl(z0), x1)) → c21(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
ACTIVE(indx(dbls(z0), x1)) → c21(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(indx(z0, z1), x1)) → c21(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1)))
ACTIVE(indx(dbl1(z0), x1)) → c21(INDX(dbl1(active(z0)), x1), ACTIVE(dbl1(z0)))
ACTIVE(indx(s1(z0), x1)) → c21(INDX(s1(active(z0)), x1), ACTIVE(s1(z0)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(active(z0), z1), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(z0, active(z1)), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(quote(z0), x1)) → c21(INDX(quote(active(z0)), x1), ACTIVE(quote(z0)))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)))
ACTIVE(indx(dbl(0), x1)) → c21(INDX(mark(0), x1))
ACTIVE(indx(dbls(nil), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(indx(indx(nil, z0), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0))))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1))
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0)))
ACTIVE(dbl1(sel(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl1(sel(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl1(sel1(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl1(sel1(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl1(quote(0))) → c22(DBL1(mark(01)), ACTIVE(quote(0)))
ACTIVE(dbl1(quote(s(z0)))) → c22(DBL1(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(dbl1(quote(dbl(z0)))) → c22(DBL1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl1(quote(sel(z0, z1)))) → c22(DBL1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl1(dbl(z0))) → c22(DBL1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl1(dbls(z0))) → c22(DBL1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(indx(z0, z1))) → c22(DBL1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl1(dbl1(z0))) → c22(DBL1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl1(s1(z0))) → c22(DBL1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(quote(z0))) → c22(DBL1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(dbl1(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(dbl(0))) → c22(DBL1(mark(0)))
ACTIVE(dbl1(dbls(nil))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(indx(nil, z0))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(dbl1(0))) → c22(DBL1(mark(01)))
ACTIVE(dbl(dbl1(s(z0)))) → c4(DBL(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(DBLS(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(INDX(mark(s1(s1(dbl1(z0)))), x1))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(DBL1(mark(s(s(dbl(z0))))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(ACTIVE(dbl(s(z0))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(DBL1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(DBL1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl1(from(z0))) → c4(DBL1(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl1(from(z0))) → c4(ACTIVE(from(z0)))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(DBL1(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(s1(dbl(s(z0)))) → c23(S1(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c23(S1(mark(cons(dbl(z0), dbls(z1)))), ACTIVE(dbls(cons(z0, z1))))
ACTIVE(s1(sel(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(s1(sel(s(z0), cons(z1, z2)))) → c23(S1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c23(S1(mark(cons(sel(z0, z2), indx(z1, z2)))), ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(s1(from(z0))) → c23(S1(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s1(dbl1(s(z0)))) → c23(S1(mark(s1(s1(dbl1(z0))))), ACTIVE(dbl1(s(z0))))
ACTIVE(s1(sel1(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(s1(sel1(s(z0), cons(z1, z2)))) → c23(S1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(s1(quote(0))) → c23(S1(mark(01)), ACTIVE(quote(0)))
ACTIVE(s1(quote(s(z0)))) → c23(S1(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(s1(quote(dbl(z0)))) → c23(S1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(s1(quote(sel(z0, z1)))) → c23(S1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(s1(dbl(z0))) → c23(S1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(s1(dbls(z0))) → c23(S1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(s1(indx(z0, z1))) → c23(S1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(s1(dbl1(z0))) → c23(S1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(s1(s1(z0))) → c23(S1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(quote(z0))) → c23(S1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(s1(dbl(0))) → c23(S1(mark(0)))
ACTIVE(s1(dbls(nil))) → c23(S1(mark(nil)))
ACTIVE(s1(indx(nil, z0))) → c23(S1(mark(nil)))
ACTIVE(s1(dbl1(0))) → c23(S1(mark(01)))
S tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
ACTIVE(quote(z0)) → c26(QUOTE(active(z0)), ACTIVE(z0))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(dbl(z0)) → c45(DBL(proper(z0)), PROPER(z0))
PROPER(s(z0)) → c47(S(proper(z0)), PROPER(z0))
PROPER(dbls(z0)) → c48(DBLS(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c50(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(sel(z0, z1)) → c51(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(indx(z0, z1)) → c52(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c53(FROM(proper(z0)), PROPER(z0))
PROPER(dbl1(z0)) → c54(DBL1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c56(S1(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c57(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)), ACTIVE(quote(0)))
ACTIVE(dbl(quote(s(z0)))) → c17(DBL(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)), ACTIVE(quote(0)))
ACTIVE(dbls(quote(s(z0)))) → c18(DBLS(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)))
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0))))))
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0))))))
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0)))
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(indx(sel1(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(indx(sel1(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel1(z0, z2)), x1), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(indx(quote(0), x1)) → c21(INDX(mark(01), x1), ACTIVE(quote(0)))
ACTIVE(indx(quote(s(z0)), x1)) → c21(INDX(mark(s1(quote(z0))), x1), ACTIVE(quote(s(z0))))
ACTIVE(indx(quote(dbl(z0)), x1)) → c21(INDX(mark(dbl1(z0)), x1), ACTIVE(quote(dbl(z0))))
ACTIVE(indx(quote(sel(z0, z1)), x1)) → c21(INDX(mark(sel1(z0, z1)), x1), ACTIVE(quote(sel(z0, z1))))
ACTIVE(indx(dbl(z0), x1)) → c21(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
ACTIVE(indx(dbls(z0), x1)) → c21(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(indx(z0, z1), x1)) → c21(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1)))
ACTIVE(indx(dbl1(z0), x1)) → c21(INDX(dbl1(active(z0)), x1), ACTIVE(dbl1(z0)))
ACTIVE(indx(s1(z0), x1)) → c21(INDX(s1(active(z0)), x1), ACTIVE(s1(z0)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(active(z0), z1), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(z0, active(z1)), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(quote(z0), x1)) → c21(INDX(quote(active(z0)), x1), ACTIVE(quote(z0)))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)))
ACTIVE(indx(dbl(0), x1)) → c21(INDX(mark(0), x1))
ACTIVE(indx(dbls(nil), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(indx(indx(nil, z0), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0))))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1))
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0)))
ACTIVE(dbl1(sel(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl1(sel(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl1(sel1(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl1(sel1(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl1(quote(0))) → c22(DBL1(mark(01)), ACTIVE(quote(0)))
ACTIVE(dbl1(quote(s(z0)))) → c22(DBL1(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(dbl1(quote(dbl(z0)))) → c22(DBL1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl1(quote(sel(z0, z1)))) → c22(DBL1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl1(dbl(z0))) → c22(DBL1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl1(dbls(z0))) → c22(DBL1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(indx(z0, z1))) → c22(DBL1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl1(dbl1(z0))) → c22(DBL1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl1(s1(z0))) → c22(DBL1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(quote(z0))) → c22(DBL1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(dbl1(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(dbl(0))) → c22(DBL1(mark(0)))
ACTIVE(dbl1(dbls(nil))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(indx(nil, z0))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(dbl1(0))) → c22(DBL1(mark(01)))
ACTIVE(dbl(dbl1(s(z0)))) → c4(DBL(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(DBLS(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(INDX(mark(s1(s1(dbl1(z0)))), x1))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(DBL1(mark(s(s(dbl(z0))))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(ACTIVE(dbl(s(z0))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(DBL1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(DBL1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl1(from(z0))) → c4(DBL1(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl1(from(z0))) → c4(ACTIVE(from(z0)))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(DBL1(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(s1(dbl(s(z0)))) → c23(S1(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c23(S1(mark(cons(dbl(z0), dbls(z1)))), ACTIVE(dbls(cons(z0, z1))))
ACTIVE(s1(sel(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(s1(sel(s(z0), cons(z1, z2)))) → c23(S1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c23(S1(mark(cons(sel(z0, z2), indx(z1, z2)))), ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(s1(from(z0))) → c23(S1(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s1(dbl1(s(z0)))) → c23(S1(mark(s1(s1(dbl1(z0))))), ACTIVE(dbl1(s(z0))))
ACTIVE(s1(sel1(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(s1(sel1(s(z0), cons(z1, z2)))) → c23(S1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(s1(quote(0))) → c23(S1(mark(01)), ACTIVE(quote(0)))
ACTIVE(s1(quote(s(z0)))) → c23(S1(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(s1(quote(dbl(z0)))) → c23(S1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(s1(quote(sel(z0, z1)))) → c23(S1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(s1(dbl(z0))) → c23(S1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(s1(dbls(z0))) → c23(S1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(s1(indx(z0, z1))) → c23(S1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(s1(dbl1(z0))) → c23(S1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(s1(s1(z0))) → c23(S1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(quote(z0))) → c23(S1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(s1(dbl(0))) → c23(S1(mark(0)))
ACTIVE(s1(dbls(nil))) → c23(S1(mark(nil)))
ACTIVE(s1(indx(nil, z0))) → c23(S1(mark(nil)))
ACTIVE(s1(dbl1(0))) → c23(S1(mark(01)))
K tuples:none
Defined Rule Symbols:
active, s, dbl, cons, dbls, sel, indx, s1, dbl1, sel1, quote, proper, from
Defined Pair Symbols:
ACTIVE, DBL, DBLS, SEL, INDX, DBL1, S1, SEL1, QUOTE, PROPER, S, CONS, FROM, TOP
Compound Symbols:
c5, c12, c15, c16, c19, c20, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c47, c48, c50, c51, c52, c53, c54, c56, c57, c58, c59, c60, c61, c62, c63, c8, c, c17, c17, c1, c18, c18, c2, c21, c21, c3, c22, c22, c4, c23, c23
(39) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID) transformation)
Split RHS of tuples not part of any SCC
(40) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(dbl(0)) → mark(0)
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
active(dbls(nil)) → mark(nil)
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1)))
active(sel(0, cons(z0, z1))) → mark(z0)
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
active(indx(nil, z0)) → mark(nil)
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2)))
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(dbl1(0)) → mark(01)
active(dbl1(s(z0))) → mark(s1(s1(dbl1(z0))))
active(sel1(0, cons(z0, z1))) → mark(z0)
active(sel1(s(z0), cons(z1, z2))) → mark(sel1(z0, z2))
active(quote(0)) → mark(01)
active(quote(s(z0))) → mark(s1(quote(z0)))
active(quote(dbl(z0))) → mark(dbl1(z0))
active(quote(sel(z0, z1))) → mark(sel1(z0, z1))
active(dbl(z0)) → dbl(active(z0))
active(dbls(z0)) → dbls(active(z0))
active(sel(z0, z1)) → sel(active(z0), z1)
active(sel(z0, z1)) → sel(z0, active(z1))
active(indx(z0, z1)) → indx(active(z0), z1)
active(dbl1(z0)) → dbl1(active(z0))
active(s1(z0)) → s1(active(z0))
active(sel1(z0, z1)) → sel1(active(z0), z1)
active(sel1(z0, z1)) → sel1(z0, active(z1))
active(quote(z0)) → quote(active(z0))
s(ok(z0)) → ok(s(z0))
dbl(mark(z0)) → mark(dbl(z0))
dbl(ok(z0)) → ok(dbl(z0))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
dbls(mark(z0)) → mark(dbls(z0))
dbls(ok(z0)) → ok(dbls(z0))
sel(mark(z0), z1) → mark(sel(z0, z1))
sel(z0, mark(z1)) → mark(sel(z0, z1))
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
indx(mark(z0), z1) → mark(indx(z0, z1))
indx(ok(z0), ok(z1)) → ok(indx(z0, z1))
s1(mark(z0)) → mark(s1(z0))
s1(ok(z0)) → ok(s1(z0))
dbl1(mark(z0)) → mark(dbl1(z0))
dbl1(ok(z0)) → ok(dbl1(z0))
sel1(mark(z0), z1) → mark(sel1(z0, z1))
sel1(z0, mark(z1)) → mark(sel1(z0, z1))
sel1(ok(z0), ok(z1)) → ok(sel1(z0, z1))
quote(mark(z0)) → mark(quote(z0))
quote(ok(z0)) → ok(quote(z0))
proper(dbl(z0)) → dbl(proper(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(dbls(z0)) → dbls(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
proper(indx(z0, z1)) → indx(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(dbl1(z0)) → dbl1(proper(z0))
proper(01) → ok(01)
proper(s1(z0)) → s1(proper(z0))
proper(sel1(z0, z1)) → sel1(proper(z0), proper(z1))
proper(quote(z0)) → quote(proper(z0))
from(ok(z0)) → ok(from(z0))
Tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
ACTIVE(quote(z0)) → c26(QUOTE(active(z0)), ACTIVE(z0))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(dbl(z0)) → c45(DBL(proper(z0)), PROPER(z0))
PROPER(s(z0)) → c47(S(proper(z0)), PROPER(z0))
PROPER(dbls(z0)) → c48(DBLS(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c50(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(sel(z0, z1)) → c51(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(indx(z0, z1)) → c52(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c53(FROM(proper(z0)), PROPER(z0))
PROPER(dbl1(z0)) → c54(DBL1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c56(S1(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c57(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)), ACTIVE(quote(0)))
ACTIVE(dbl(quote(s(z0)))) → c17(DBL(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)), ACTIVE(quote(0)))
ACTIVE(dbls(quote(s(z0)))) → c18(DBLS(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)))
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0))))))
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0))))))
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0)))
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(indx(sel1(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(indx(sel1(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel1(z0, z2)), x1), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(indx(quote(0), x1)) → c21(INDX(mark(01), x1), ACTIVE(quote(0)))
ACTIVE(indx(quote(s(z0)), x1)) → c21(INDX(mark(s1(quote(z0))), x1), ACTIVE(quote(s(z0))))
ACTIVE(indx(quote(dbl(z0)), x1)) → c21(INDX(mark(dbl1(z0)), x1), ACTIVE(quote(dbl(z0))))
ACTIVE(indx(quote(sel(z0, z1)), x1)) → c21(INDX(mark(sel1(z0, z1)), x1), ACTIVE(quote(sel(z0, z1))))
ACTIVE(indx(dbl(z0), x1)) → c21(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
ACTIVE(indx(dbls(z0), x1)) → c21(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(indx(z0, z1), x1)) → c21(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1)))
ACTIVE(indx(dbl1(z0), x1)) → c21(INDX(dbl1(active(z0)), x1), ACTIVE(dbl1(z0)))
ACTIVE(indx(s1(z0), x1)) → c21(INDX(s1(active(z0)), x1), ACTIVE(s1(z0)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(active(z0), z1), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(z0, active(z1)), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(quote(z0), x1)) → c21(INDX(quote(active(z0)), x1), ACTIVE(quote(z0)))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)))
ACTIVE(indx(dbl(0), x1)) → c21(INDX(mark(0), x1))
ACTIVE(indx(dbls(nil), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(indx(indx(nil, z0), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0))))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1))
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0)))
ACTIVE(dbl1(sel(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl1(sel(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl1(sel1(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl1(sel1(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl1(quote(0))) → c22(DBL1(mark(01)), ACTIVE(quote(0)))
ACTIVE(dbl1(quote(s(z0)))) → c22(DBL1(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(dbl1(quote(dbl(z0)))) → c22(DBL1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl1(quote(sel(z0, z1)))) → c22(DBL1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl1(dbl(z0))) → c22(DBL1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl1(dbls(z0))) → c22(DBL1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(indx(z0, z1))) → c22(DBL1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl1(dbl1(z0))) → c22(DBL1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl1(s1(z0))) → c22(DBL1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(quote(z0))) → c22(DBL1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(dbl1(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(dbl(0))) → c22(DBL1(mark(0)))
ACTIVE(dbl1(dbls(nil))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(indx(nil, z0))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(dbl1(0))) → c22(DBL1(mark(01)))
ACTIVE(dbl(dbl1(s(z0)))) → c4(DBL(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(DBLS(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(INDX(mark(s1(s1(dbl1(z0)))), x1))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(DBL1(mark(s(s(dbl(z0))))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(ACTIVE(dbl(s(z0))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(DBL1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(DBL1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl1(from(z0))) → c4(DBL1(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl1(from(z0))) → c4(ACTIVE(from(z0)))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(DBL1(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(s1(sel(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(s1(sel(s(z0), cons(z1, z2)))) → c23(S1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(s1(sel1(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(s1(sel1(s(z0), cons(z1, z2)))) → c23(S1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(s1(quote(0))) → c23(S1(mark(01)), ACTIVE(quote(0)))
ACTIVE(s1(quote(s(z0)))) → c23(S1(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(s1(quote(dbl(z0)))) → c23(S1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(s1(quote(sel(z0, z1)))) → c23(S1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(s1(dbl(z0))) → c23(S1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(s1(dbls(z0))) → c23(S1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(s1(indx(z0, z1))) → c23(S1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(s1(dbl1(z0))) → c23(S1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(s1(s1(z0))) → c23(S1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(quote(z0))) → c23(S1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(s1(dbl(0))) → c23(S1(mark(0)))
ACTIVE(s1(dbls(nil))) → c23(S1(mark(nil)))
ACTIVE(s1(indx(nil, z0))) → c23(S1(mark(nil)))
ACTIVE(s1(dbl1(0))) → c23(S1(mark(01)))
ACTIVE(s1(dbl(s(z0)))) → c6(S1(mark(s(s(dbl(z0))))))
ACTIVE(s1(dbl(s(z0)))) → c6(ACTIVE(dbl(s(z0))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(S1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(S1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(s1(from(z0))) → c6(S1(mark(cons(z0, from(s(z0))))))
ACTIVE(s1(from(z0))) → c6(ACTIVE(from(z0)))
ACTIVE(s1(dbl1(s(z0)))) → c6(S1(mark(s1(s1(dbl1(z0))))))
ACTIVE(s1(dbl1(s(z0)))) → c6(ACTIVE(dbl1(s(z0))))
S tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
ACTIVE(quote(z0)) → c26(QUOTE(active(z0)), ACTIVE(z0))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(dbl(z0)) → c45(DBL(proper(z0)), PROPER(z0))
PROPER(s(z0)) → c47(S(proper(z0)), PROPER(z0))
PROPER(dbls(z0)) → c48(DBLS(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c50(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(sel(z0, z1)) → c51(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(indx(z0, z1)) → c52(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c53(FROM(proper(z0)), PROPER(z0))
PROPER(dbl1(z0)) → c54(DBL1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c56(S1(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c57(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)), ACTIVE(quote(0)))
ACTIVE(dbl(quote(s(z0)))) → c17(DBL(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)), ACTIVE(quote(0)))
ACTIVE(dbls(quote(s(z0)))) → c18(DBLS(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)))
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0))))))
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0))))))
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0)))
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(indx(sel1(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(indx(sel1(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel1(z0, z2)), x1), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(indx(quote(0), x1)) → c21(INDX(mark(01), x1), ACTIVE(quote(0)))
ACTIVE(indx(quote(s(z0)), x1)) → c21(INDX(mark(s1(quote(z0))), x1), ACTIVE(quote(s(z0))))
ACTIVE(indx(quote(dbl(z0)), x1)) → c21(INDX(mark(dbl1(z0)), x1), ACTIVE(quote(dbl(z0))))
ACTIVE(indx(quote(sel(z0, z1)), x1)) → c21(INDX(mark(sel1(z0, z1)), x1), ACTIVE(quote(sel(z0, z1))))
ACTIVE(indx(dbl(z0), x1)) → c21(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
ACTIVE(indx(dbls(z0), x1)) → c21(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(indx(z0, z1), x1)) → c21(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1)))
ACTIVE(indx(dbl1(z0), x1)) → c21(INDX(dbl1(active(z0)), x1), ACTIVE(dbl1(z0)))
ACTIVE(indx(s1(z0), x1)) → c21(INDX(s1(active(z0)), x1), ACTIVE(s1(z0)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(active(z0), z1), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(z0, active(z1)), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(quote(z0), x1)) → c21(INDX(quote(active(z0)), x1), ACTIVE(quote(z0)))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)))
ACTIVE(indx(dbl(0), x1)) → c21(INDX(mark(0), x1))
ACTIVE(indx(dbls(nil), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(indx(indx(nil, z0), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0))))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1))
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0)))
ACTIVE(dbl1(sel(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl1(sel(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl1(sel1(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl1(sel1(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl1(quote(0))) → c22(DBL1(mark(01)), ACTIVE(quote(0)))
ACTIVE(dbl1(quote(s(z0)))) → c22(DBL1(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(dbl1(quote(dbl(z0)))) → c22(DBL1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl1(quote(sel(z0, z1)))) → c22(DBL1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl1(dbl(z0))) → c22(DBL1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl1(dbls(z0))) → c22(DBL1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(indx(z0, z1))) → c22(DBL1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl1(dbl1(z0))) → c22(DBL1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl1(s1(z0))) → c22(DBL1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(quote(z0))) → c22(DBL1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(dbl1(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(dbl(0))) → c22(DBL1(mark(0)))
ACTIVE(dbl1(dbls(nil))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(indx(nil, z0))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(dbl1(0))) → c22(DBL1(mark(01)))
ACTIVE(dbl(dbl1(s(z0)))) → c4(DBL(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(DBLS(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(INDX(mark(s1(s1(dbl1(z0)))), x1))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(DBL1(mark(s(s(dbl(z0))))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(ACTIVE(dbl(s(z0))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(DBL1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(DBL1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl1(from(z0))) → c4(DBL1(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl1(from(z0))) → c4(ACTIVE(from(z0)))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(DBL1(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(s1(sel(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(s1(sel(s(z0), cons(z1, z2)))) → c23(S1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(s1(sel1(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(s1(sel1(s(z0), cons(z1, z2)))) → c23(S1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(s1(quote(0))) → c23(S1(mark(01)), ACTIVE(quote(0)))
ACTIVE(s1(quote(s(z0)))) → c23(S1(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(s1(quote(dbl(z0)))) → c23(S1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(s1(quote(sel(z0, z1)))) → c23(S1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(s1(dbl(z0))) → c23(S1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(s1(dbls(z0))) → c23(S1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(s1(indx(z0, z1))) → c23(S1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(s1(dbl1(z0))) → c23(S1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(s1(s1(z0))) → c23(S1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(quote(z0))) → c23(S1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(s1(dbl(0))) → c23(S1(mark(0)))
ACTIVE(s1(dbls(nil))) → c23(S1(mark(nil)))
ACTIVE(s1(indx(nil, z0))) → c23(S1(mark(nil)))
ACTIVE(s1(dbl1(0))) → c23(S1(mark(01)))
ACTIVE(s1(dbl(s(z0)))) → c6(S1(mark(s(s(dbl(z0))))))
ACTIVE(s1(dbl(s(z0)))) → c6(ACTIVE(dbl(s(z0))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(S1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(S1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(s1(from(z0))) → c6(S1(mark(cons(z0, from(s(z0))))))
ACTIVE(s1(from(z0))) → c6(ACTIVE(from(z0)))
ACTIVE(s1(dbl1(s(z0)))) → c6(S1(mark(s1(s1(dbl1(z0))))))
ACTIVE(s1(dbl1(s(z0)))) → c6(ACTIVE(dbl1(s(z0))))
K tuples:none
Defined Rule Symbols:
active, s, dbl, cons, dbls, sel, indx, s1, dbl1, sel1, quote, proper, from
Defined Pair Symbols:
ACTIVE, DBL, DBLS, SEL, INDX, DBL1, S1, SEL1, QUOTE, PROPER, S, CONS, FROM, TOP
Compound Symbols:
c5, c12, c15, c16, c19, c20, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c47, c48, c50, c51, c52, c53, c54, c56, c57, c58, c59, c60, c61, c62, c63, c8, c, c17, c17, c1, c18, c18, c2, c21, c21, c3, c22, c22, c4, c23, c23, c6
(41) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
ACTIVE(
quote(
z0)) →
c26(
QUOTE(
active(
z0)),
ACTIVE(
z0)) by
ACTIVE(quote(dbl(0))) → c26(QUOTE(mark(0)), ACTIVE(dbl(0)))
ACTIVE(quote(dbl(s(z0)))) → c26(QUOTE(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
ACTIVE(quote(dbls(nil))) → c26(QUOTE(mark(nil)), ACTIVE(dbls(nil)))
ACTIVE(quote(dbls(cons(z0, z1)))) → c26(QUOTE(mark(cons(dbl(z0), dbls(z1)))), ACTIVE(dbls(cons(z0, z1))))
ACTIVE(quote(sel(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(quote(sel(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(quote(indx(nil, z0))) → c26(QUOTE(mark(nil)), ACTIVE(indx(nil, z0)))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c26(QUOTE(mark(cons(sel(z0, z2), indx(z1, z2)))), ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(quote(from(z0))) → c26(QUOTE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(quote(dbl1(0))) → c26(QUOTE(mark(01)), ACTIVE(dbl1(0)))
ACTIVE(quote(dbl1(s(z0)))) → c26(QUOTE(mark(s1(s1(dbl1(z0))))), ACTIVE(dbl1(s(z0))))
ACTIVE(quote(sel1(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(quote(sel1(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(quote(quote(0))) → c26(QUOTE(mark(01)), ACTIVE(quote(0)))
ACTIVE(quote(quote(s(z0)))) → c26(QUOTE(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(quote(quote(dbl(z0)))) → c26(QUOTE(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(quote(quote(sel(z0, z1)))) → c26(QUOTE(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(quote(dbl(z0))) → c26(QUOTE(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(quote(dbls(z0))) → c26(QUOTE(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(quote(indx(z0, z1))) → c26(QUOTE(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(quote(dbl1(z0))) → c26(QUOTE(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(quote(s1(z0))) → c26(QUOTE(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(quote(z0))) → c26(QUOTE(quote(active(z0))), ACTIVE(quote(z0)))
(42) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(dbl(0)) → mark(0)
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
active(dbls(nil)) → mark(nil)
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1)))
active(sel(0, cons(z0, z1))) → mark(z0)
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
active(indx(nil, z0)) → mark(nil)
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2)))
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(dbl1(0)) → mark(01)
active(dbl1(s(z0))) → mark(s1(s1(dbl1(z0))))
active(sel1(0, cons(z0, z1))) → mark(z0)
active(sel1(s(z0), cons(z1, z2))) → mark(sel1(z0, z2))
active(quote(0)) → mark(01)
active(quote(s(z0))) → mark(s1(quote(z0)))
active(quote(dbl(z0))) → mark(dbl1(z0))
active(quote(sel(z0, z1))) → mark(sel1(z0, z1))
active(dbl(z0)) → dbl(active(z0))
active(dbls(z0)) → dbls(active(z0))
active(sel(z0, z1)) → sel(active(z0), z1)
active(sel(z0, z1)) → sel(z0, active(z1))
active(indx(z0, z1)) → indx(active(z0), z1)
active(dbl1(z0)) → dbl1(active(z0))
active(s1(z0)) → s1(active(z0))
active(sel1(z0, z1)) → sel1(active(z0), z1)
active(sel1(z0, z1)) → sel1(z0, active(z1))
active(quote(z0)) → quote(active(z0))
s(ok(z0)) → ok(s(z0))
dbl(mark(z0)) → mark(dbl(z0))
dbl(ok(z0)) → ok(dbl(z0))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
dbls(mark(z0)) → mark(dbls(z0))
dbls(ok(z0)) → ok(dbls(z0))
sel(mark(z0), z1) → mark(sel(z0, z1))
sel(z0, mark(z1)) → mark(sel(z0, z1))
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
indx(mark(z0), z1) → mark(indx(z0, z1))
indx(ok(z0), ok(z1)) → ok(indx(z0, z1))
s1(mark(z0)) → mark(s1(z0))
s1(ok(z0)) → ok(s1(z0))
dbl1(mark(z0)) → mark(dbl1(z0))
dbl1(ok(z0)) → ok(dbl1(z0))
sel1(mark(z0), z1) → mark(sel1(z0, z1))
sel1(z0, mark(z1)) → mark(sel1(z0, z1))
sel1(ok(z0), ok(z1)) → ok(sel1(z0, z1))
quote(mark(z0)) → mark(quote(z0))
quote(ok(z0)) → ok(quote(z0))
proper(dbl(z0)) → dbl(proper(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(dbls(z0)) → dbls(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
proper(indx(z0, z1)) → indx(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(dbl1(z0)) → dbl1(proper(z0))
proper(01) → ok(01)
proper(s1(z0)) → s1(proper(z0))
proper(sel1(z0, z1)) → sel1(proper(z0), proper(z1))
proper(quote(z0)) → quote(proper(z0))
from(ok(z0)) → ok(from(z0))
Tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(dbl(z0)) → c45(DBL(proper(z0)), PROPER(z0))
PROPER(s(z0)) → c47(S(proper(z0)), PROPER(z0))
PROPER(dbls(z0)) → c48(DBLS(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c50(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(sel(z0, z1)) → c51(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(indx(z0, z1)) → c52(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c53(FROM(proper(z0)), PROPER(z0))
PROPER(dbl1(z0)) → c54(DBL1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c56(S1(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c57(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)), ACTIVE(quote(0)))
ACTIVE(dbl(quote(s(z0)))) → c17(DBL(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)), ACTIVE(quote(0)))
ACTIVE(dbls(quote(s(z0)))) → c18(DBLS(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)))
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0))))))
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0))))))
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0)))
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(indx(sel1(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(indx(sel1(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel1(z0, z2)), x1), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(indx(quote(0), x1)) → c21(INDX(mark(01), x1), ACTIVE(quote(0)))
ACTIVE(indx(quote(s(z0)), x1)) → c21(INDX(mark(s1(quote(z0))), x1), ACTIVE(quote(s(z0))))
ACTIVE(indx(quote(dbl(z0)), x1)) → c21(INDX(mark(dbl1(z0)), x1), ACTIVE(quote(dbl(z0))))
ACTIVE(indx(quote(sel(z0, z1)), x1)) → c21(INDX(mark(sel1(z0, z1)), x1), ACTIVE(quote(sel(z0, z1))))
ACTIVE(indx(dbl(z0), x1)) → c21(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
ACTIVE(indx(dbls(z0), x1)) → c21(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(indx(z0, z1), x1)) → c21(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1)))
ACTIVE(indx(dbl1(z0), x1)) → c21(INDX(dbl1(active(z0)), x1), ACTIVE(dbl1(z0)))
ACTIVE(indx(s1(z0), x1)) → c21(INDX(s1(active(z0)), x1), ACTIVE(s1(z0)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(active(z0), z1), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(z0, active(z1)), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(quote(z0), x1)) → c21(INDX(quote(active(z0)), x1), ACTIVE(quote(z0)))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)))
ACTIVE(indx(dbl(0), x1)) → c21(INDX(mark(0), x1))
ACTIVE(indx(dbls(nil), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(indx(indx(nil, z0), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0))))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1))
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0)))
ACTIVE(dbl1(sel(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl1(sel(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl1(sel1(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl1(sel1(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl1(quote(0))) → c22(DBL1(mark(01)), ACTIVE(quote(0)))
ACTIVE(dbl1(quote(s(z0)))) → c22(DBL1(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(dbl1(quote(dbl(z0)))) → c22(DBL1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl1(quote(sel(z0, z1)))) → c22(DBL1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl1(dbl(z0))) → c22(DBL1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl1(dbls(z0))) → c22(DBL1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(indx(z0, z1))) → c22(DBL1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl1(dbl1(z0))) → c22(DBL1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl1(s1(z0))) → c22(DBL1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(quote(z0))) → c22(DBL1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(dbl1(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(dbl(0))) → c22(DBL1(mark(0)))
ACTIVE(dbl1(dbls(nil))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(indx(nil, z0))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(dbl1(0))) → c22(DBL1(mark(01)))
ACTIVE(dbl(dbl1(s(z0)))) → c4(DBL(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(DBLS(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(INDX(mark(s1(s1(dbl1(z0)))), x1))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(DBL1(mark(s(s(dbl(z0))))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(ACTIVE(dbl(s(z0))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(DBL1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(DBL1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl1(from(z0))) → c4(DBL1(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl1(from(z0))) → c4(ACTIVE(from(z0)))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(DBL1(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(s1(sel(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(s1(sel(s(z0), cons(z1, z2)))) → c23(S1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(s1(sel1(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(s1(sel1(s(z0), cons(z1, z2)))) → c23(S1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(s1(quote(0))) → c23(S1(mark(01)), ACTIVE(quote(0)))
ACTIVE(s1(quote(s(z0)))) → c23(S1(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(s1(quote(dbl(z0)))) → c23(S1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(s1(quote(sel(z0, z1)))) → c23(S1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(s1(dbl(z0))) → c23(S1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(s1(dbls(z0))) → c23(S1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(s1(indx(z0, z1))) → c23(S1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(s1(dbl1(z0))) → c23(S1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(s1(s1(z0))) → c23(S1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(quote(z0))) → c23(S1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(s1(dbl(0))) → c23(S1(mark(0)))
ACTIVE(s1(dbls(nil))) → c23(S1(mark(nil)))
ACTIVE(s1(indx(nil, z0))) → c23(S1(mark(nil)))
ACTIVE(s1(dbl1(0))) → c23(S1(mark(01)))
ACTIVE(s1(dbl(s(z0)))) → c6(S1(mark(s(s(dbl(z0))))))
ACTIVE(s1(dbl(s(z0)))) → c6(ACTIVE(dbl(s(z0))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(S1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(S1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(s1(from(z0))) → c6(S1(mark(cons(z0, from(s(z0))))))
ACTIVE(s1(from(z0))) → c6(ACTIVE(from(z0)))
ACTIVE(s1(dbl1(s(z0)))) → c6(S1(mark(s1(s1(dbl1(z0))))))
ACTIVE(s1(dbl1(s(z0)))) → c6(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(dbl(0))) → c26(QUOTE(mark(0)), ACTIVE(dbl(0)))
ACTIVE(quote(dbl(s(z0)))) → c26(QUOTE(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
ACTIVE(quote(dbls(nil))) → c26(QUOTE(mark(nil)), ACTIVE(dbls(nil)))
ACTIVE(quote(dbls(cons(z0, z1)))) → c26(QUOTE(mark(cons(dbl(z0), dbls(z1)))), ACTIVE(dbls(cons(z0, z1))))
ACTIVE(quote(sel(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(quote(sel(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(quote(indx(nil, z0))) → c26(QUOTE(mark(nil)), ACTIVE(indx(nil, z0)))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c26(QUOTE(mark(cons(sel(z0, z2), indx(z1, z2)))), ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(quote(from(z0))) → c26(QUOTE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(quote(dbl1(0))) → c26(QUOTE(mark(01)), ACTIVE(dbl1(0)))
ACTIVE(quote(dbl1(s(z0)))) → c26(QUOTE(mark(s1(s1(dbl1(z0))))), ACTIVE(dbl1(s(z0))))
ACTIVE(quote(sel1(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(quote(sel1(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(quote(quote(0))) → c26(QUOTE(mark(01)), ACTIVE(quote(0)))
ACTIVE(quote(quote(s(z0)))) → c26(QUOTE(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(quote(quote(dbl(z0)))) → c26(QUOTE(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(quote(quote(sel(z0, z1)))) → c26(QUOTE(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(quote(dbl(z0))) → c26(QUOTE(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(quote(dbls(z0))) → c26(QUOTE(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(quote(indx(z0, z1))) → c26(QUOTE(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(quote(dbl1(z0))) → c26(QUOTE(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(quote(s1(z0))) → c26(QUOTE(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(quote(z0))) → c26(QUOTE(quote(active(z0))), ACTIVE(quote(z0)))
S tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(dbl(z0)) → c45(DBL(proper(z0)), PROPER(z0))
PROPER(s(z0)) → c47(S(proper(z0)), PROPER(z0))
PROPER(dbls(z0)) → c48(DBLS(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c50(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(sel(z0, z1)) → c51(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(indx(z0, z1)) → c52(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c53(FROM(proper(z0)), PROPER(z0))
PROPER(dbl1(z0)) → c54(DBL1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c56(S1(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c57(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)), ACTIVE(quote(0)))
ACTIVE(dbl(quote(s(z0)))) → c17(DBL(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)), ACTIVE(quote(0)))
ACTIVE(dbls(quote(s(z0)))) → c18(DBLS(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)))
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0))))))
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0))))))
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0)))
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(indx(sel1(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(indx(sel1(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel1(z0, z2)), x1), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(indx(quote(0), x1)) → c21(INDX(mark(01), x1), ACTIVE(quote(0)))
ACTIVE(indx(quote(s(z0)), x1)) → c21(INDX(mark(s1(quote(z0))), x1), ACTIVE(quote(s(z0))))
ACTIVE(indx(quote(dbl(z0)), x1)) → c21(INDX(mark(dbl1(z0)), x1), ACTIVE(quote(dbl(z0))))
ACTIVE(indx(quote(sel(z0, z1)), x1)) → c21(INDX(mark(sel1(z0, z1)), x1), ACTIVE(quote(sel(z0, z1))))
ACTIVE(indx(dbl(z0), x1)) → c21(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
ACTIVE(indx(dbls(z0), x1)) → c21(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(indx(z0, z1), x1)) → c21(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1)))
ACTIVE(indx(dbl1(z0), x1)) → c21(INDX(dbl1(active(z0)), x1), ACTIVE(dbl1(z0)))
ACTIVE(indx(s1(z0), x1)) → c21(INDX(s1(active(z0)), x1), ACTIVE(s1(z0)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(active(z0), z1), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(z0, active(z1)), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(quote(z0), x1)) → c21(INDX(quote(active(z0)), x1), ACTIVE(quote(z0)))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)))
ACTIVE(indx(dbl(0), x1)) → c21(INDX(mark(0), x1))
ACTIVE(indx(dbls(nil), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(indx(indx(nil, z0), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0))))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1))
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0)))
ACTIVE(dbl1(sel(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl1(sel(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl1(sel1(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl1(sel1(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl1(quote(0))) → c22(DBL1(mark(01)), ACTIVE(quote(0)))
ACTIVE(dbl1(quote(s(z0)))) → c22(DBL1(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(dbl1(quote(dbl(z0)))) → c22(DBL1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl1(quote(sel(z0, z1)))) → c22(DBL1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl1(dbl(z0))) → c22(DBL1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl1(dbls(z0))) → c22(DBL1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(indx(z0, z1))) → c22(DBL1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl1(dbl1(z0))) → c22(DBL1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl1(s1(z0))) → c22(DBL1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(quote(z0))) → c22(DBL1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(dbl1(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(dbl(0))) → c22(DBL1(mark(0)))
ACTIVE(dbl1(dbls(nil))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(indx(nil, z0))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(dbl1(0))) → c22(DBL1(mark(01)))
ACTIVE(dbl(dbl1(s(z0)))) → c4(DBL(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(DBLS(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(INDX(mark(s1(s1(dbl1(z0)))), x1))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(DBL1(mark(s(s(dbl(z0))))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(ACTIVE(dbl(s(z0))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(DBL1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(DBL1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl1(from(z0))) → c4(DBL1(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl1(from(z0))) → c4(ACTIVE(from(z0)))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(DBL1(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(s1(sel(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(s1(sel(s(z0), cons(z1, z2)))) → c23(S1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(s1(sel1(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(s1(sel1(s(z0), cons(z1, z2)))) → c23(S1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(s1(quote(0))) → c23(S1(mark(01)), ACTIVE(quote(0)))
ACTIVE(s1(quote(s(z0)))) → c23(S1(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(s1(quote(dbl(z0)))) → c23(S1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(s1(quote(sel(z0, z1)))) → c23(S1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(s1(dbl(z0))) → c23(S1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(s1(dbls(z0))) → c23(S1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(s1(indx(z0, z1))) → c23(S1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(s1(dbl1(z0))) → c23(S1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(s1(s1(z0))) → c23(S1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(quote(z0))) → c23(S1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(s1(dbl(0))) → c23(S1(mark(0)))
ACTIVE(s1(dbls(nil))) → c23(S1(mark(nil)))
ACTIVE(s1(indx(nil, z0))) → c23(S1(mark(nil)))
ACTIVE(s1(dbl1(0))) → c23(S1(mark(01)))
ACTIVE(s1(dbl(s(z0)))) → c6(S1(mark(s(s(dbl(z0))))))
ACTIVE(s1(dbl(s(z0)))) → c6(ACTIVE(dbl(s(z0))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(S1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(S1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(s1(from(z0))) → c6(S1(mark(cons(z0, from(s(z0))))))
ACTIVE(s1(from(z0))) → c6(ACTIVE(from(z0)))
ACTIVE(s1(dbl1(s(z0)))) → c6(S1(mark(s1(s1(dbl1(z0))))))
ACTIVE(s1(dbl1(s(z0)))) → c6(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(dbl(0))) → c26(QUOTE(mark(0)), ACTIVE(dbl(0)))
ACTIVE(quote(dbl(s(z0)))) → c26(QUOTE(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
ACTIVE(quote(dbls(nil))) → c26(QUOTE(mark(nil)), ACTIVE(dbls(nil)))
ACTIVE(quote(dbls(cons(z0, z1)))) → c26(QUOTE(mark(cons(dbl(z0), dbls(z1)))), ACTIVE(dbls(cons(z0, z1))))
ACTIVE(quote(sel(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(quote(sel(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(quote(indx(nil, z0))) → c26(QUOTE(mark(nil)), ACTIVE(indx(nil, z0)))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c26(QUOTE(mark(cons(sel(z0, z2), indx(z1, z2)))), ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(quote(from(z0))) → c26(QUOTE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(quote(dbl1(0))) → c26(QUOTE(mark(01)), ACTIVE(dbl1(0)))
ACTIVE(quote(dbl1(s(z0)))) → c26(QUOTE(mark(s1(s1(dbl1(z0))))), ACTIVE(dbl1(s(z0))))
ACTIVE(quote(sel1(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(quote(sel1(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(quote(quote(0))) → c26(QUOTE(mark(01)), ACTIVE(quote(0)))
ACTIVE(quote(quote(s(z0)))) → c26(QUOTE(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(quote(quote(dbl(z0)))) → c26(QUOTE(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(quote(quote(sel(z0, z1)))) → c26(QUOTE(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(quote(dbl(z0))) → c26(QUOTE(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(quote(dbls(z0))) → c26(QUOTE(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(quote(indx(z0, z1))) → c26(QUOTE(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(quote(dbl1(z0))) → c26(QUOTE(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(quote(s1(z0))) → c26(QUOTE(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(quote(z0))) → c26(QUOTE(quote(active(z0))), ACTIVE(quote(z0)))
K tuples:none
Defined Rule Symbols:
active, s, dbl, cons, dbls, sel, indx, s1, dbl1, sel1, quote, proper, from
Defined Pair Symbols:
ACTIVE, DBL, DBLS, SEL, INDX, DBL1, S1, SEL1, QUOTE, PROPER, S, CONS, FROM, TOP
Compound Symbols:
c5, c12, c15, c16, c19, c20, c24, c25, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c47, c48, c50, c51, c52, c53, c54, c56, c57, c58, c59, c60, c61, c62, c63, c8, c, c17, c17, c1, c18, c18, c2, c21, c21, c3, c22, c22, c4, c23, c23, c6, c26
(43) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 10 trailing tuple parts
(44) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(dbl(0)) → mark(0)
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
active(dbls(nil)) → mark(nil)
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1)))
active(sel(0, cons(z0, z1))) → mark(z0)
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
active(indx(nil, z0)) → mark(nil)
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2)))
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(dbl1(0)) → mark(01)
active(dbl1(s(z0))) → mark(s1(s1(dbl1(z0))))
active(sel1(0, cons(z0, z1))) → mark(z0)
active(sel1(s(z0), cons(z1, z2))) → mark(sel1(z0, z2))
active(quote(0)) → mark(01)
active(quote(s(z0))) → mark(s1(quote(z0)))
active(quote(dbl(z0))) → mark(dbl1(z0))
active(quote(sel(z0, z1))) → mark(sel1(z0, z1))
active(dbl(z0)) → dbl(active(z0))
active(dbls(z0)) → dbls(active(z0))
active(sel(z0, z1)) → sel(active(z0), z1)
active(sel(z0, z1)) → sel(z0, active(z1))
active(indx(z0, z1)) → indx(active(z0), z1)
active(dbl1(z0)) → dbl1(active(z0))
active(s1(z0)) → s1(active(z0))
active(sel1(z0, z1)) → sel1(active(z0), z1)
active(sel1(z0, z1)) → sel1(z0, active(z1))
active(quote(z0)) → quote(active(z0))
s(ok(z0)) → ok(s(z0))
dbl(mark(z0)) → mark(dbl(z0))
dbl(ok(z0)) → ok(dbl(z0))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
dbls(mark(z0)) → mark(dbls(z0))
dbls(ok(z0)) → ok(dbls(z0))
sel(mark(z0), z1) → mark(sel(z0, z1))
sel(z0, mark(z1)) → mark(sel(z0, z1))
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
indx(mark(z0), z1) → mark(indx(z0, z1))
indx(ok(z0), ok(z1)) → ok(indx(z0, z1))
s1(mark(z0)) → mark(s1(z0))
s1(ok(z0)) → ok(s1(z0))
dbl1(mark(z0)) → mark(dbl1(z0))
dbl1(ok(z0)) → ok(dbl1(z0))
sel1(mark(z0), z1) → mark(sel1(z0, z1))
sel1(z0, mark(z1)) → mark(sel1(z0, z1))
sel1(ok(z0), ok(z1)) → ok(sel1(z0, z1))
quote(mark(z0)) → mark(quote(z0))
quote(ok(z0)) → ok(quote(z0))
proper(dbl(z0)) → dbl(proper(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(dbls(z0)) → dbls(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
proper(indx(z0, z1)) → indx(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(dbl1(z0)) → dbl1(proper(z0))
proper(01) → ok(01)
proper(s1(z0)) → s1(proper(z0))
proper(sel1(z0, z1)) → sel1(proper(z0), proper(z1))
proper(quote(z0)) → quote(proper(z0))
from(ok(z0)) → ok(from(z0))
Tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(dbl(z0)) → c45(DBL(proper(z0)), PROPER(z0))
PROPER(s(z0)) → c47(S(proper(z0)), PROPER(z0))
PROPER(dbls(z0)) → c48(DBLS(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c50(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(sel(z0, z1)) → c51(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(indx(z0, z1)) → c52(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c53(FROM(proper(z0)), PROPER(z0))
PROPER(dbl1(z0)) → c54(DBL1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c56(S1(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c57(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(s(z0)))) → c17(DBL(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(s(z0)))) → c18(DBLS(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)))
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0))))))
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0))))))
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0)))
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(indx(sel1(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(indx(sel1(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel1(z0, z2)), x1), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(indx(quote(s(z0)), x1)) → c21(INDX(mark(s1(quote(z0))), x1), ACTIVE(quote(s(z0))))
ACTIVE(indx(quote(dbl(z0)), x1)) → c21(INDX(mark(dbl1(z0)), x1), ACTIVE(quote(dbl(z0))))
ACTIVE(indx(quote(sel(z0, z1)), x1)) → c21(INDX(mark(sel1(z0, z1)), x1), ACTIVE(quote(sel(z0, z1))))
ACTIVE(indx(dbl(z0), x1)) → c21(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
ACTIVE(indx(dbls(z0), x1)) → c21(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(indx(z0, z1), x1)) → c21(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1)))
ACTIVE(indx(dbl1(z0), x1)) → c21(INDX(dbl1(active(z0)), x1), ACTIVE(dbl1(z0)))
ACTIVE(indx(s1(z0), x1)) → c21(INDX(s1(active(z0)), x1), ACTIVE(s1(z0)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(active(z0), z1), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(z0, active(z1)), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(quote(z0), x1)) → c21(INDX(quote(active(z0)), x1), ACTIVE(quote(z0)))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)))
ACTIVE(indx(dbl(0), x1)) → c21(INDX(mark(0), x1))
ACTIVE(indx(dbls(nil), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(indx(indx(nil, z0), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0))))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1))
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0)))
ACTIVE(dbl1(sel(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl1(sel(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl1(sel1(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl1(sel1(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl1(quote(s(z0)))) → c22(DBL1(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(dbl1(quote(dbl(z0)))) → c22(DBL1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl1(quote(sel(z0, z1)))) → c22(DBL1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl1(dbl(z0))) → c22(DBL1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl1(dbls(z0))) → c22(DBL1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(indx(z0, z1))) → c22(DBL1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl1(dbl1(z0))) → c22(DBL1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl1(s1(z0))) → c22(DBL1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(quote(z0))) → c22(DBL1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(dbl1(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(dbl(0))) → c22(DBL1(mark(0)))
ACTIVE(dbl1(dbls(nil))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(indx(nil, z0))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(dbl1(0))) → c22(DBL1(mark(01)))
ACTIVE(dbl(dbl1(s(z0)))) → c4(DBL(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(DBLS(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(INDX(mark(s1(s1(dbl1(z0)))), x1))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(DBL1(mark(s(s(dbl(z0))))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(ACTIVE(dbl(s(z0))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(DBL1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(DBL1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl1(from(z0))) → c4(DBL1(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl1(from(z0))) → c4(ACTIVE(from(z0)))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(DBL1(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(s1(sel(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(s1(sel(s(z0), cons(z1, z2)))) → c23(S1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(s1(sel1(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(s1(sel1(s(z0), cons(z1, z2)))) → c23(S1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(s1(quote(s(z0)))) → c23(S1(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(s1(quote(dbl(z0)))) → c23(S1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(s1(quote(sel(z0, z1)))) → c23(S1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(s1(dbl(z0))) → c23(S1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(s1(dbls(z0))) → c23(S1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(s1(indx(z0, z1))) → c23(S1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(s1(dbl1(z0))) → c23(S1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(s1(s1(z0))) → c23(S1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(quote(z0))) → c23(S1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(s1(dbl(0))) → c23(S1(mark(0)))
ACTIVE(s1(dbls(nil))) → c23(S1(mark(nil)))
ACTIVE(s1(indx(nil, z0))) → c23(S1(mark(nil)))
ACTIVE(s1(dbl1(0))) → c23(S1(mark(01)))
ACTIVE(s1(dbl(s(z0)))) → c6(S1(mark(s(s(dbl(z0))))))
ACTIVE(s1(dbl(s(z0)))) → c6(ACTIVE(dbl(s(z0))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(S1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(S1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(s1(from(z0))) → c6(S1(mark(cons(z0, from(s(z0))))))
ACTIVE(s1(from(z0))) → c6(ACTIVE(from(z0)))
ACTIVE(s1(dbl1(s(z0)))) → c6(S1(mark(s1(s1(dbl1(z0))))))
ACTIVE(s1(dbl1(s(z0)))) → c6(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(dbl(s(z0)))) → c26(QUOTE(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c26(QUOTE(mark(cons(dbl(z0), dbls(z1)))), ACTIVE(dbls(cons(z0, z1))))
ACTIVE(quote(sel(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(quote(sel(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c26(QUOTE(mark(cons(sel(z0, z2), indx(z1, z2)))), ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(quote(from(z0))) → c26(QUOTE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(quote(dbl1(s(z0)))) → c26(QUOTE(mark(s1(s1(dbl1(z0))))), ACTIVE(dbl1(s(z0))))
ACTIVE(quote(sel1(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(quote(sel1(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(quote(quote(s(z0)))) → c26(QUOTE(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(quote(quote(dbl(z0)))) → c26(QUOTE(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(quote(quote(sel(z0, z1)))) → c26(QUOTE(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(quote(dbl(z0))) → c26(QUOTE(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(quote(dbls(z0))) → c26(QUOTE(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(quote(indx(z0, z1))) → c26(QUOTE(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(quote(dbl1(z0))) → c26(QUOTE(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(quote(s1(z0))) → c26(QUOTE(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(quote(z0))) → c26(QUOTE(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(quote(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(quote(0))) → c22(DBL1(mark(01)))
ACTIVE(s1(quote(0))) → c23(S1(mark(01)))
ACTIVE(quote(dbl(0))) → c26(QUOTE(mark(0)))
ACTIVE(quote(dbls(nil))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(indx(nil, z0))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(dbl1(0))) → c26(QUOTE(mark(01)))
ACTIVE(quote(quote(0))) → c26(QUOTE(mark(01)))
S tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(dbl(z0)) → c45(DBL(proper(z0)), PROPER(z0))
PROPER(s(z0)) → c47(S(proper(z0)), PROPER(z0))
PROPER(dbls(z0)) → c48(DBLS(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c50(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(sel(z0, z1)) → c51(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(indx(z0, z1)) → c52(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c53(FROM(proper(z0)), PROPER(z0))
PROPER(dbl1(z0)) → c54(DBL1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c56(S1(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c57(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(s(z0)))) → c17(DBL(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(s(z0)))) → c18(DBLS(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)))
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0))))))
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0))))))
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0)))
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(indx(sel1(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(indx(sel1(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel1(z0, z2)), x1), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(indx(quote(s(z0)), x1)) → c21(INDX(mark(s1(quote(z0))), x1), ACTIVE(quote(s(z0))))
ACTIVE(indx(quote(dbl(z0)), x1)) → c21(INDX(mark(dbl1(z0)), x1), ACTIVE(quote(dbl(z0))))
ACTIVE(indx(quote(sel(z0, z1)), x1)) → c21(INDX(mark(sel1(z0, z1)), x1), ACTIVE(quote(sel(z0, z1))))
ACTIVE(indx(dbl(z0), x1)) → c21(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
ACTIVE(indx(dbls(z0), x1)) → c21(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(indx(z0, z1), x1)) → c21(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1)))
ACTIVE(indx(dbl1(z0), x1)) → c21(INDX(dbl1(active(z0)), x1), ACTIVE(dbl1(z0)))
ACTIVE(indx(s1(z0), x1)) → c21(INDX(s1(active(z0)), x1), ACTIVE(s1(z0)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(active(z0), z1), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(z0, active(z1)), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(quote(z0), x1)) → c21(INDX(quote(active(z0)), x1), ACTIVE(quote(z0)))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)))
ACTIVE(indx(dbl(0), x1)) → c21(INDX(mark(0), x1))
ACTIVE(indx(dbls(nil), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(indx(indx(nil, z0), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0))))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1))
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0)))
ACTIVE(dbl1(sel(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl1(sel(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl1(sel1(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl1(sel1(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl1(quote(s(z0)))) → c22(DBL1(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(dbl1(quote(dbl(z0)))) → c22(DBL1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl1(quote(sel(z0, z1)))) → c22(DBL1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl1(dbl(z0))) → c22(DBL1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl1(dbls(z0))) → c22(DBL1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(indx(z0, z1))) → c22(DBL1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl1(dbl1(z0))) → c22(DBL1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl1(s1(z0))) → c22(DBL1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(quote(z0))) → c22(DBL1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(dbl1(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(dbl(0))) → c22(DBL1(mark(0)))
ACTIVE(dbl1(dbls(nil))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(indx(nil, z0))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(dbl1(0))) → c22(DBL1(mark(01)))
ACTIVE(dbl(dbl1(s(z0)))) → c4(DBL(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(DBLS(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(INDX(mark(s1(s1(dbl1(z0)))), x1))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(DBL1(mark(s(s(dbl(z0))))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(ACTIVE(dbl(s(z0))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(DBL1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(DBL1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl1(from(z0))) → c4(DBL1(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl1(from(z0))) → c4(ACTIVE(from(z0)))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(DBL1(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(s1(sel(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(s1(sel(s(z0), cons(z1, z2)))) → c23(S1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(s1(sel1(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(s1(sel1(s(z0), cons(z1, z2)))) → c23(S1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(s1(quote(s(z0)))) → c23(S1(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(s1(quote(dbl(z0)))) → c23(S1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(s1(quote(sel(z0, z1)))) → c23(S1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(s1(dbl(z0))) → c23(S1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(s1(dbls(z0))) → c23(S1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(s1(indx(z0, z1))) → c23(S1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(s1(dbl1(z0))) → c23(S1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(s1(s1(z0))) → c23(S1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(quote(z0))) → c23(S1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(s1(dbl(0))) → c23(S1(mark(0)))
ACTIVE(s1(dbls(nil))) → c23(S1(mark(nil)))
ACTIVE(s1(indx(nil, z0))) → c23(S1(mark(nil)))
ACTIVE(s1(dbl1(0))) → c23(S1(mark(01)))
ACTIVE(s1(dbl(s(z0)))) → c6(S1(mark(s(s(dbl(z0))))))
ACTIVE(s1(dbl(s(z0)))) → c6(ACTIVE(dbl(s(z0))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(S1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(S1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(s1(from(z0))) → c6(S1(mark(cons(z0, from(s(z0))))))
ACTIVE(s1(from(z0))) → c6(ACTIVE(from(z0)))
ACTIVE(s1(dbl1(s(z0)))) → c6(S1(mark(s1(s1(dbl1(z0))))))
ACTIVE(s1(dbl1(s(z0)))) → c6(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(dbl(s(z0)))) → c26(QUOTE(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c26(QUOTE(mark(cons(dbl(z0), dbls(z1)))), ACTIVE(dbls(cons(z0, z1))))
ACTIVE(quote(sel(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(quote(sel(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c26(QUOTE(mark(cons(sel(z0, z2), indx(z1, z2)))), ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(quote(from(z0))) → c26(QUOTE(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(quote(dbl1(s(z0)))) → c26(QUOTE(mark(s1(s1(dbl1(z0))))), ACTIVE(dbl1(s(z0))))
ACTIVE(quote(sel1(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(quote(sel1(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(quote(quote(s(z0)))) → c26(QUOTE(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(quote(quote(dbl(z0)))) → c26(QUOTE(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(quote(quote(sel(z0, z1)))) → c26(QUOTE(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(quote(dbl(z0))) → c26(QUOTE(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(quote(dbls(z0))) → c26(QUOTE(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(quote(indx(z0, z1))) → c26(QUOTE(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(quote(dbl1(z0))) → c26(QUOTE(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(quote(s1(z0))) → c26(QUOTE(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(quote(z0))) → c26(QUOTE(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(quote(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(quote(0))) → c22(DBL1(mark(01)))
ACTIVE(s1(quote(0))) → c23(S1(mark(01)))
ACTIVE(quote(dbl(0))) → c26(QUOTE(mark(0)))
ACTIVE(quote(dbls(nil))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(indx(nil, z0))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(dbl1(0))) → c26(QUOTE(mark(01)))
ACTIVE(quote(quote(0))) → c26(QUOTE(mark(01)))
K tuples:none
Defined Rule Symbols:
active, s, dbl, cons, dbls, sel, indx, s1, dbl1, sel1, quote, proper, from
Defined Pair Symbols:
ACTIVE, DBL, DBLS, SEL, INDX, DBL1, S1, SEL1, QUOTE, PROPER, S, CONS, FROM, TOP
Compound Symbols:
c5, c12, c15, c16, c19, c20, c24, c25, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c47, c48, c50, c51, c52, c53, c54, c56, c57, c58, c59, c60, c61, c62, c63, c8, c, c17, c17, c1, c18, c18, c2, c21, c21, c3, c22, c22, c4, c23, c23, c6, c26, c26
(45) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID) transformation)
Split RHS of tuples not part of any SCC
(46) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(dbl(0)) → mark(0)
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
active(dbls(nil)) → mark(nil)
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1)))
active(sel(0, cons(z0, z1))) → mark(z0)
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
active(indx(nil, z0)) → mark(nil)
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2)))
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(dbl1(0)) → mark(01)
active(dbl1(s(z0))) → mark(s1(s1(dbl1(z0))))
active(sel1(0, cons(z0, z1))) → mark(z0)
active(sel1(s(z0), cons(z1, z2))) → mark(sel1(z0, z2))
active(quote(0)) → mark(01)
active(quote(s(z0))) → mark(s1(quote(z0)))
active(quote(dbl(z0))) → mark(dbl1(z0))
active(quote(sel(z0, z1))) → mark(sel1(z0, z1))
active(dbl(z0)) → dbl(active(z0))
active(dbls(z0)) → dbls(active(z0))
active(sel(z0, z1)) → sel(active(z0), z1)
active(sel(z0, z1)) → sel(z0, active(z1))
active(indx(z0, z1)) → indx(active(z0), z1)
active(dbl1(z0)) → dbl1(active(z0))
active(s1(z0)) → s1(active(z0))
active(sel1(z0, z1)) → sel1(active(z0), z1)
active(sel1(z0, z1)) → sel1(z0, active(z1))
active(quote(z0)) → quote(active(z0))
s(ok(z0)) → ok(s(z0))
dbl(mark(z0)) → mark(dbl(z0))
dbl(ok(z0)) → ok(dbl(z0))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
dbls(mark(z0)) → mark(dbls(z0))
dbls(ok(z0)) → ok(dbls(z0))
sel(mark(z0), z1) → mark(sel(z0, z1))
sel(z0, mark(z1)) → mark(sel(z0, z1))
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
indx(mark(z0), z1) → mark(indx(z0, z1))
indx(ok(z0), ok(z1)) → ok(indx(z0, z1))
s1(mark(z0)) → mark(s1(z0))
s1(ok(z0)) → ok(s1(z0))
dbl1(mark(z0)) → mark(dbl1(z0))
dbl1(ok(z0)) → ok(dbl1(z0))
sel1(mark(z0), z1) → mark(sel1(z0, z1))
sel1(z0, mark(z1)) → mark(sel1(z0, z1))
sel1(ok(z0), ok(z1)) → ok(sel1(z0, z1))
quote(mark(z0)) → mark(quote(z0))
quote(ok(z0)) → ok(quote(z0))
proper(dbl(z0)) → dbl(proper(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(dbls(z0)) → dbls(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
proper(indx(z0, z1)) → indx(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(dbl1(z0)) → dbl1(proper(z0))
proper(01) → ok(01)
proper(s1(z0)) → s1(proper(z0))
proper(sel1(z0, z1)) → sel1(proper(z0), proper(z1))
proper(quote(z0)) → quote(proper(z0))
from(ok(z0)) → ok(from(z0))
Tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(dbl(z0)) → c45(DBL(proper(z0)), PROPER(z0))
PROPER(s(z0)) → c47(S(proper(z0)), PROPER(z0))
PROPER(dbls(z0)) → c48(DBLS(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c50(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(sel(z0, z1)) → c51(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(indx(z0, z1)) → c52(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c53(FROM(proper(z0)), PROPER(z0))
PROPER(dbl1(z0)) → c54(DBL1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c56(S1(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c57(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)))
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0))))))
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0))))))
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0)))
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(indx(sel1(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(indx(sel1(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel1(z0, z2)), x1), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(indx(quote(dbl(z0)), x1)) → c21(INDX(mark(dbl1(z0)), x1), ACTIVE(quote(dbl(z0))))
ACTIVE(indx(quote(sel(z0, z1)), x1)) → c21(INDX(mark(sel1(z0, z1)), x1), ACTIVE(quote(sel(z0, z1))))
ACTIVE(indx(dbl(z0), x1)) → c21(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
ACTIVE(indx(dbls(z0), x1)) → c21(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(indx(z0, z1), x1)) → c21(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1)))
ACTIVE(indx(dbl1(z0), x1)) → c21(INDX(dbl1(active(z0)), x1), ACTIVE(dbl1(z0)))
ACTIVE(indx(s1(z0), x1)) → c21(INDX(s1(active(z0)), x1), ACTIVE(s1(z0)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(active(z0), z1), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(z0, active(z1)), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(quote(z0), x1)) → c21(INDX(quote(active(z0)), x1), ACTIVE(quote(z0)))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)))
ACTIVE(indx(dbl(0), x1)) → c21(INDX(mark(0), x1))
ACTIVE(indx(dbls(nil), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(indx(indx(nil, z0), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0))))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1))
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0)))
ACTIVE(dbl1(sel(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl1(sel(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl1(sel1(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl1(sel1(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl1(quote(dbl(z0)))) → c22(DBL1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl1(quote(sel(z0, z1)))) → c22(DBL1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl1(dbl(z0))) → c22(DBL1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl1(dbls(z0))) → c22(DBL1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(indx(z0, z1))) → c22(DBL1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl1(dbl1(z0))) → c22(DBL1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl1(s1(z0))) → c22(DBL1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(quote(z0))) → c22(DBL1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(dbl1(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(dbl(0))) → c22(DBL1(mark(0)))
ACTIVE(dbl1(dbls(nil))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(indx(nil, z0))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(dbl1(0))) → c22(DBL1(mark(01)))
ACTIVE(dbl(dbl1(s(z0)))) → c4(DBL(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(DBLS(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(INDX(mark(s1(s1(dbl1(z0)))), x1))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(DBL1(mark(s(s(dbl(z0))))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(ACTIVE(dbl(s(z0))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(DBL1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(DBL1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl1(from(z0))) → c4(DBL1(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl1(from(z0))) → c4(ACTIVE(from(z0)))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(DBL1(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(s1(sel(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(s1(sel(s(z0), cons(z1, z2)))) → c23(S1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(s1(sel1(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(s1(sel1(s(z0), cons(z1, z2)))) → c23(S1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(s1(quote(dbl(z0)))) → c23(S1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(s1(quote(sel(z0, z1)))) → c23(S1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(s1(dbl(z0))) → c23(S1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(s1(dbls(z0))) → c23(S1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(s1(indx(z0, z1))) → c23(S1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(s1(dbl1(z0))) → c23(S1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(s1(s1(z0))) → c23(S1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(quote(z0))) → c23(S1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(s1(dbl(0))) → c23(S1(mark(0)))
ACTIVE(s1(dbls(nil))) → c23(S1(mark(nil)))
ACTIVE(s1(indx(nil, z0))) → c23(S1(mark(nil)))
ACTIVE(s1(dbl1(0))) → c23(S1(mark(01)))
ACTIVE(s1(dbl(s(z0)))) → c6(S1(mark(s(s(dbl(z0))))))
ACTIVE(s1(dbl(s(z0)))) → c6(ACTIVE(dbl(s(z0))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(S1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(S1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(s1(from(z0))) → c6(S1(mark(cons(z0, from(s(z0))))))
ACTIVE(s1(from(z0))) → c6(ACTIVE(from(z0)))
ACTIVE(s1(dbl1(s(z0)))) → c6(S1(mark(s1(s1(dbl1(z0))))))
ACTIVE(s1(dbl1(s(z0)))) → c6(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(sel(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(quote(sel(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(quote(sel1(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(quote(sel1(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(quote(quote(dbl(z0)))) → c26(QUOTE(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(quote(quote(sel(z0, z1)))) → c26(QUOTE(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(quote(dbl(z0))) → c26(QUOTE(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(quote(dbls(z0))) → c26(QUOTE(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(quote(indx(z0, z1))) → c26(QUOTE(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(quote(dbl1(z0))) → c26(QUOTE(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(quote(s1(z0))) → c26(QUOTE(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(quote(z0))) → c26(QUOTE(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(quote(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(quote(0))) → c22(DBL1(mark(01)))
ACTIVE(s1(quote(0))) → c23(S1(mark(01)))
ACTIVE(quote(dbl(0))) → c26(QUOTE(mark(0)))
ACTIVE(quote(dbls(nil))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(indx(nil, z0))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(dbl1(0))) → c26(QUOTE(mark(01)))
ACTIVE(quote(quote(0))) → c26(QUOTE(mark(01)))
ACTIVE(dbl(quote(s(z0)))) → c7(DBL(mark(s1(quote(z0)))))
ACTIVE(dbl(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(s(z0)))) → c7(DBLS(mark(s1(quote(z0)))))
ACTIVE(dbls(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(indx(quote(s(z0)), x1)) → c7(INDX(mark(s1(quote(z0))), x1))
ACTIVE(indx(quote(s(z0)), x1)) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbl1(quote(s(z0)))) → c7(DBL1(mark(s1(quote(z0)))))
ACTIVE(dbl1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(s1(quote(s(z0)))) → c7(S1(mark(s1(quote(z0)))))
ACTIVE(s1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(quote(dbl(s(z0)))) → c7(QUOTE(mark(s(s(dbl(z0))))))
ACTIVE(quote(dbl(s(z0)))) → c7(ACTIVE(dbl(s(z0))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(QUOTE(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(QUOTE(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(quote(from(z0))) → c7(QUOTE(mark(cons(z0, from(s(z0))))))
ACTIVE(quote(from(z0))) → c7(ACTIVE(from(z0)))
ACTIVE(quote(dbl1(s(z0)))) → c7(QUOTE(mark(s1(s1(dbl1(z0))))))
ACTIVE(quote(dbl1(s(z0)))) → c7(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(quote(s(z0)))) → c7(QUOTE(mark(s1(quote(z0)))))
ACTIVE(quote(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
S tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(dbl(z0)) → c45(DBL(proper(z0)), PROPER(z0))
PROPER(s(z0)) → c47(S(proper(z0)), PROPER(z0))
PROPER(dbls(z0)) → c48(DBLS(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c50(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(sel(z0, z1)) → c51(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(indx(z0, z1)) → c52(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c53(FROM(proper(z0)), PROPER(z0))
PROPER(dbl1(z0)) → c54(DBL1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c56(S1(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c57(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)))
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0))))))
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0))))))
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0)))
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(indx(sel1(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(indx(sel1(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel1(z0, z2)), x1), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(indx(quote(dbl(z0)), x1)) → c21(INDX(mark(dbl1(z0)), x1), ACTIVE(quote(dbl(z0))))
ACTIVE(indx(quote(sel(z0, z1)), x1)) → c21(INDX(mark(sel1(z0, z1)), x1), ACTIVE(quote(sel(z0, z1))))
ACTIVE(indx(dbl(z0), x1)) → c21(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
ACTIVE(indx(dbls(z0), x1)) → c21(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(indx(z0, z1), x1)) → c21(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1)))
ACTIVE(indx(dbl1(z0), x1)) → c21(INDX(dbl1(active(z0)), x1), ACTIVE(dbl1(z0)))
ACTIVE(indx(s1(z0), x1)) → c21(INDX(s1(active(z0)), x1), ACTIVE(s1(z0)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(active(z0), z1), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(z0, active(z1)), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(quote(z0), x1)) → c21(INDX(quote(active(z0)), x1), ACTIVE(quote(z0)))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)))
ACTIVE(indx(dbl(0), x1)) → c21(INDX(mark(0), x1))
ACTIVE(indx(dbls(nil), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(indx(indx(nil, z0), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0))))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1))
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0)))
ACTIVE(dbl1(sel(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl1(sel(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl1(sel1(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl1(sel1(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl1(quote(dbl(z0)))) → c22(DBL1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl1(quote(sel(z0, z1)))) → c22(DBL1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl1(dbl(z0))) → c22(DBL1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl1(dbls(z0))) → c22(DBL1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(indx(z0, z1))) → c22(DBL1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl1(dbl1(z0))) → c22(DBL1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl1(s1(z0))) → c22(DBL1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(quote(z0))) → c22(DBL1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(dbl1(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(dbl(0))) → c22(DBL1(mark(0)))
ACTIVE(dbl1(dbls(nil))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(indx(nil, z0))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(dbl1(0))) → c22(DBL1(mark(01)))
ACTIVE(dbl(dbl1(s(z0)))) → c4(DBL(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(DBLS(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(INDX(mark(s1(s1(dbl1(z0)))), x1))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(DBL1(mark(s(s(dbl(z0))))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(ACTIVE(dbl(s(z0))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(DBL1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(DBL1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl1(from(z0))) → c4(DBL1(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl1(from(z0))) → c4(ACTIVE(from(z0)))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(DBL1(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(s1(sel(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(s1(sel(s(z0), cons(z1, z2)))) → c23(S1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(s1(sel1(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(s1(sel1(s(z0), cons(z1, z2)))) → c23(S1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(s1(quote(dbl(z0)))) → c23(S1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(s1(quote(sel(z0, z1)))) → c23(S1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(s1(dbl(z0))) → c23(S1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(s1(dbls(z0))) → c23(S1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(s1(indx(z0, z1))) → c23(S1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(s1(dbl1(z0))) → c23(S1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(s1(s1(z0))) → c23(S1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(quote(z0))) → c23(S1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(s1(dbl(0))) → c23(S1(mark(0)))
ACTIVE(s1(dbls(nil))) → c23(S1(mark(nil)))
ACTIVE(s1(indx(nil, z0))) → c23(S1(mark(nil)))
ACTIVE(s1(dbl1(0))) → c23(S1(mark(01)))
ACTIVE(s1(dbl(s(z0)))) → c6(S1(mark(s(s(dbl(z0))))))
ACTIVE(s1(dbl(s(z0)))) → c6(ACTIVE(dbl(s(z0))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(S1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(S1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(s1(from(z0))) → c6(S1(mark(cons(z0, from(s(z0))))))
ACTIVE(s1(from(z0))) → c6(ACTIVE(from(z0)))
ACTIVE(s1(dbl1(s(z0)))) → c6(S1(mark(s1(s1(dbl1(z0))))))
ACTIVE(s1(dbl1(s(z0)))) → c6(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(sel(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(quote(sel(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(quote(sel1(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(quote(sel1(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(quote(quote(dbl(z0)))) → c26(QUOTE(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(quote(quote(sel(z0, z1)))) → c26(QUOTE(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(quote(dbl(z0))) → c26(QUOTE(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(quote(dbls(z0))) → c26(QUOTE(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(quote(indx(z0, z1))) → c26(QUOTE(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(quote(dbl1(z0))) → c26(QUOTE(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(quote(s1(z0))) → c26(QUOTE(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(quote(z0))) → c26(QUOTE(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(quote(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(quote(0))) → c22(DBL1(mark(01)))
ACTIVE(s1(quote(0))) → c23(S1(mark(01)))
ACTIVE(quote(dbl(0))) → c26(QUOTE(mark(0)))
ACTIVE(quote(dbls(nil))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(indx(nil, z0))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(dbl1(0))) → c26(QUOTE(mark(01)))
ACTIVE(quote(quote(0))) → c26(QUOTE(mark(01)))
ACTIVE(dbl(quote(s(z0)))) → c7(DBL(mark(s1(quote(z0)))))
ACTIVE(dbl(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(s(z0)))) → c7(DBLS(mark(s1(quote(z0)))))
ACTIVE(dbls(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(indx(quote(s(z0)), x1)) → c7(INDX(mark(s1(quote(z0))), x1))
ACTIVE(indx(quote(s(z0)), x1)) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbl1(quote(s(z0)))) → c7(DBL1(mark(s1(quote(z0)))))
ACTIVE(dbl1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(s1(quote(s(z0)))) → c7(S1(mark(s1(quote(z0)))))
ACTIVE(s1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(quote(dbl(s(z0)))) → c7(QUOTE(mark(s(s(dbl(z0))))))
ACTIVE(quote(dbl(s(z0)))) → c7(ACTIVE(dbl(s(z0))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(QUOTE(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(QUOTE(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(quote(from(z0))) → c7(QUOTE(mark(cons(z0, from(s(z0))))))
ACTIVE(quote(from(z0))) → c7(ACTIVE(from(z0)))
ACTIVE(quote(dbl1(s(z0)))) → c7(QUOTE(mark(s1(s1(dbl1(z0))))))
ACTIVE(quote(dbl1(s(z0)))) → c7(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(quote(s(z0)))) → c7(QUOTE(mark(s1(quote(z0)))))
ACTIVE(quote(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
K tuples:none
Defined Rule Symbols:
active, s, dbl, cons, dbls, sel, indx, s1, dbl1, sel1, quote, proper, from
Defined Pair Symbols:
ACTIVE, DBL, DBLS, SEL, INDX, DBL1, S1, SEL1, QUOTE, PROPER, S, CONS, FROM, TOP
Compound Symbols:
c5, c12, c15, c16, c19, c20, c24, c25, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c47, c48, c50, c51, c52, c53, c54, c56, c57, c58, c59, c60, c61, c62, c63, c8, c, c17, c17, c1, c18, c18, c2, c21, c21, c3, c22, c22, c4, c23, c23, c6, c26, c26, c7
(47) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
PROPER(
dbl(
z0)) →
c45(
DBL(
proper(
z0)),
PROPER(
z0)) by
PROPER(dbl(dbl(z0))) → c45(DBL(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbl(0)) → c45(DBL(ok(0)), PROPER(0))
PROPER(dbl(s(z0))) → c45(DBL(s(proper(z0))), PROPER(s(z0)))
PROPER(dbl(dbls(z0))) → c45(DBL(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbl(nil)) → c45(DBL(ok(nil)), PROPER(nil))
PROPER(dbl(cons(z0, z1))) → c45(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbl(sel(z0, z1))) → c45(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbl(indx(z0, z1))) → c45(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbl(from(z0))) → c45(DBL(from(proper(z0))), PROPER(from(z0)))
PROPER(dbl(dbl1(z0))) → c45(DBL(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbl(01)) → c45(DBL(ok(01)), PROPER(01))
PROPER(dbl(s1(z0))) → c45(DBL(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbl(sel1(z0, z1))) → c45(DBL(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbl(quote(z0))) → c45(DBL(quote(proper(z0))), PROPER(quote(z0)))
(48) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(dbl(0)) → mark(0)
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
active(dbls(nil)) → mark(nil)
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1)))
active(sel(0, cons(z0, z1))) → mark(z0)
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
active(indx(nil, z0)) → mark(nil)
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2)))
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(dbl1(0)) → mark(01)
active(dbl1(s(z0))) → mark(s1(s1(dbl1(z0))))
active(sel1(0, cons(z0, z1))) → mark(z0)
active(sel1(s(z0), cons(z1, z2))) → mark(sel1(z0, z2))
active(quote(0)) → mark(01)
active(quote(s(z0))) → mark(s1(quote(z0)))
active(quote(dbl(z0))) → mark(dbl1(z0))
active(quote(sel(z0, z1))) → mark(sel1(z0, z1))
active(dbl(z0)) → dbl(active(z0))
active(dbls(z0)) → dbls(active(z0))
active(sel(z0, z1)) → sel(active(z0), z1)
active(sel(z0, z1)) → sel(z0, active(z1))
active(indx(z0, z1)) → indx(active(z0), z1)
active(dbl1(z0)) → dbl1(active(z0))
active(s1(z0)) → s1(active(z0))
active(sel1(z0, z1)) → sel1(active(z0), z1)
active(sel1(z0, z1)) → sel1(z0, active(z1))
active(quote(z0)) → quote(active(z0))
s(ok(z0)) → ok(s(z0))
dbl(mark(z0)) → mark(dbl(z0))
dbl(ok(z0)) → ok(dbl(z0))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
dbls(mark(z0)) → mark(dbls(z0))
dbls(ok(z0)) → ok(dbls(z0))
sel(mark(z0), z1) → mark(sel(z0, z1))
sel(z0, mark(z1)) → mark(sel(z0, z1))
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
indx(mark(z0), z1) → mark(indx(z0, z1))
indx(ok(z0), ok(z1)) → ok(indx(z0, z1))
s1(mark(z0)) → mark(s1(z0))
s1(ok(z0)) → ok(s1(z0))
dbl1(mark(z0)) → mark(dbl1(z0))
dbl1(ok(z0)) → ok(dbl1(z0))
sel1(mark(z0), z1) → mark(sel1(z0, z1))
sel1(z0, mark(z1)) → mark(sel1(z0, z1))
sel1(ok(z0), ok(z1)) → ok(sel1(z0, z1))
quote(mark(z0)) → mark(quote(z0))
quote(ok(z0)) → ok(quote(z0))
proper(dbl(z0)) → dbl(proper(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(dbls(z0)) → dbls(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
proper(indx(z0, z1)) → indx(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(dbl1(z0)) → dbl1(proper(z0))
proper(01) → ok(01)
proper(s1(z0)) → s1(proper(z0))
proper(sel1(z0, z1)) → sel1(proper(z0), proper(z1))
proper(quote(z0)) → quote(proper(z0))
from(ok(z0)) → ok(from(z0))
Tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(s(z0)) → c47(S(proper(z0)), PROPER(z0))
PROPER(dbls(z0)) → c48(DBLS(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c50(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(sel(z0, z1)) → c51(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(indx(z0, z1)) → c52(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c53(FROM(proper(z0)), PROPER(z0))
PROPER(dbl1(z0)) → c54(DBL1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c56(S1(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c57(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)))
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0))))))
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0))))))
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0)))
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(indx(sel1(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(indx(sel1(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel1(z0, z2)), x1), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(indx(quote(dbl(z0)), x1)) → c21(INDX(mark(dbl1(z0)), x1), ACTIVE(quote(dbl(z0))))
ACTIVE(indx(quote(sel(z0, z1)), x1)) → c21(INDX(mark(sel1(z0, z1)), x1), ACTIVE(quote(sel(z0, z1))))
ACTIVE(indx(dbl(z0), x1)) → c21(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
ACTIVE(indx(dbls(z0), x1)) → c21(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(indx(z0, z1), x1)) → c21(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1)))
ACTIVE(indx(dbl1(z0), x1)) → c21(INDX(dbl1(active(z0)), x1), ACTIVE(dbl1(z0)))
ACTIVE(indx(s1(z0), x1)) → c21(INDX(s1(active(z0)), x1), ACTIVE(s1(z0)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(active(z0), z1), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(z0, active(z1)), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(quote(z0), x1)) → c21(INDX(quote(active(z0)), x1), ACTIVE(quote(z0)))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)))
ACTIVE(indx(dbl(0), x1)) → c21(INDX(mark(0), x1))
ACTIVE(indx(dbls(nil), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(indx(indx(nil, z0), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0))))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1))
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0)))
ACTIVE(dbl1(sel(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl1(sel(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl1(sel1(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl1(sel1(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl1(quote(dbl(z0)))) → c22(DBL1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl1(quote(sel(z0, z1)))) → c22(DBL1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl1(dbl(z0))) → c22(DBL1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl1(dbls(z0))) → c22(DBL1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(indx(z0, z1))) → c22(DBL1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl1(dbl1(z0))) → c22(DBL1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl1(s1(z0))) → c22(DBL1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(quote(z0))) → c22(DBL1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(dbl1(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(dbl(0))) → c22(DBL1(mark(0)))
ACTIVE(dbl1(dbls(nil))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(indx(nil, z0))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(dbl1(0))) → c22(DBL1(mark(01)))
ACTIVE(dbl(dbl1(s(z0)))) → c4(DBL(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(DBLS(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(INDX(mark(s1(s1(dbl1(z0)))), x1))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(DBL1(mark(s(s(dbl(z0))))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(ACTIVE(dbl(s(z0))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(DBL1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(DBL1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl1(from(z0))) → c4(DBL1(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl1(from(z0))) → c4(ACTIVE(from(z0)))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(DBL1(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(s1(sel(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(s1(sel(s(z0), cons(z1, z2)))) → c23(S1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(s1(sel1(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(s1(sel1(s(z0), cons(z1, z2)))) → c23(S1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(s1(quote(dbl(z0)))) → c23(S1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(s1(quote(sel(z0, z1)))) → c23(S1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(s1(dbl(z0))) → c23(S1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(s1(dbls(z0))) → c23(S1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(s1(indx(z0, z1))) → c23(S1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(s1(dbl1(z0))) → c23(S1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(s1(s1(z0))) → c23(S1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(quote(z0))) → c23(S1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(s1(dbl(0))) → c23(S1(mark(0)))
ACTIVE(s1(dbls(nil))) → c23(S1(mark(nil)))
ACTIVE(s1(indx(nil, z0))) → c23(S1(mark(nil)))
ACTIVE(s1(dbl1(0))) → c23(S1(mark(01)))
ACTIVE(s1(dbl(s(z0)))) → c6(S1(mark(s(s(dbl(z0))))))
ACTIVE(s1(dbl(s(z0)))) → c6(ACTIVE(dbl(s(z0))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(S1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(S1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(s1(from(z0))) → c6(S1(mark(cons(z0, from(s(z0))))))
ACTIVE(s1(from(z0))) → c6(ACTIVE(from(z0)))
ACTIVE(s1(dbl1(s(z0)))) → c6(S1(mark(s1(s1(dbl1(z0))))))
ACTIVE(s1(dbl1(s(z0)))) → c6(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(sel(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(quote(sel(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(quote(sel1(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(quote(sel1(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(quote(quote(dbl(z0)))) → c26(QUOTE(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(quote(quote(sel(z0, z1)))) → c26(QUOTE(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(quote(dbl(z0))) → c26(QUOTE(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(quote(dbls(z0))) → c26(QUOTE(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(quote(indx(z0, z1))) → c26(QUOTE(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(quote(dbl1(z0))) → c26(QUOTE(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(quote(s1(z0))) → c26(QUOTE(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(quote(z0))) → c26(QUOTE(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(quote(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(quote(0))) → c22(DBL1(mark(01)))
ACTIVE(s1(quote(0))) → c23(S1(mark(01)))
ACTIVE(quote(dbl(0))) → c26(QUOTE(mark(0)))
ACTIVE(quote(dbls(nil))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(indx(nil, z0))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(dbl1(0))) → c26(QUOTE(mark(01)))
ACTIVE(quote(quote(0))) → c26(QUOTE(mark(01)))
ACTIVE(dbl(quote(s(z0)))) → c7(DBL(mark(s1(quote(z0)))))
ACTIVE(dbl(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(s(z0)))) → c7(DBLS(mark(s1(quote(z0)))))
ACTIVE(dbls(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(indx(quote(s(z0)), x1)) → c7(INDX(mark(s1(quote(z0))), x1))
ACTIVE(indx(quote(s(z0)), x1)) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbl1(quote(s(z0)))) → c7(DBL1(mark(s1(quote(z0)))))
ACTIVE(dbl1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(s1(quote(s(z0)))) → c7(S1(mark(s1(quote(z0)))))
ACTIVE(s1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(quote(dbl(s(z0)))) → c7(QUOTE(mark(s(s(dbl(z0))))))
ACTIVE(quote(dbl(s(z0)))) → c7(ACTIVE(dbl(s(z0))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(QUOTE(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(QUOTE(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(quote(from(z0))) → c7(QUOTE(mark(cons(z0, from(s(z0))))))
ACTIVE(quote(from(z0))) → c7(ACTIVE(from(z0)))
ACTIVE(quote(dbl1(s(z0)))) → c7(QUOTE(mark(s1(s1(dbl1(z0))))))
ACTIVE(quote(dbl1(s(z0)))) → c7(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(quote(s(z0)))) → c7(QUOTE(mark(s1(quote(z0)))))
ACTIVE(quote(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
PROPER(dbl(dbl(z0))) → c45(DBL(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbl(0)) → c45(DBL(ok(0)), PROPER(0))
PROPER(dbl(s(z0))) → c45(DBL(s(proper(z0))), PROPER(s(z0)))
PROPER(dbl(dbls(z0))) → c45(DBL(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbl(nil)) → c45(DBL(ok(nil)), PROPER(nil))
PROPER(dbl(cons(z0, z1))) → c45(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbl(sel(z0, z1))) → c45(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbl(indx(z0, z1))) → c45(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbl(from(z0))) → c45(DBL(from(proper(z0))), PROPER(from(z0)))
PROPER(dbl(dbl1(z0))) → c45(DBL(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbl(01)) → c45(DBL(ok(01)), PROPER(01))
PROPER(dbl(s1(z0))) → c45(DBL(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbl(sel1(z0, z1))) → c45(DBL(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbl(quote(z0))) → c45(DBL(quote(proper(z0))), PROPER(quote(z0)))
S tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(s(z0)) → c47(S(proper(z0)), PROPER(z0))
PROPER(dbls(z0)) → c48(DBLS(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c50(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(sel(z0, z1)) → c51(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(indx(z0, z1)) → c52(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c53(FROM(proper(z0)), PROPER(z0))
PROPER(dbl1(z0)) → c54(DBL1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c56(S1(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c57(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)))
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0))))))
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0))))))
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0)))
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(indx(sel1(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(indx(sel1(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel1(z0, z2)), x1), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(indx(quote(dbl(z0)), x1)) → c21(INDX(mark(dbl1(z0)), x1), ACTIVE(quote(dbl(z0))))
ACTIVE(indx(quote(sel(z0, z1)), x1)) → c21(INDX(mark(sel1(z0, z1)), x1), ACTIVE(quote(sel(z0, z1))))
ACTIVE(indx(dbl(z0), x1)) → c21(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
ACTIVE(indx(dbls(z0), x1)) → c21(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(indx(z0, z1), x1)) → c21(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1)))
ACTIVE(indx(dbl1(z0), x1)) → c21(INDX(dbl1(active(z0)), x1), ACTIVE(dbl1(z0)))
ACTIVE(indx(s1(z0), x1)) → c21(INDX(s1(active(z0)), x1), ACTIVE(s1(z0)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(active(z0), z1), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(z0, active(z1)), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(quote(z0), x1)) → c21(INDX(quote(active(z0)), x1), ACTIVE(quote(z0)))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)))
ACTIVE(indx(dbl(0), x1)) → c21(INDX(mark(0), x1))
ACTIVE(indx(dbls(nil), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(indx(indx(nil, z0), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0))))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1))
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0)))
ACTIVE(dbl1(sel(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl1(sel(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl1(sel1(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl1(sel1(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl1(quote(dbl(z0)))) → c22(DBL1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl1(quote(sel(z0, z1)))) → c22(DBL1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl1(dbl(z0))) → c22(DBL1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl1(dbls(z0))) → c22(DBL1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(indx(z0, z1))) → c22(DBL1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl1(dbl1(z0))) → c22(DBL1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl1(s1(z0))) → c22(DBL1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(quote(z0))) → c22(DBL1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(dbl1(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(dbl(0))) → c22(DBL1(mark(0)))
ACTIVE(dbl1(dbls(nil))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(indx(nil, z0))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(dbl1(0))) → c22(DBL1(mark(01)))
ACTIVE(dbl(dbl1(s(z0)))) → c4(DBL(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(DBLS(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(INDX(mark(s1(s1(dbl1(z0)))), x1))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(DBL1(mark(s(s(dbl(z0))))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(ACTIVE(dbl(s(z0))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(DBL1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(DBL1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl1(from(z0))) → c4(DBL1(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl1(from(z0))) → c4(ACTIVE(from(z0)))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(DBL1(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(s1(sel(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(s1(sel(s(z0), cons(z1, z2)))) → c23(S1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(s1(sel1(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(s1(sel1(s(z0), cons(z1, z2)))) → c23(S1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(s1(quote(dbl(z0)))) → c23(S1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(s1(quote(sel(z0, z1)))) → c23(S1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(s1(dbl(z0))) → c23(S1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(s1(dbls(z0))) → c23(S1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(s1(indx(z0, z1))) → c23(S1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(s1(dbl1(z0))) → c23(S1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(s1(s1(z0))) → c23(S1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(quote(z0))) → c23(S1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(s1(dbl(0))) → c23(S1(mark(0)))
ACTIVE(s1(dbls(nil))) → c23(S1(mark(nil)))
ACTIVE(s1(indx(nil, z0))) → c23(S1(mark(nil)))
ACTIVE(s1(dbl1(0))) → c23(S1(mark(01)))
ACTIVE(s1(dbl(s(z0)))) → c6(S1(mark(s(s(dbl(z0))))))
ACTIVE(s1(dbl(s(z0)))) → c6(ACTIVE(dbl(s(z0))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(S1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(S1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(s1(from(z0))) → c6(S1(mark(cons(z0, from(s(z0))))))
ACTIVE(s1(from(z0))) → c6(ACTIVE(from(z0)))
ACTIVE(s1(dbl1(s(z0)))) → c6(S1(mark(s1(s1(dbl1(z0))))))
ACTIVE(s1(dbl1(s(z0)))) → c6(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(sel(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(quote(sel(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(quote(sel1(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(quote(sel1(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(quote(quote(dbl(z0)))) → c26(QUOTE(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(quote(quote(sel(z0, z1)))) → c26(QUOTE(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(quote(dbl(z0))) → c26(QUOTE(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(quote(dbls(z0))) → c26(QUOTE(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(quote(indx(z0, z1))) → c26(QUOTE(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(quote(dbl1(z0))) → c26(QUOTE(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(quote(s1(z0))) → c26(QUOTE(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(quote(z0))) → c26(QUOTE(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(quote(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(quote(0))) → c22(DBL1(mark(01)))
ACTIVE(s1(quote(0))) → c23(S1(mark(01)))
ACTIVE(quote(dbl(0))) → c26(QUOTE(mark(0)))
ACTIVE(quote(dbls(nil))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(indx(nil, z0))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(dbl1(0))) → c26(QUOTE(mark(01)))
ACTIVE(quote(quote(0))) → c26(QUOTE(mark(01)))
ACTIVE(dbl(quote(s(z0)))) → c7(DBL(mark(s1(quote(z0)))))
ACTIVE(dbl(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(s(z0)))) → c7(DBLS(mark(s1(quote(z0)))))
ACTIVE(dbls(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(indx(quote(s(z0)), x1)) → c7(INDX(mark(s1(quote(z0))), x1))
ACTIVE(indx(quote(s(z0)), x1)) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbl1(quote(s(z0)))) → c7(DBL1(mark(s1(quote(z0)))))
ACTIVE(dbl1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(s1(quote(s(z0)))) → c7(S1(mark(s1(quote(z0)))))
ACTIVE(s1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(quote(dbl(s(z0)))) → c7(QUOTE(mark(s(s(dbl(z0))))))
ACTIVE(quote(dbl(s(z0)))) → c7(ACTIVE(dbl(s(z0))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(QUOTE(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(QUOTE(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(quote(from(z0))) → c7(QUOTE(mark(cons(z0, from(s(z0))))))
ACTIVE(quote(from(z0))) → c7(ACTIVE(from(z0)))
ACTIVE(quote(dbl1(s(z0)))) → c7(QUOTE(mark(s1(s1(dbl1(z0))))))
ACTIVE(quote(dbl1(s(z0)))) → c7(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(quote(s(z0)))) → c7(QUOTE(mark(s1(quote(z0)))))
ACTIVE(quote(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
PROPER(dbl(dbl(z0))) → c45(DBL(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbl(0)) → c45(DBL(ok(0)), PROPER(0))
PROPER(dbl(s(z0))) → c45(DBL(s(proper(z0))), PROPER(s(z0)))
PROPER(dbl(dbls(z0))) → c45(DBL(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbl(nil)) → c45(DBL(ok(nil)), PROPER(nil))
PROPER(dbl(cons(z0, z1))) → c45(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbl(sel(z0, z1))) → c45(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbl(indx(z0, z1))) → c45(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbl(from(z0))) → c45(DBL(from(proper(z0))), PROPER(from(z0)))
PROPER(dbl(dbl1(z0))) → c45(DBL(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbl(01)) → c45(DBL(ok(01)), PROPER(01))
PROPER(dbl(s1(z0))) → c45(DBL(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbl(sel1(z0, z1))) → c45(DBL(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbl(quote(z0))) → c45(DBL(quote(proper(z0))), PROPER(quote(z0)))
K tuples:none
Defined Rule Symbols:
active, s, dbl, cons, dbls, sel, indx, s1, dbl1, sel1, quote, proper, from
Defined Pair Symbols:
ACTIVE, DBL, DBLS, SEL, INDX, DBL1, S1, SEL1, QUOTE, PROPER, S, CONS, FROM, TOP
Compound Symbols:
c5, c12, c15, c16, c19, c20, c24, c25, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c47, c48, c50, c51, c52, c53, c54, c56, c57, c58, c59, c60, c61, c62, c63, c8, c, c17, c17, c1, c18, c18, c2, c21, c21, c3, c22, c22, c4, c23, c23, c6, c26, c26, c7, c45
(49) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 3 trailing tuple parts
(50) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(dbl(0)) → mark(0)
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
active(dbls(nil)) → mark(nil)
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1)))
active(sel(0, cons(z0, z1))) → mark(z0)
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
active(indx(nil, z0)) → mark(nil)
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2)))
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(dbl1(0)) → mark(01)
active(dbl1(s(z0))) → mark(s1(s1(dbl1(z0))))
active(sel1(0, cons(z0, z1))) → mark(z0)
active(sel1(s(z0), cons(z1, z2))) → mark(sel1(z0, z2))
active(quote(0)) → mark(01)
active(quote(s(z0))) → mark(s1(quote(z0)))
active(quote(dbl(z0))) → mark(dbl1(z0))
active(quote(sel(z0, z1))) → mark(sel1(z0, z1))
active(dbl(z0)) → dbl(active(z0))
active(dbls(z0)) → dbls(active(z0))
active(sel(z0, z1)) → sel(active(z0), z1)
active(sel(z0, z1)) → sel(z0, active(z1))
active(indx(z0, z1)) → indx(active(z0), z1)
active(dbl1(z0)) → dbl1(active(z0))
active(s1(z0)) → s1(active(z0))
active(sel1(z0, z1)) → sel1(active(z0), z1)
active(sel1(z0, z1)) → sel1(z0, active(z1))
active(quote(z0)) → quote(active(z0))
s(ok(z0)) → ok(s(z0))
dbl(mark(z0)) → mark(dbl(z0))
dbl(ok(z0)) → ok(dbl(z0))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
dbls(mark(z0)) → mark(dbls(z0))
dbls(ok(z0)) → ok(dbls(z0))
sel(mark(z0), z1) → mark(sel(z0, z1))
sel(z0, mark(z1)) → mark(sel(z0, z1))
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
indx(mark(z0), z1) → mark(indx(z0, z1))
indx(ok(z0), ok(z1)) → ok(indx(z0, z1))
s1(mark(z0)) → mark(s1(z0))
s1(ok(z0)) → ok(s1(z0))
dbl1(mark(z0)) → mark(dbl1(z0))
dbl1(ok(z0)) → ok(dbl1(z0))
sel1(mark(z0), z1) → mark(sel1(z0, z1))
sel1(z0, mark(z1)) → mark(sel1(z0, z1))
sel1(ok(z0), ok(z1)) → ok(sel1(z0, z1))
quote(mark(z0)) → mark(quote(z0))
quote(ok(z0)) → ok(quote(z0))
proper(dbl(z0)) → dbl(proper(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(dbls(z0)) → dbls(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
proper(indx(z0, z1)) → indx(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(dbl1(z0)) → dbl1(proper(z0))
proper(01) → ok(01)
proper(s1(z0)) → s1(proper(z0))
proper(sel1(z0, z1)) → sel1(proper(z0), proper(z1))
proper(quote(z0)) → quote(proper(z0))
from(ok(z0)) → ok(from(z0))
Tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(s(z0)) → c47(S(proper(z0)), PROPER(z0))
PROPER(dbls(z0)) → c48(DBLS(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c50(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(sel(z0, z1)) → c51(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(indx(z0, z1)) → c52(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c53(FROM(proper(z0)), PROPER(z0))
PROPER(dbl1(z0)) → c54(DBL1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c56(S1(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c57(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)))
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0))))))
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0))))))
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0)))
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(indx(sel1(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(indx(sel1(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel1(z0, z2)), x1), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(indx(quote(dbl(z0)), x1)) → c21(INDX(mark(dbl1(z0)), x1), ACTIVE(quote(dbl(z0))))
ACTIVE(indx(quote(sel(z0, z1)), x1)) → c21(INDX(mark(sel1(z0, z1)), x1), ACTIVE(quote(sel(z0, z1))))
ACTIVE(indx(dbl(z0), x1)) → c21(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
ACTIVE(indx(dbls(z0), x1)) → c21(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(indx(z0, z1), x1)) → c21(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1)))
ACTIVE(indx(dbl1(z0), x1)) → c21(INDX(dbl1(active(z0)), x1), ACTIVE(dbl1(z0)))
ACTIVE(indx(s1(z0), x1)) → c21(INDX(s1(active(z0)), x1), ACTIVE(s1(z0)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(active(z0), z1), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(z0, active(z1)), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(quote(z0), x1)) → c21(INDX(quote(active(z0)), x1), ACTIVE(quote(z0)))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)))
ACTIVE(indx(dbl(0), x1)) → c21(INDX(mark(0), x1))
ACTIVE(indx(dbls(nil), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(indx(indx(nil, z0), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0))))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1))
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0)))
ACTIVE(dbl1(sel(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl1(sel(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl1(sel1(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl1(sel1(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl1(quote(dbl(z0)))) → c22(DBL1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl1(quote(sel(z0, z1)))) → c22(DBL1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl1(dbl(z0))) → c22(DBL1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl1(dbls(z0))) → c22(DBL1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(indx(z0, z1))) → c22(DBL1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl1(dbl1(z0))) → c22(DBL1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl1(s1(z0))) → c22(DBL1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(quote(z0))) → c22(DBL1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(dbl1(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(dbl(0))) → c22(DBL1(mark(0)))
ACTIVE(dbl1(dbls(nil))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(indx(nil, z0))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(dbl1(0))) → c22(DBL1(mark(01)))
ACTIVE(dbl(dbl1(s(z0)))) → c4(DBL(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(DBLS(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(INDX(mark(s1(s1(dbl1(z0)))), x1))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(DBL1(mark(s(s(dbl(z0))))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(ACTIVE(dbl(s(z0))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(DBL1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(DBL1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl1(from(z0))) → c4(DBL1(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl1(from(z0))) → c4(ACTIVE(from(z0)))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(DBL1(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(s1(sel(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(s1(sel(s(z0), cons(z1, z2)))) → c23(S1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(s1(sel1(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(s1(sel1(s(z0), cons(z1, z2)))) → c23(S1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(s1(quote(dbl(z0)))) → c23(S1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(s1(quote(sel(z0, z1)))) → c23(S1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(s1(dbl(z0))) → c23(S1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(s1(dbls(z0))) → c23(S1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(s1(indx(z0, z1))) → c23(S1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(s1(dbl1(z0))) → c23(S1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(s1(s1(z0))) → c23(S1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(quote(z0))) → c23(S1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(s1(dbl(0))) → c23(S1(mark(0)))
ACTIVE(s1(dbls(nil))) → c23(S1(mark(nil)))
ACTIVE(s1(indx(nil, z0))) → c23(S1(mark(nil)))
ACTIVE(s1(dbl1(0))) → c23(S1(mark(01)))
ACTIVE(s1(dbl(s(z0)))) → c6(S1(mark(s(s(dbl(z0))))))
ACTIVE(s1(dbl(s(z0)))) → c6(ACTIVE(dbl(s(z0))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(S1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(S1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(s1(from(z0))) → c6(S1(mark(cons(z0, from(s(z0))))))
ACTIVE(s1(from(z0))) → c6(ACTIVE(from(z0)))
ACTIVE(s1(dbl1(s(z0)))) → c6(S1(mark(s1(s1(dbl1(z0))))))
ACTIVE(s1(dbl1(s(z0)))) → c6(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(sel(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(quote(sel(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(quote(sel1(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(quote(sel1(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(quote(quote(dbl(z0)))) → c26(QUOTE(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(quote(quote(sel(z0, z1)))) → c26(QUOTE(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(quote(dbl(z0))) → c26(QUOTE(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(quote(dbls(z0))) → c26(QUOTE(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(quote(indx(z0, z1))) → c26(QUOTE(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(quote(dbl1(z0))) → c26(QUOTE(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(quote(s1(z0))) → c26(QUOTE(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(quote(z0))) → c26(QUOTE(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(quote(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(quote(0))) → c22(DBL1(mark(01)))
ACTIVE(s1(quote(0))) → c23(S1(mark(01)))
ACTIVE(quote(dbl(0))) → c26(QUOTE(mark(0)))
ACTIVE(quote(dbls(nil))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(indx(nil, z0))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(dbl1(0))) → c26(QUOTE(mark(01)))
ACTIVE(quote(quote(0))) → c26(QUOTE(mark(01)))
ACTIVE(dbl(quote(s(z0)))) → c7(DBL(mark(s1(quote(z0)))))
ACTIVE(dbl(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(s(z0)))) → c7(DBLS(mark(s1(quote(z0)))))
ACTIVE(dbls(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(indx(quote(s(z0)), x1)) → c7(INDX(mark(s1(quote(z0))), x1))
ACTIVE(indx(quote(s(z0)), x1)) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbl1(quote(s(z0)))) → c7(DBL1(mark(s1(quote(z0)))))
ACTIVE(dbl1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(s1(quote(s(z0)))) → c7(S1(mark(s1(quote(z0)))))
ACTIVE(s1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(quote(dbl(s(z0)))) → c7(QUOTE(mark(s(s(dbl(z0))))))
ACTIVE(quote(dbl(s(z0)))) → c7(ACTIVE(dbl(s(z0))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(QUOTE(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(QUOTE(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(quote(from(z0))) → c7(QUOTE(mark(cons(z0, from(s(z0))))))
ACTIVE(quote(from(z0))) → c7(ACTIVE(from(z0)))
ACTIVE(quote(dbl1(s(z0)))) → c7(QUOTE(mark(s1(s1(dbl1(z0))))))
ACTIVE(quote(dbl1(s(z0)))) → c7(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(quote(s(z0)))) → c7(QUOTE(mark(s1(quote(z0)))))
ACTIVE(quote(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
PROPER(dbl(dbl(z0))) → c45(DBL(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbl(s(z0))) → c45(DBL(s(proper(z0))), PROPER(s(z0)))
PROPER(dbl(dbls(z0))) → c45(DBL(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbl(cons(z0, z1))) → c45(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbl(sel(z0, z1))) → c45(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbl(indx(z0, z1))) → c45(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbl(from(z0))) → c45(DBL(from(proper(z0))), PROPER(from(z0)))
PROPER(dbl(dbl1(z0))) → c45(DBL(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbl(s1(z0))) → c45(DBL(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbl(sel1(z0, z1))) → c45(DBL(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbl(quote(z0))) → c45(DBL(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbl(0)) → c45(DBL(ok(0)))
PROPER(dbl(nil)) → c45(DBL(ok(nil)))
PROPER(dbl(01)) → c45(DBL(ok(01)))
S tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(s(z0)) → c47(S(proper(z0)), PROPER(z0))
PROPER(dbls(z0)) → c48(DBLS(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c50(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(sel(z0, z1)) → c51(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(indx(z0, z1)) → c52(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c53(FROM(proper(z0)), PROPER(z0))
PROPER(dbl1(z0)) → c54(DBL1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c56(S1(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c57(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)))
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0))))))
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0))))))
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0)))
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(indx(sel1(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(indx(sel1(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel1(z0, z2)), x1), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(indx(quote(dbl(z0)), x1)) → c21(INDX(mark(dbl1(z0)), x1), ACTIVE(quote(dbl(z0))))
ACTIVE(indx(quote(sel(z0, z1)), x1)) → c21(INDX(mark(sel1(z0, z1)), x1), ACTIVE(quote(sel(z0, z1))))
ACTIVE(indx(dbl(z0), x1)) → c21(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
ACTIVE(indx(dbls(z0), x1)) → c21(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(indx(z0, z1), x1)) → c21(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1)))
ACTIVE(indx(dbl1(z0), x1)) → c21(INDX(dbl1(active(z0)), x1), ACTIVE(dbl1(z0)))
ACTIVE(indx(s1(z0), x1)) → c21(INDX(s1(active(z0)), x1), ACTIVE(s1(z0)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(active(z0), z1), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(z0, active(z1)), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(quote(z0), x1)) → c21(INDX(quote(active(z0)), x1), ACTIVE(quote(z0)))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)))
ACTIVE(indx(dbl(0), x1)) → c21(INDX(mark(0), x1))
ACTIVE(indx(dbls(nil), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(indx(indx(nil, z0), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0))))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1))
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0)))
ACTIVE(dbl1(sel(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl1(sel(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl1(sel1(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl1(sel1(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl1(quote(dbl(z0)))) → c22(DBL1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl1(quote(sel(z0, z1)))) → c22(DBL1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl1(dbl(z0))) → c22(DBL1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl1(dbls(z0))) → c22(DBL1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(indx(z0, z1))) → c22(DBL1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl1(dbl1(z0))) → c22(DBL1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl1(s1(z0))) → c22(DBL1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(quote(z0))) → c22(DBL1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(dbl1(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(dbl(0))) → c22(DBL1(mark(0)))
ACTIVE(dbl1(dbls(nil))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(indx(nil, z0))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(dbl1(0))) → c22(DBL1(mark(01)))
ACTIVE(dbl(dbl1(s(z0)))) → c4(DBL(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(DBLS(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(INDX(mark(s1(s1(dbl1(z0)))), x1))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(DBL1(mark(s(s(dbl(z0))))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(ACTIVE(dbl(s(z0))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(DBL1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(DBL1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl1(from(z0))) → c4(DBL1(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl1(from(z0))) → c4(ACTIVE(from(z0)))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(DBL1(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(s1(sel(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(s1(sel(s(z0), cons(z1, z2)))) → c23(S1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(s1(sel1(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(s1(sel1(s(z0), cons(z1, z2)))) → c23(S1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(s1(quote(dbl(z0)))) → c23(S1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(s1(quote(sel(z0, z1)))) → c23(S1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(s1(dbl(z0))) → c23(S1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(s1(dbls(z0))) → c23(S1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(s1(indx(z0, z1))) → c23(S1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(s1(dbl1(z0))) → c23(S1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(s1(s1(z0))) → c23(S1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(quote(z0))) → c23(S1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(s1(dbl(0))) → c23(S1(mark(0)))
ACTIVE(s1(dbls(nil))) → c23(S1(mark(nil)))
ACTIVE(s1(indx(nil, z0))) → c23(S1(mark(nil)))
ACTIVE(s1(dbl1(0))) → c23(S1(mark(01)))
ACTIVE(s1(dbl(s(z0)))) → c6(S1(mark(s(s(dbl(z0))))))
ACTIVE(s1(dbl(s(z0)))) → c6(ACTIVE(dbl(s(z0))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(S1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(S1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(s1(from(z0))) → c6(S1(mark(cons(z0, from(s(z0))))))
ACTIVE(s1(from(z0))) → c6(ACTIVE(from(z0)))
ACTIVE(s1(dbl1(s(z0)))) → c6(S1(mark(s1(s1(dbl1(z0))))))
ACTIVE(s1(dbl1(s(z0)))) → c6(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(sel(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(quote(sel(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(quote(sel1(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(quote(sel1(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(quote(quote(dbl(z0)))) → c26(QUOTE(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(quote(quote(sel(z0, z1)))) → c26(QUOTE(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(quote(dbl(z0))) → c26(QUOTE(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(quote(dbls(z0))) → c26(QUOTE(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(quote(indx(z0, z1))) → c26(QUOTE(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(quote(dbl1(z0))) → c26(QUOTE(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(quote(s1(z0))) → c26(QUOTE(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(quote(z0))) → c26(QUOTE(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(quote(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(quote(0))) → c22(DBL1(mark(01)))
ACTIVE(s1(quote(0))) → c23(S1(mark(01)))
ACTIVE(quote(dbl(0))) → c26(QUOTE(mark(0)))
ACTIVE(quote(dbls(nil))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(indx(nil, z0))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(dbl1(0))) → c26(QUOTE(mark(01)))
ACTIVE(quote(quote(0))) → c26(QUOTE(mark(01)))
ACTIVE(dbl(quote(s(z0)))) → c7(DBL(mark(s1(quote(z0)))))
ACTIVE(dbl(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(s(z0)))) → c7(DBLS(mark(s1(quote(z0)))))
ACTIVE(dbls(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(indx(quote(s(z0)), x1)) → c7(INDX(mark(s1(quote(z0))), x1))
ACTIVE(indx(quote(s(z0)), x1)) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbl1(quote(s(z0)))) → c7(DBL1(mark(s1(quote(z0)))))
ACTIVE(dbl1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(s1(quote(s(z0)))) → c7(S1(mark(s1(quote(z0)))))
ACTIVE(s1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(quote(dbl(s(z0)))) → c7(QUOTE(mark(s(s(dbl(z0))))))
ACTIVE(quote(dbl(s(z0)))) → c7(ACTIVE(dbl(s(z0))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(QUOTE(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(QUOTE(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(quote(from(z0))) → c7(QUOTE(mark(cons(z0, from(s(z0))))))
ACTIVE(quote(from(z0))) → c7(ACTIVE(from(z0)))
ACTIVE(quote(dbl1(s(z0)))) → c7(QUOTE(mark(s1(s1(dbl1(z0))))))
ACTIVE(quote(dbl1(s(z0)))) → c7(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(quote(s(z0)))) → c7(QUOTE(mark(s1(quote(z0)))))
ACTIVE(quote(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
PROPER(dbl(dbl(z0))) → c45(DBL(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbl(s(z0))) → c45(DBL(s(proper(z0))), PROPER(s(z0)))
PROPER(dbl(dbls(z0))) → c45(DBL(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbl(cons(z0, z1))) → c45(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbl(sel(z0, z1))) → c45(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbl(indx(z0, z1))) → c45(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbl(from(z0))) → c45(DBL(from(proper(z0))), PROPER(from(z0)))
PROPER(dbl(dbl1(z0))) → c45(DBL(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbl(s1(z0))) → c45(DBL(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbl(sel1(z0, z1))) → c45(DBL(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbl(quote(z0))) → c45(DBL(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbl(0)) → c45(DBL(ok(0)))
PROPER(dbl(nil)) → c45(DBL(ok(nil)))
PROPER(dbl(01)) → c45(DBL(ok(01)))
K tuples:none
Defined Rule Symbols:
active, s, dbl, cons, dbls, sel, indx, s1, dbl1, sel1, quote, proper, from
Defined Pair Symbols:
ACTIVE, DBL, DBLS, SEL, INDX, DBL1, S1, SEL1, QUOTE, PROPER, S, CONS, FROM, TOP
Compound Symbols:
c5, c12, c15, c16, c19, c20, c24, c25, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c47, c48, c50, c51, c52, c53, c54, c56, c57, c58, c59, c60, c61, c62, c63, c8, c, c17, c17, c1, c18, c18, c2, c21, c21, c3, c22, c22, c4, c23, c23, c6, c26, c26, c7, c45, c45
(51) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
PROPER(
s(
z0)) →
c47(
S(
proper(
z0)),
PROPER(
z0)) by
PROPER(s(dbl(z0))) → c47(S(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(s(0)) → c47(S(ok(0)), PROPER(0))
PROPER(s(s(z0))) → c47(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(dbls(z0))) → c47(S(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(s(nil)) → c47(S(ok(nil)), PROPER(nil))
PROPER(s(cons(z0, z1))) → c47(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(sel(z0, z1))) → c47(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(s(indx(z0, z1))) → c47(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(s(from(z0))) → c47(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(dbl1(z0))) → c47(S(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(s(01)) → c47(S(ok(01)), PROPER(01))
PROPER(s(s1(z0))) → c47(S(s1(proper(z0))), PROPER(s1(z0)))
PROPER(s(sel1(z0, z1))) → c47(S(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(s(quote(z0))) → c47(S(quote(proper(z0))), PROPER(quote(z0)))
(52) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(dbl(0)) → mark(0)
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
active(dbls(nil)) → mark(nil)
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1)))
active(sel(0, cons(z0, z1))) → mark(z0)
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
active(indx(nil, z0)) → mark(nil)
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2)))
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(dbl1(0)) → mark(01)
active(dbl1(s(z0))) → mark(s1(s1(dbl1(z0))))
active(sel1(0, cons(z0, z1))) → mark(z0)
active(sel1(s(z0), cons(z1, z2))) → mark(sel1(z0, z2))
active(quote(0)) → mark(01)
active(quote(s(z0))) → mark(s1(quote(z0)))
active(quote(dbl(z0))) → mark(dbl1(z0))
active(quote(sel(z0, z1))) → mark(sel1(z0, z1))
active(dbl(z0)) → dbl(active(z0))
active(dbls(z0)) → dbls(active(z0))
active(sel(z0, z1)) → sel(active(z0), z1)
active(sel(z0, z1)) → sel(z0, active(z1))
active(indx(z0, z1)) → indx(active(z0), z1)
active(dbl1(z0)) → dbl1(active(z0))
active(s1(z0)) → s1(active(z0))
active(sel1(z0, z1)) → sel1(active(z0), z1)
active(sel1(z0, z1)) → sel1(z0, active(z1))
active(quote(z0)) → quote(active(z0))
s(ok(z0)) → ok(s(z0))
dbl(mark(z0)) → mark(dbl(z0))
dbl(ok(z0)) → ok(dbl(z0))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
dbls(mark(z0)) → mark(dbls(z0))
dbls(ok(z0)) → ok(dbls(z0))
sel(mark(z0), z1) → mark(sel(z0, z1))
sel(z0, mark(z1)) → mark(sel(z0, z1))
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
indx(mark(z0), z1) → mark(indx(z0, z1))
indx(ok(z0), ok(z1)) → ok(indx(z0, z1))
s1(mark(z0)) → mark(s1(z0))
s1(ok(z0)) → ok(s1(z0))
dbl1(mark(z0)) → mark(dbl1(z0))
dbl1(ok(z0)) → ok(dbl1(z0))
sel1(mark(z0), z1) → mark(sel1(z0, z1))
sel1(z0, mark(z1)) → mark(sel1(z0, z1))
sel1(ok(z0), ok(z1)) → ok(sel1(z0, z1))
quote(mark(z0)) → mark(quote(z0))
quote(ok(z0)) → ok(quote(z0))
proper(dbl(z0)) → dbl(proper(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(dbls(z0)) → dbls(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
proper(indx(z0, z1)) → indx(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(dbl1(z0)) → dbl1(proper(z0))
proper(01) → ok(01)
proper(s1(z0)) → s1(proper(z0))
proper(sel1(z0, z1)) → sel1(proper(z0), proper(z1))
proper(quote(z0)) → quote(proper(z0))
from(ok(z0)) → ok(from(z0))
Tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(dbls(z0)) → c48(DBLS(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c50(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(sel(z0, z1)) → c51(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(indx(z0, z1)) → c52(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c53(FROM(proper(z0)), PROPER(z0))
PROPER(dbl1(z0)) → c54(DBL1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c56(S1(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c57(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)))
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0))))))
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0))))))
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0)))
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(indx(sel1(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(indx(sel1(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel1(z0, z2)), x1), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(indx(quote(dbl(z0)), x1)) → c21(INDX(mark(dbl1(z0)), x1), ACTIVE(quote(dbl(z0))))
ACTIVE(indx(quote(sel(z0, z1)), x1)) → c21(INDX(mark(sel1(z0, z1)), x1), ACTIVE(quote(sel(z0, z1))))
ACTIVE(indx(dbl(z0), x1)) → c21(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
ACTIVE(indx(dbls(z0), x1)) → c21(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(indx(z0, z1), x1)) → c21(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1)))
ACTIVE(indx(dbl1(z0), x1)) → c21(INDX(dbl1(active(z0)), x1), ACTIVE(dbl1(z0)))
ACTIVE(indx(s1(z0), x1)) → c21(INDX(s1(active(z0)), x1), ACTIVE(s1(z0)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(active(z0), z1), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(z0, active(z1)), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(quote(z0), x1)) → c21(INDX(quote(active(z0)), x1), ACTIVE(quote(z0)))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)))
ACTIVE(indx(dbl(0), x1)) → c21(INDX(mark(0), x1))
ACTIVE(indx(dbls(nil), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(indx(indx(nil, z0), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0))))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1))
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0)))
ACTIVE(dbl1(sel(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl1(sel(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl1(sel1(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl1(sel1(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl1(quote(dbl(z0)))) → c22(DBL1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl1(quote(sel(z0, z1)))) → c22(DBL1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl1(dbl(z0))) → c22(DBL1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl1(dbls(z0))) → c22(DBL1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(indx(z0, z1))) → c22(DBL1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl1(dbl1(z0))) → c22(DBL1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl1(s1(z0))) → c22(DBL1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(quote(z0))) → c22(DBL1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(dbl1(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(dbl(0))) → c22(DBL1(mark(0)))
ACTIVE(dbl1(dbls(nil))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(indx(nil, z0))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(dbl1(0))) → c22(DBL1(mark(01)))
ACTIVE(dbl(dbl1(s(z0)))) → c4(DBL(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(DBLS(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(INDX(mark(s1(s1(dbl1(z0)))), x1))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(DBL1(mark(s(s(dbl(z0))))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(ACTIVE(dbl(s(z0))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(DBL1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(DBL1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl1(from(z0))) → c4(DBL1(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl1(from(z0))) → c4(ACTIVE(from(z0)))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(DBL1(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(s1(sel(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(s1(sel(s(z0), cons(z1, z2)))) → c23(S1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(s1(sel1(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(s1(sel1(s(z0), cons(z1, z2)))) → c23(S1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(s1(quote(dbl(z0)))) → c23(S1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(s1(quote(sel(z0, z1)))) → c23(S1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(s1(dbl(z0))) → c23(S1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(s1(dbls(z0))) → c23(S1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(s1(indx(z0, z1))) → c23(S1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(s1(dbl1(z0))) → c23(S1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(s1(s1(z0))) → c23(S1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(quote(z0))) → c23(S1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(s1(dbl(0))) → c23(S1(mark(0)))
ACTIVE(s1(dbls(nil))) → c23(S1(mark(nil)))
ACTIVE(s1(indx(nil, z0))) → c23(S1(mark(nil)))
ACTIVE(s1(dbl1(0))) → c23(S1(mark(01)))
ACTIVE(s1(dbl(s(z0)))) → c6(S1(mark(s(s(dbl(z0))))))
ACTIVE(s1(dbl(s(z0)))) → c6(ACTIVE(dbl(s(z0))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(S1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(S1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(s1(from(z0))) → c6(S1(mark(cons(z0, from(s(z0))))))
ACTIVE(s1(from(z0))) → c6(ACTIVE(from(z0)))
ACTIVE(s1(dbl1(s(z0)))) → c6(S1(mark(s1(s1(dbl1(z0))))))
ACTIVE(s1(dbl1(s(z0)))) → c6(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(sel(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(quote(sel(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(quote(sel1(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(quote(sel1(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(quote(quote(dbl(z0)))) → c26(QUOTE(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(quote(quote(sel(z0, z1)))) → c26(QUOTE(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(quote(dbl(z0))) → c26(QUOTE(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(quote(dbls(z0))) → c26(QUOTE(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(quote(indx(z0, z1))) → c26(QUOTE(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(quote(dbl1(z0))) → c26(QUOTE(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(quote(s1(z0))) → c26(QUOTE(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(quote(z0))) → c26(QUOTE(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(quote(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(quote(0))) → c22(DBL1(mark(01)))
ACTIVE(s1(quote(0))) → c23(S1(mark(01)))
ACTIVE(quote(dbl(0))) → c26(QUOTE(mark(0)))
ACTIVE(quote(dbls(nil))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(indx(nil, z0))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(dbl1(0))) → c26(QUOTE(mark(01)))
ACTIVE(quote(quote(0))) → c26(QUOTE(mark(01)))
ACTIVE(dbl(quote(s(z0)))) → c7(DBL(mark(s1(quote(z0)))))
ACTIVE(dbl(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(s(z0)))) → c7(DBLS(mark(s1(quote(z0)))))
ACTIVE(dbls(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(indx(quote(s(z0)), x1)) → c7(INDX(mark(s1(quote(z0))), x1))
ACTIVE(indx(quote(s(z0)), x1)) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbl1(quote(s(z0)))) → c7(DBL1(mark(s1(quote(z0)))))
ACTIVE(dbl1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(s1(quote(s(z0)))) → c7(S1(mark(s1(quote(z0)))))
ACTIVE(s1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(quote(dbl(s(z0)))) → c7(QUOTE(mark(s(s(dbl(z0))))))
ACTIVE(quote(dbl(s(z0)))) → c7(ACTIVE(dbl(s(z0))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(QUOTE(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(QUOTE(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(quote(from(z0))) → c7(QUOTE(mark(cons(z0, from(s(z0))))))
ACTIVE(quote(from(z0))) → c7(ACTIVE(from(z0)))
ACTIVE(quote(dbl1(s(z0)))) → c7(QUOTE(mark(s1(s1(dbl1(z0))))))
ACTIVE(quote(dbl1(s(z0)))) → c7(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(quote(s(z0)))) → c7(QUOTE(mark(s1(quote(z0)))))
ACTIVE(quote(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
PROPER(dbl(dbl(z0))) → c45(DBL(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbl(s(z0))) → c45(DBL(s(proper(z0))), PROPER(s(z0)))
PROPER(dbl(dbls(z0))) → c45(DBL(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbl(cons(z0, z1))) → c45(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbl(sel(z0, z1))) → c45(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbl(indx(z0, z1))) → c45(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbl(from(z0))) → c45(DBL(from(proper(z0))), PROPER(from(z0)))
PROPER(dbl(dbl1(z0))) → c45(DBL(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbl(s1(z0))) → c45(DBL(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbl(sel1(z0, z1))) → c45(DBL(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbl(quote(z0))) → c45(DBL(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbl(0)) → c45(DBL(ok(0)))
PROPER(dbl(nil)) → c45(DBL(ok(nil)))
PROPER(dbl(01)) → c45(DBL(ok(01)))
PROPER(s(dbl(z0))) → c47(S(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(s(0)) → c47(S(ok(0)), PROPER(0))
PROPER(s(s(z0))) → c47(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(dbls(z0))) → c47(S(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(s(nil)) → c47(S(ok(nil)), PROPER(nil))
PROPER(s(cons(z0, z1))) → c47(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(sel(z0, z1))) → c47(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(s(indx(z0, z1))) → c47(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(s(from(z0))) → c47(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(dbl1(z0))) → c47(S(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(s(01)) → c47(S(ok(01)), PROPER(01))
PROPER(s(s1(z0))) → c47(S(s1(proper(z0))), PROPER(s1(z0)))
PROPER(s(sel1(z0, z1))) → c47(S(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(s(quote(z0))) → c47(S(quote(proper(z0))), PROPER(quote(z0)))
S tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(dbls(z0)) → c48(DBLS(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c50(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(sel(z0, z1)) → c51(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(indx(z0, z1)) → c52(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c53(FROM(proper(z0)), PROPER(z0))
PROPER(dbl1(z0)) → c54(DBL1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c56(S1(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c57(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)))
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0))))))
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0))))))
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0)))
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(indx(sel1(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(indx(sel1(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel1(z0, z2)), x1), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(indx(quote(dbl(z0)), x1)) → c21(INDX(mark(dbl1(z0)), x1), ACTIVE(quote(dbl(z0))))
ACTIVE(indx(quote(sel(z0, z1)), x1)) → c21(INDX(mark(sel1(z0, z1)), x1), ACTIVE(quote(sel(z0, z1))))
ACTIVE(indx(dbl(z0), x1)) → c21(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
ACTIVE(indx(dbls(z0), x1)) → c21(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(indx(z0, z1), x1)) → c21(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1)))
ACTIVE(indx(dbl1(z0), x1)) → c21(INDX(dbl1(active(z0)), x1), ACTIVE(dbl1(z0)))
ACTIVE(indx(s1(z0), x1)) → c21(INDX(s1(active(z0)), x1), ACTIVE(s1(z0)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(active(z0), z1), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(z0, active(z1)), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(quote(z0), x1)) → c21(INDX(quote(active(z0)), x1), ACTIVE(quote(z0)))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)))
ACTIVE(indx(dbl(0), x1)) → c21(INDX(mark(0), x1))
ACTIVE(indx(dbls(nil), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(indx(indx(nil, z0), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0))))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1))
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0)))
ACTIVE(dbl1(sel(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl1(sel(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl1(sel1(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl1(sel1(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl1(quote(dbl(z0)))) → c22(DBL1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl1(quote(sel(z0, z1)))) → c22(DBL1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl1(dbl(z0))) → c22(DBL1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl1(dbls(z0))) → c22(DBL1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(indx(z0, z1))) → c22(DBL1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl1(dbl1(z0))) → c22(DBL1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl1(s1(z0))) → c22(DBL1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(quote(z0))) → c22(DBL1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(dbl1(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(dbl(0))) → c22(DBL1(mark(0)))
ACTIVE(dbl1(dbls(nil))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(indx(nil, z0))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(dbl1(0))) → c22(DBL1(mark(01)))
ACTIVE(dbl(dbl1(s(z0)))) → c4(DBL(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(DBLS(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(INDX(mark(s1(s1(dbl1(z0)))), x1))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(DBL1(mark(s(s(dbl(z0))))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(ACTIVE(dbl(s(z0))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(DBL1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(DBL1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl1(from(z0))) → c4(DBL1(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl1(from(z0))) → c4(ACTIVE(from(z0)))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(DBL1(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(s1(sel(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(s1(sel(s(z0), cons(z1, z2)))) → c23(S1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(s1(sel1(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(s1(sel1(s(z0), cons(z1, z2)))) → c23(S1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(s1(quote(dbl(z0)))) → c23(S1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(s1(quote(sel(z0, z1)))) → c23(S1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(s1(dbl(z0))) → c23(S1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(s1(dbls(z0))) → c23(S1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(s1(indx(z0, z1))) → c23(S1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(s1(dbl1(z0))) → c23(S1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(s1(s1(z0))) → c23(S1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(quote(z0))) → c23(S1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(s1(dbl(0))) → c23(S1(mark(0)))
ACTIVE(s1(dbls(nil))) → c23(S1(mark(nil)))
ACTIVE(s1(indx(nil, z0))) → c23(S1(mark(nil)))
ACTIVE(s1(dbl1(0))) → c23(S1(mark(01)))
ACTIVE(s1(dbl(s(z0)))) → c6(S1(mark(s(s(dbl(z0))))))
ACTIVE(s1(dbl(s(z0)))) → c6(ACTIVE(dbl(s(z0))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(S1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(S1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(s1(from(z0))) → c6(S1(mark(cons(z0, from(s(z0))))))
ACTIVE(s1(from(z0))) → c6(ACTIVE(from(z0)))
ACTIVE(s1(dbl1(s(z0)))) → c6(S1(mark(s1(s1(dbl1(z0))))))
ACTIVE(s1(dbl1(s(z0)))) → c6(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(sel(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(quote(sel(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(quote(sel1(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(quote(sel1(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(quote(quote(dbl(z0)))) → c26(QUOTE(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(quote(quote(sel(z0, z1)))) → c26(QUOTE(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(quote(dbl(z0))) → c26(QUOTE(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(quote(dbls(z0))) → c26(QUOTE(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(quote(indx(z0, z1))) → c26(QUOTE(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(quote(dbl1(z0))) → c26(QUOTE(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(quote(s1(z0))) → c26(QUOTE(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(quote(z0))) → c26(QUOTE(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(quote(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(quote(0))) → c22(DBL1(mark(01)))
ACTIVE(s1(quote(0))) → c23(S1(mark(01)))
ACTIVE(quote(dbl(0))) → c26(QUOTE(mark(0)))
ACTIVE(quote(dbls(nil))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(indx(nil, z0))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(dbl1(0))) → c26(QUOTE(mark(01)))
ACTIVE(quote(quote(0))) → c26(QUOTE(mark(01)))
ACTIVE(dbl(quote(s(z0)))) → c7(DBL(mark(s1(quote(z0)))))
ACTIVE(dbl(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(s(z0)))) → c7(DBLS(mark(s1(quote(z0)))))
ACTIVE(dbls(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(indx(quote(s(z0)), x1)) → c7(INDX(mark(s1(quote(z0))), x1))
ACTIVE(indx(quote(s(z0)), x1)) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbl1(quote(s(z0)))) → c7(DBL1(mark(s1(quote(z0)))))
ACTIVE(dbl1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(s1(quote(s(z0)))) → c7(S1(mark(s1(quote(z0)))))
ACTIVE(s1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(quote(dbl(s(z0)))) → c7(QUOTE(mark(s(s(dbl(z0))))))
ACTIVE(quote(dbl(s(z0)))) → c7(ACTIVE(dbl(s(z0))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(QUOTE(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(QUOTE(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(quote(from(z0))) → c7(QUOTE(mark(cons(z0, from(s(z0))))))
ACTIVE(quote(from(z0))) → c7(ACTIVE(from(z0)))
ACTIVE(quote(dbl1(s(z0)))) → c7(QUOTE(mark(s1(s1(dbl1(z0))))))
ACTIVE(quote(dbl1(s(z0)))) → c7(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(quote(s(z0)))) → c7(QUOTE(mark(s1(quote(z0)))))
ACTIVE(quote(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
PROPER(dbl(dbl(z0))) → c45(DBL(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbl(s(z0))) → c45(DBL(s(proper(z0))), PROPER(s(z0)))
PROPER(dbl(dbls(z0))) → c45(DBL(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbl(cons(z0, z1))) → c45(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbl(sel(z0, z1))) → c45(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbl(indx(z0, z1))) → c45(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbl(from(z0))) → c45(DBL(from(proper(z0))), PROPER(from(z0)))
PROPER(dbl(dbl1(z0))) → c45(DBL(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbl(s1(z0))) → c45(DBL(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbl(sel1(z0, z1))) → c45(DBL(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbl(quote(z0))) → c45(DBL(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbl(0)) → c45(DBL(ok(0)))
PROPER(dbl(nil)) → c45(DBL(ok(nil)))
PROPER(dbl(01)) → c45(DBL(ok(01)))
PROPER(s(dbl(z0))) → c47(S(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(s(0)) → c47(S(ok(0)), PROPER(0))
PROPER(s(s(z0))) → c47(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(dbls(z0))) → c47(S(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(s(nil)) → c47(S(ok(nil)), PROPER(nil))
PROPER(s(cons(z0, z1))) → c47(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(sel(z0, z1))) → c47(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(s(indx(z0, z1))) → c47(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(s(from(z0))) → c47(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(dbl1(z0))) → c47(S(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(s(01)) → c47(S(ok(01)), PROPER(01))
PROPER(s(s1(z0))) → c47(S(s1(proper(z0))), PROPER(s1(z0)))
PROPER(s(sel1(z0, z1))) → c47(S(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(s(quote(z0))) → c47(S(quote(proper(z0))), PROPER(quote(z0)))
K tuples:none
Defined Rule Symbols:
active, s, dbl, cons, dbls, sel, indx, s1, dbl1, sel1, quote, proper, from
Defined Pair Symbols:
ACTIVE, DBL, DBLS, SEL, INDX, DBL1, S1, SEL1, QUOTE, PROPER, S, CONS, FROM, TOP
Compound Symbols:
c5, c12, c15, c16, c19, c20, c24, c25, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c48, c50, c51, c52, c53, c54, c56, c57, c58, c59, c60, c61, c62, c63, c8, c, c17, c17, c1, c18, c18, c2, c21, c21, c3, c22, c22, c4, c23, c23, c6, c26, c26, c7, c45, c45, c47
(53) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 3 trailing tuple parts
(54) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(dbl(0)) → mark(0)
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
active(dbls(nil)) → mark(nil)
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1)))
active(sel(0, cons(z0, z1))) → mark(z0)
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
active(indx(nil, z0)) → mark(nil)
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2)))
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(dbl1(0)) → mark(01)
active(dbl1(s(z0))) → mark(s1(s1(dbl1(z0))))
active(sel1(0, cons(z0, z1))) → mark(z0)
active(sel1(s(z0), cons(z1, z2))) → mark(sel1(z0, z2))
active(quote(0)) → mark(01)
active(quote(s(z0))) → mark(s1(quote(z0)))
active(quote(dbl(z0))) → mark(dbl1(z0))
active(quote(sel(z0, z1))) → mark(sel1(z0, z1))
active(dbl(z0)) → dbl(active(z0))
active(dbls(z0)) → dbls(active(z0))
active(sel(z0, z1)) → sel(active(z0), z1)
active(sel(z0, z1)) → sel(z0, active(z1))
active(indx(z0, z1)) → indx(active(z0), z1)
active(dbl1(z0)) → dbl1(active(z0))
active(s1(z0)) → s1(active(z0))
active(sel1(z0, z1)) → sel1(active(z0), z1)
active(sel1(z0, z1)) → sel1(z0, active(z1))
active(quote(z0)) → quote(active(z0))
s(ok(z0)) → ok(s(z0))
dbl(mark(z0)) → mark(dbl(z0))
dbl(ok(z0)) → ok(dbl(z0))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
dbls(mark(z0)) → mark(dbls(z0))
dbls(ok(z0)) → ok(dbls(z0))
sel(mark(z0), z1) → mark(sel(z0, z1))
sel(z0, mark(z1)) → mark(sel(z0, z1))
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
indx(mark(z0), z1) → mark(indx(z0, z1))
indx(ok(z0), ok(z1)) → ok(indx(z0, z1))
s1(mark(z0)) → mark(s1(z0))
s1(ok(z0)) → ok(s1(z0))
dbl1(mark(z0)) → mark(dbl1(z0))
dbl1(ok(z0)) → ok(dbl1(z0))
sel1(mark(z0), z1) → mark(sel1(z0, z1))
sel1(z0, mark(z1)) → mark(sel1(z0, z1))
sel1(ok(z0), ok(z1)) → ok(sel1(z0, z1))
quote(mark(z0)) → mark(quote(z0))
quote(ok(z0)) → ok(quote(z0))
proper(dbl(z0)) → dbl(proper(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(dbls(z0)) → dbls(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
proper(indx(z0, z1)) → indx(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(dbl1(z0)) → dbl1(proper(z0))
proper(01) → ok(01)
proper(s1(z0)) → s1(proper(z0))
proper(sel1(z0, z1)) → sel1(proper(z0), proper(z1))
proper(quote(z0)) → quote(proper(z0))
from(ok(z0)) → ok(from(z0))
Tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(dbls(z0)) → c48(DBLS(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c50(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(sel(z0, z1)) → c51(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(indx(z0, z1)) → c52(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c53(FROM(proper(z0)), PROPER(z0))
PROPER(dbl1(z0)) → c54(DBL1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c56(S1(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c57(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)))
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0))))))
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0))))))
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0)))
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(indx(sel1(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(indx(sel1(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel1(z0, z2)), x1), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(indx(quote(dbl(z0)), x1)) → c21(INDX(mark(dbl1(z0)), x1), ACTIVE(quote(dbl(z0))))
ACTIVE(indx(quote(sel(z0, z1)), x1)) → c21(INDX(mark(sel1(z0, z1)), x1), ACTIVE(quote(sel(z0, z1))))
ACTIVE(indx(dbl(z0), x1)) → c21(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
ACTIVE(indx(dbls(z0), x1)) → c21(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(indx(z0, z1), x1)) → c21(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1)))
ACTIVE(indx(dbl1(z0), x1)) → c21(INDX(dbl1(active(z0)), x1), ACTIVE(dbl1(z0)))
ACTIVE(indx(s1(z0), x1)) → c21(INDX(s1(active(z0)), x1), ACTIVE(s1(z0)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(active(z0), z1), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(z0, active(z1)), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(quote(z0), x1)) → c21(INDX(quote(active(z0)), x1), ACTIVE(quote(z0)))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)))
ACTIVE(indx(dbl(0), x1)) → c21(INDX(mark(0), x1))
ACTIVE(indx(dbls(nil), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(indx(indx(nil, z0), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0))))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1))
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0)))
ACTIVE(dbl1(sel(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl1(sel(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl1(sel1(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl1(sel1(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl1(quote(dbl(z0)))) → c22(DBL1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl1(quote(sel(z0, z1)))) → c22(DBL1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl1(dbl(z0))) → c22(DBL1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl1(dbls(z0))) → c22(DBL1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(indx(z0, z1))) → c22(DBL1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl1(dbl1(z0))) → c22(DBL1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl1(s1(z0))) → c22(DBL1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(quote(z0))) → c22(DBL1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(dbl1(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(dbl(0))) → c22(DBL1(mark(0)))
ACTIVE(dbl1(dbls(nil))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(indx(nil, z0))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(dbl1(0))) → c22(DBL1(mark(01)))
ACTIVE(dbl(dbl1(s(z0)))) → c4(DBL(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(DBLS(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(INDX(mark(s1(s1(dbl1(z0)))), x1))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(DBL1(mark(s(s(dbl(z0))))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(ACTIVE(dbl(s(z0))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(DBL1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(DBL1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl1(from(z0))) → c4(DBL1(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl1(from(z0))) → c4(ACTIVE(from(z0)))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(DBL1(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(s1(sel(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(s1(sel(s(z0), cons(z1, z2)))) → c23(S1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(s1(sel1(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(s1(sel1(s(z0), cons(z1, z2)))) → c23(S1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(s1(quote(dbl(z0)))) → c23(S1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(s1(quote(sel(z0, z1)))) → c23(S1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(s1(dbl(z0))) → c23(S1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(s1(dbls(z0))) → c23(S1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(s1(indx(z0, z1))) → c23(S1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(s1(dbl1(z0))) → c23(S1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(s1(s1(z0))) → c23(S1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(quote(z0))) → c23(S1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(s1(dbl(0))) → c23(S1(mark(0)))
ACTIVE(s1(dbls(nil))) → c23(S1(mark(nil)))
ACTIVE(s1(indx(nil, z0))) → c23(S1(mark(nil)))
ACTIVE(s1(dbl1(0))) → c23(S1(mark(01)))
ACTIVE(s1(dbl(s(z0)))) → c6(S1(mark(s(s(dbl(z0))))))
ACTIVE(s1(dbl(s(z0)))) → c6(ACTIVE(dbl(s(z0))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(S1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(S1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(s1(from(z0))) → c6(S1(mark(cons(z0, from(s(z0))))))
ACTIVE(s1(from(z0))) → c6(ACTIVE(from(z0)))
ACTIVE(s1(dbl1(s(z0)))) → c6(S1(mark(s1(s1(dbl1(z0))))))
ACTIVE(s1(dbl1(s(z0)))) → c6(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(sel(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(quote(sel(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(quote(sel1(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(quote(sel1(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(quote(quote(dbl(z0)))) → c26(QUOTE(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(quote(quote(sel(z0, z1)))) → c26(QUOTE(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(quote(dbl(z0))) → c26(QUOTE(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(quote(dbls(z0))) → c26(QUOTE(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(quote(indx(z0, z1))) → c26(QUOTE(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(quote(dbl1(z0))) → c26(QUOTE(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(quote(s1(z0))) → c26(QUOTE(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(quote(z0))) → c26(QUOTE(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(quote(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(quote(0))) → c22(DBL1(mark(01)))
ACTIVE(s1(quote(0))) → c23(S1(mark(01)))
ACTIVE(quote(dbl(0))) → c26(QUOTE(mark(0)))
ACTIVE(quote(dbls(nil))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(indx(nil, z0))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(dbl1(0))) → c26(QUOTE(mark(01)))
ACTIVE(quote(quote(0))) → c26(QUOTE(mark(01)))
ACTIVE(dbl(quote(s(z0)))) → c7(DBL(mark(s1(quote(z0)))))
ACTIVE(dbl(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(s(z0)))) → c7(DBLS(mark(s1(quote(z0)))))
ACTIVE(dbls(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(indx(quote(s(z0)), x1)) → c7(INDX(mark(s1(quote(z0))), x1))
ACTIVE(indx(quote(s(z0)), x1)) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbl1(quote(s(z0)))) → c7(DBL1(mark(s1(quote(z0)))))
ACTIVE(dbl1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(s1(quote(s(z0)))) → c7(S1(mark(s1(quote(z0)))))
ACTIVE(s1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(quote(dbl(s(z0)))) → c7(QUOTE(mark(s(s(dbl(z0))))))
ACTIVE(quote(dbl(s(z0)))) → c7(ACTIVE(dbl(s(z0))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(QUOTE(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(QUOTE(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(quote(from(z0))) → c7(QUOTE(mark(cons(z0, from(s(z0))))))
ACTIVE(quote(from(z0))) → c7(ACTIVE(from(z0)))
ACTIVE(quote(dbl1(s(z0)))) → c7(QUOTE(mark(s1(s1(dbl1(z0))))))
ACTIVE(quote(dbl1(s(z0)))) → c7(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(quote(s(z0)))) → c7(QUOTE(mark(s1(quote(z0)))))
ACTIVE(quote(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
PROPER(dbl(dbl(z0))) → c45(DBL(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbl(s(z0))) → c45(DBL(s(proper(z0))), PROPER(s(z0)))
PROPER(dbl(dbls(z0))) → c45(DBL(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbl(cons(z0, z1))) → c45(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbl(sel(z0, z1))) → c45(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbl(indx(z0, z1))) → c45(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbl(from(z0))) → c45(DBL(from(proper(z0))), PROPER(from(z0)))
PROPER(dbl(dbl1(z0))) → c45(DBL(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbl(s1(z0))) → c45(DBL(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbl(sel1(z0, z1))) → c45(DBL(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbl(quote(z0))) → c45(DBL(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbl(0)) → c45(DBL(ok(0)))
PROPER(dbl(nil)) → c45(DBL(ok(nil)))
PROPER(dbl(01)) → c45(DBL(ok(01)))
PROPER(s(dbl(z0))) → c47(S(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(s(s(z0))) → c47(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(dbls(z0))) → c47(S(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(s(cons(z0, z1))) → c47(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(sel(z0, z1))) → c47(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(s(indx(z0, z1))) → c47(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(s(from(z0))) → c47(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(dbl1(z0))) → c47(S(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(s(s1(z0))) → c47(S(s1(proper(z0))), PROPER(s1(z0)))
PROPER(s(sel1(z0, z1))) → c47(S(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(s(quote(z0))) → c47(S(quote(proper(z0))), PROPER(quote(z0)))
PROPER(s(0)) → c47(S(ok(0)))
PROPER(s(nil)) → c47(S(ok(nil)))
PROPER(s(01)) → c47(S(ok(01)))
S tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(dbls(z0)) → c48(DBLS(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c50(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(sel(z0, z1)) → c51(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(indx(z0, z1)) → c52(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c53(FROM(proper(z0)), PROPER(z0))
PROPER(dbl1(z0)) → c54(DBL1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c56(S1(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c57(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)))
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0))))))
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0))))))
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0)))
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(indx(sel1(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(indx(sel1(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel1(z0, z2)), x1), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(indx(quote(dbl(z0)), x1)) → c21(INDX(mark(dbl1(z0)), x1), ACTIVE(quote(dbl(z0))))
ACTIVE(indx(quote(sel(z0, z1)), x1)) → c21(INDX(mark(sel1(z0, z1)), x1), ACTIVE(quote(sel(z0, z1))))
ACTIVE(indx(dbl(z0), x1)) → c21(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
ACTIVE(indx(dbls(z0), x1)) → c21(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(indx(z0, z1), x1)) → c21(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1)))
ACTIVE(indx(dbl1(z0), x1)) → c21(INDX(dbl1(active(z0)), x1), ACTIVE(dbl1(z0)))
ACTIVE(indx(s1(z0), x1)) → c21(INDX(s1(active(z0)), x1), ACTIVE(s1(z0)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(active(z0), z1), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(z0, active(z1)), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(quote(z0), x1)) → c21(INDX(quote(active(z0)), x1), ACTIVE(quote(z0)))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)))
ACTIVE(indx(dbl(0), x1)) → c21(INDX(mark(0), x1))
ACTIVE(indx(dbls(nil), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(indx(indx(nil, z0), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0))))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1))
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0)))
ACTIVE(dbl1(sel(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl1(sel(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl1(sel1(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl1(sel1(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl1(quote(dbl(z0)))) → c22(DBL1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl1(quote(sel(z0, z1)))) → c22(DBL1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl1(dbl(z0))) → c22(DBL1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl1(dbls(z0))) → c22(DBL1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(indx(z0, z1))) → c22(DBL1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl1(dbl1(z0))) → c22(DBL1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl1(s1(z0))) → c22(DBL1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(quote(z0))) → c22(DBL1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(dbl1(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(dbl(0))) → c22(DBL1(mark(0)))
ACTIVE(dbl1(dbls(nil))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(indx(nil, z0))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(dbl1(0))) → c22(DBL1(mark(01)))
ACTIVE(dbl(dbl1(s(z0)))) → c4(DBL(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(DBLS(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(INDX(mark(s1(s1(dbl1(z0)))), x1))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(DBL1(mark(s(s(dbl(z0))))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(ACTIVE(dbl(s(z0))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(DBL1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(DBL1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl1(from(z0))) → c4(DBL1(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl1(from(z0))) → c4(ACTIVE(from(z0)))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(DBL1(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(s1(sel(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(s1(sel(s(z0), cons(z1, z2)))) → c23(S1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(s1(sel1(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(s1(sel1(s(z0), cons(z1, z2)))) → c23(S1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(s1(quote(dbl(z0)))) → c23(S1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(s1(quote(sel(z0, z1)))) → c23(S1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(s1(dbl(z0))) → c23(S1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(s1(dbls(z0))) → c23(S1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(s1(indx(z0, z1))) → c23(S1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(s1(dbl1(z0))) → c23(S1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(s1(s1(z0))) → c23(S1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(quote(z0))) → c23(S1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(s1(dbl(0))) → c23(S1(mark(0)))
ACTIVE(s1(dbls(nil))) → c23(S1(mark(nil)))
ACTIVE(s1(indx(nil, z0))) → c23(S1(mark(nil)))
ACTIVE(s1(dbl1(0))) → c23(S1(mark(01)))
ACTIVE(s1(dbl(s(z0)))) → c6(S1(mark(s(s(dbl(z0))))))
ACTIVE(s1(dbl(s(z0)))) → c6(ACTIVE(dbl(s(z0))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(S1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(S1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(s1(from(z0))) → c6(S1(mark(cons(z0, from(s(z0))))))
ACTIVE(s1(from(z0))) → c6(ACTIVE(from(z0)))
ACTIVE(s1(dbl1(s(z0)))) → c6(S1(mark(s1(s1(dbl1(z0))))))
ACTIVE(s1(dbl1(s(z0)))) → c6(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(sel(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(quote(sel(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(quote(sel1(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(quote(sel1(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(quote(quote(dbl(z0)))) → c26(QUOTE(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(quote(quote(sel(z0, z1)))) → c26(QUOTE(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(quote(dbl(z0))) → c26(QUOTE(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(quote(dbls(z0))) → c26(QUOTE(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(quote(indx(z0, z1))) → c26(QUOTE(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(quote(dbl1(z0))) → c26(QUOTE(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(quote(s1(z0))) → c26(QUOTE(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(quote(z0))) → c26(QUOTE(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(quote(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(quote(0))) → c22(DBL1(mark(01)))
ACTIVE(s1(quote(0))) → c23(S1(mark(01)))
ACTIVE(quote(dbl(0))) → c26(QUOTE(mark(0)))
ACTIVE(quote(dbls(nil))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(indx(nil, z0))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(dbl1(0))) → c26(QUOTE(mark(01)))
ACTIVE(quote(quote(0))) → c26(QUOTE(mark(01)))
ACTIVE(dbl(quote(s(z0)))) → c7(DBL(mark(s1(quote(z0)))))
ACTIVE(dbl(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(s(z0)))) → c7(DBLS(mark(s1(quote(z0)))))
ACTIVE(dbls(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(indx(quote(s(z0)), x1)) → c7(INDX(mark(s1(quote(z0))), x1))
ACTIVE(indx(quote(s(z0)), x1)) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbl1(quote(s(z0)))) → c7(DBL1(mark(s1(quote(z0)))))
ACTIVE(dbl1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(s1(quote(s(z0)))) → c7(S1(mark(s1(quote(z0)))))
ACTIVE(s1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(quote(dbl(s(z0)))) → c7(QUOTE(mark(s(s(dbl(z0))))))
ACTIVE(quote(dbl(s(z0)))) → c7(ACTIVE(dbl(s(z0))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(QUOTE(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(QUOTE(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(quote(from(z0))) → c7(QUOTE(mark(cons(z0, from(s(z0))))))
ACTIVE(quote(from(z0))) → c7(ACTIVE(from(z0)))
ACTIVE(quote(dbl1(s(z0)))) → c7(QUOTE(mark(s1(s1(dbl1(z0))))))
ACTIVE(quote(dbl1(s(z0)))) → c7(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(quote(s(z0)))) → c7(QUOTE(mark(s1(quote(z0)))))
ACTIVE(quote(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
PROPER(dbl(dbl(z0))) → c45(DBL(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbl(s(z0))) → c45(DBL(s(proper(z0))), PROPER(s(z0)))
PROPER(dbl(dbls(z0))) → c45(DBL(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbl(cons(z0, z1))) → c45(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbl(sel(z0, z1))) → c45(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbl(indx(z0, z1))) → c45(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbl(from(z0))) → c45(DBL(from(proper(z0))), PROPER(from(z0)))
PROPER(dbl(dbl1(z0))) → c45(DBL(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbl(s1(z0))) → c45(DBL(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbl(sel1(z0, z1))) → c45(DBL(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbl(quote(z0))) → c45(DBL(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbl(0)) → c45(DBL(ok(0)))
PROPER(dbl(nil)) → c45(DBL(ok(nil)))
PROPER(dbl(01)) → c45(DBL(ok(01)))
PROPER(s(dbl(z0))) → c47(S(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(s(s(z0))) → c47(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(dbls(z0))) → c47(S(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(s(cons(z0, z1))) → c47(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(sel(z0, z1))) → c47(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(s(indx(z0, z1))) → c47(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(s(from(z0))) → c47(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(dbl1(z0))) → c47(S(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(s(s1(z0))) → c47(S(s1(proper(z0))), PROPER(s1(z0)))
PROPER(s(sel1(z0, z1))) → c47(S(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(s(quote(z0))) → c47(S(quote(proper(z0))), PROPER(quote(z0)))
PROPER(s(0)) → c47(S(ok(0)))
PROPER(s(nil)) → c47(S(ok(nil)))
PROPER(s(01)) → c47(S(ok(01)))
K tuples:none
Defined Rule Symbols:
active, s, dbl, cons, dbls, sel, indx, s1, dbl1, sel1, quote, proper, from
Defined Pair Symbols:
ACTIVE, DBL, DBLS, SEL, INDX, DBL1, S1, SEL1, QUOTE, PROPER, S, CONS, FROM, TOP
Compound Symbols:
c5, c12, c15, c16, c19, c20, c24, c25, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c48, c50, c51, c52, c53, c54, c56, c57, c58, c59, c60, c61, c62, c63, c8, c, c17, c17, c1, c18, c18, c2, c21, c21, c3, c22, c22, c4, c23, c23, c6, c26, c26, c7, c45, c45, c47, c47
(55) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
PROPER(
dbls(
z0)) →
c48(
DBLS(
proper(
z0)),
PROPER(
z0)) by
PROPER(dbls(dbl(z0))) → c48(DBLS(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbls(0)) → c48(DBLS(ok(0)), PROPER(0))
PROPER(dbls(s(z0))) → c48(DBLS(s(proper(z0))), PROPER(s(z0)))
PROPER(dbls(dbls(z0))) → c48(DBLS(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbls(nil)) → c48(DBLS(ok(nil)), PROPER(nil))
PROPER(dbls(cons(z0, z1))) → c48(DBLS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbls(sel(z0, z1))) → c48(DBLS(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbls(indx(z0, z1))) → c48(DBLS(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbls(from(z0))) → c48(DBLS(from(proper(z0))), PROPER(from(z0)))
PROPER(dbls(dbl1(z0))) → c48(DBLS(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbls(01)) → c48(DBLS(ok(01)), PROPER(01))
PROPER(dbls(s1(z0))) → c48(DBLS(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbls(sel1(z0, z1))) → c48(DBLS(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbls(quote(z0))) → c48(DBLS(quote(proper(z0))), PROPER(quote(z0)))
(56) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(dbl(0)) → mark(0)
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
active(dbls(nil)) → mark(nil)
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1)))
active(sel(0, cons(z0, z1))) → mark(z0)
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
active(indx(nil, z0)) → mark(nil)
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2)))
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(dbl1(0)) → mark(01)
active(dbl1(s(z0))) → mark(s1(s1(dbl1(z0))))
active(sel1(0, cons(z0, z1))) → mark(z0)
active(sel1(s(z0), cons(z1, z2))) → mark(sel1(z0, z2))
active(quote(0)) → mark(01)
active(quote(s(z0))) → mark(s1(quote(z0)))
active(quote(dbl(z0))) → mark(dbl1(z0))
active(quote(sel(z0, z1))) → mark(sel1(z0, z1))
active(dbl(z0)) → dbl(active(z0))
active(dbls(z0)) → dbls(active(z0))
active(sel(z0, z1)) → sel(active(z0), z1)
active(sel(z0, z1)) → sel(z0, active(z1))
active(indx(z0, z1)) → indx(active(z0), z1)
active(dbl1(z0)) → dbl1(active(z0))
active(s1(z0)) → s1(active(z0))
active(sel1(z0, z1)) → sel1(active(z0), z1)
active(sel1(z0, z1)) → sel1(z0, active(z1))
active(quote(z0)) → quote(active(z0))
s(ok(z0)) → ok(s(z0))
dbl(mark(z0)) → mark(dbl(z0))
dbl(ok(z0)) → ok(dbl(z0))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
dbls(mark(z0)) → mark(dbls(z0))
dbls(ok(z0)) → ok(dbls(z0))
sel(mark(z0), z1) → mark(sel(z0, z1))
sel(z0, mark(z1)) → mark(sel(z0, z1))
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
indx(mark(z0), z1) → mark(indx(z0, z1))
indx(ok(z0), ok(z1)) → ok(indx(z0, z1))
s1(mark(z0)) → mark(s1(z0))
s1(ok(z0)) → ok(s1(z0))
dbl1(mark(z0)) → mark(dbl1(z0))
dbl1(ok(z0)) → ok(dbl1(z0))
sel1(mark(z0), z1) → mark(sel1(z0, z1))
sel1(z0, mark(z1)) → mark(sel1(z0, z1))
sel1(ok(z0), ok(z1)) → ok(sel1(z0, z1))
quote(mark(z0)) → mark(quote(z0))
quote(ok(z0)) → ok(quote(z0))
proper(dbl(z0)) → dbl(proper(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(dbls(z0)) → dbls(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
proper(indx(z0, z1)) → indx(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(dbl1(z0)) → dbl1(proper(z0))
proper(01) → ok(01)
proper(s1(z0)) → s1(proper(z0))
proper(sel1(z0, z1)) → sel1(proper(z0), proper(z1))
proper(quote(z0)) → quote(proper(z0))
from(ok(z0)) → ok(from(z0))
Tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(cons(z0, z1)) → c50(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(sel(z0, z1)) → c51(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(indx(z0, z1)) → c52(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c53(FROM(proper(z0)), PROPER(z0))
PROPER(dbl1(z0)) → c54(DBL1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c56(S1(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c57(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)))
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0))))))
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0))))))
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0)))
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(indx(sel1(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(indx(sel1(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel1(z0, z2)), x1), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(indx(quote(dbl(z0)), x1)) → c21(INDX(mark(dbl1(z0)), x1), ACTIVE(quote(dbl(z0))))
ACTIVE(indx(quote(sel(z0, z1)), x1)) → c21(INDX(mark(sel1(z0, z1)), x1), ACTIVE(quote(sel(z0, z1))))
ACTIVE(indx(dbl(z0), x1)) → c21(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
ACTIVE(indx(dbls(z0), x1)) → c21(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(indx(z0, z1), x1)) → c21(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1)))
ACTIVE(indx(dbl1(z0), x1)) → c21(INDX(dbl1(active(z0)), x1), ACTIVE(dbl1(z0)))
ACTIVE(indx(s1(z0), x1)) → c21(INDX(s1(active(z0)), x1), ACTIVE(s1(z0)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(active(z0), z1), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(z0, active(z1)), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(quote(z0), x1)) → c21(INDX(quote(active(z0)), x1), ACTIVE(quote(z0)))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)))
ACTIVE(indx(dbl(0), x1)) → c21(INDX(mark(0), x1))
ACTIVE(indx(dbls(nil), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(indx(indx(nil, z0), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0))))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1))
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0)))
ACTIVE(dbl1(sel(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl1(sel(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl1(sel1(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl1(sel1(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl1(quote(dbl(z0)))) → c22(DBL1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl1(quote(sel(z0, z1)))) → c22(DBL1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl1(dbl(z0))) → c22(DBL1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl1(dbls(z0))) → c22(DBL1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(indx(z0, z1))) → c22(DBL1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl1(dbl1(z0))) → c22(DBL1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl1(s1(z0))) → c22(DBL1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(quote(z0))) → c22(DBL1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(dbl1(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(dbl(0))) → c22(DBL1(mark(0)))
ACTIVE(dbl1(dbls(nil))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(indx(nil, z0))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(dbl1(0))) → c22(DBL1(mark(01)))
ACTIVE(dbl(dbl1(s(z0)))) → c4(DBL(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(DBLS(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(INDX(mark(s1(s1(dbl1(z0)))), x1))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(DBL1(mark(s(s(dbl(z0))))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(ACTIVE(dbl(s(z0))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(DBL1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(DBL1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl1(from(z0))) → c4(DBL1(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl1(from(z0))) → c4(ACTIVE(from(z0)))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(DBL1(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(s1(sel(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(s1(sel(s(z0), cons(z1, z2)))) → c23(S1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(s1(sel1(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(s1(sel1(s(z0), cons(z1, z2)))) → c23(S1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(s1(quote(dbl(z0)))) → c23(S1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(s1(quote(sel(z0, z1)))) → c23(S1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(s1(dbl(z0))) → c23(S1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(s1(dbls(z0))) → c23(S1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(s1(indx(z0, z1))) → c23(S1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(s1(dbl1(z0))) → c23(S1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(s1(s1(z0))) → c23(S1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(quote(z0))) → c23(S1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(s1(dbl(0))) → c23(S1(mark(0)))
ACTIVE(s1(dbls(nil))) → c23(S1(mark(nil)))
ACTIVE(s1(indx(nil, z0))) → c23(S1(mark(nil)))
ACTIVE(s1(dbl1(0))) → c23(S1(mark(01)))
ACTIVE(s1(dbl(s(z0)))) → c6(S1(mark(s(s(dbl(z0))))))
ACTIVE(s1(dbl(s(z0)))) → c6(ACTIVE(dbl(s(z0))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(S1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(S1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(s1(from(z0))) → c6(S1(mark(cons(z0, from(s(z0))))))
ACTIVE(s1(from(z0))) → c6(ACTIVE(from(z0)))
ACTIVE(s1(dbl1(s(z0)))) → c6(S1(mark(s1(s1(dbl1(z0))))))
ACTIVE(s1(dbl1(s(z0)))) → c6(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(sel(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(quote(sel(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(quote(sel1(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(quote(sel1(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(quote(quote(dbl(z0)))) → c26(QUOTE(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(quote(quote(sel(z0, z1)))) → c26(QUOTE(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(quote(dbl(z0))) → c26(QUOTE(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(quote(dbls(z0))) → c26(QUOTE(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(quote(indx(z0, z1))) → c26(QUOTE(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(quote(dbl1(z0))) → c26(QUOTE(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(quote(s1(z0))) → c26(QUOTE(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(quote(z0))) → c26(QUOTE(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(quote(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(quote(0))) → c22(DBL1(mark(01)))
ACTIVE(s1(quote(0))) → c23(S1(mark(01)))
ACTIVE(quote(dbl(0))) → c26(QUOTE(mark(0)))
ACTIVE(quote(dbls(nil))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(indx(nil, z0))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(dbl1(0))) → c26(QUOTE(mark(01)))
ACTIVE(quote(quote(0))) → c26(QUOTE(mark(01)))
ACTIVE(dbl(quote(s(z0)))) → c7(DBL(mark(s1(quote(z0)))))
ACTIVE(dbl(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(s(z0)))) → c7(DBLS(mark(s1(quote(z0)))))
ACTIVE(dbls(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(indx(quote(s(z0)), x1)) → c7(INDX(mark(s1(quote(z0))), x1))
ACTIVE(indx(quote(s(z0)), x1)) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbl1(quote(s(z0)))) → c7(DBL1(mark(s1(quote(z0)))))
ACTIVE(dbl1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(s1(quote(s(z0)))) → c7(S1(mark(s1(quote(z0)))))
ACTIVE(s1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(quote(dbl(s(z0)))) → c7(QUOTE(mark(s(s(dbl(z0))))))
ACTIVE(quote(dbl(s(z0)))) → c7(ACTIVE(dbl(s(z0))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(QUOTE(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(QUOTE(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(quote(from(z0))) → c7(QUOTE(mark(cons(z0, from(s(z0))))))
ACTIVE(quote(from(z0))) → c7(ACTIVE(from(z0)))
ACTIVE(quote(dbl1(s(z0)))) → c7(QUOTE(mark(s1(s1(dbl1(z0))))))
ACTIVE(quote(dbl1(s(z0)))) → c7(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(quote(s(z0)))) → c7(QUOTE(mark(s1(quote(z0)))))
ACTIVE(quote(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
PROPER(dbl(dbl(z0))) → c45(DBL(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbl(s(z0))) → c45(DBL(s(proper(z0))), PROPER(s(z0)))
PROPER(dbl(dbls(z0))) → c45(DBL(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbl(cons(z0, z1))) → c45(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbl(sel(z0, z1))) → c45(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbl(indx(z0, z1))) → c45(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbl(from(z0))) → c45(DBL(from(proper(z0))), PROPER(from(z0)))
PROPER(dbl(dbl1(z0))) → c45(DBL(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbl(s1(z0))) → c45(DBL(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbl(sel1(z0, z1))) → c45(DBL(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbl(quote(z0))) → c45(DBL(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbl(0)) → c45(DBL(ok(0)))
PROPER(dbl(nil)) → c45(DBL(ok(nil)))
PROPER(dbl(01)) → c45(DBL(ok(01)))
PROPER(s(dbl(z0))) → c47(S(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(s(s(z0))) → c47(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(dbls(z0))) → c47(S(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(s(cons(z0, z1))) → c47(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(sel(z0, z1))) → c47(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(s(indx(z0, z1))) → c47(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(s(from(z0))) → c47(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(dbl1(z0))) → c47(S(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(s(s1(z0))) → c47(S(s1(proper(z0))), PROPER(s1(z0)))
PROPER(s(sel1(z0, z1))) → c47(S(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(s(quote(z0))) → c47(S(quote(proper(z0))), PROPER(quote(z0)))
PROPER(s(0)) → c47(S(ok(0)))
PROPER(s(nil)) → c47(S(ok(nil)))
PROPER(s(01)) → c47(S(ok(01)))
PROPER(dbls(dbl(z0))) → c48(DBLS(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbls(0)) → c48(DBLS(ok(0)), PROPER(0))
PROPER(dbls(s(z0))) → c48(DBLS(s(proper(z0))), PROPER(s(z0)))
PROPER(dbls(dbls(z0))) → c48(DBLS(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbls(nil)) → c48(DBLS(ok(nil)), PROPER(nil))
PROPER(dbls(cons(z0, z1))) → c48(DBLS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbls(sel(z0, z1))) → c48(DBLS(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbls(indx(z0, z1))) → c48(DBLS(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbls(from(z0))) → c48(DBLS(from(proper(z0))), PROPER(from(z0)))
PROPER(dbls(dbl1(z0))) → c48(DBLS(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbls(01)) → c48(DBLS(ok(01)), PROPER(01))
PROPER(dbls(s1(z0))) → c48(DBLS(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbls(sel1(z0, z1))) → c48(DBLS(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbls(quote(z0))) → c48(DBLS(quote(proper(z0))), PROPER(quote(z0)))
S tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(cons(z0, z1)) → c50(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(sel(z0, z1)) → c51(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(indx(z0, z1)) → c52(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c53(FROM(proper(z0)), PROPER(z0))
PROPER(dbl1(z0)) → c54(DBL1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c56(S1(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c57(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)))
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0))))))
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0))))))
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0)))
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(indx(sel1(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(indx(sel1(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel1(z0, z2)), x1), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(indx(quote(dbl(z0)), x1)) → c21(INDX(mark(dbl1(z0)), x1), ACTIVE(quote(dbl(z0))))
ACTIVE(indx(quote(sel(z0, z1)), x1)) → c21(INDX(mark(sel1(z0, z1)), x1), ACTIVE(quote(sel(z0, z1))))
ACTIVE(indx(dbl(z0), x1)) → c21(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
ACTIVE(indx(dbls(z0), x1)) → c21(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(indx(z0, z1), x1)) → c21(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1)))
ACTIVE(indx(dbl1(z0), x1)) → c21(INDX(dbl1(active(z0)), x1), ACTIVE(dbl1(z0)))
ACTIVE(indx(s1(z0), x1)) → c21(INDX(s1(active(z0)), x1), ACTIVE(s1(z0)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(active(z0), z1), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(z0, active(z1)), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(quote(z0), x1)) → c21(INDX(quote(active(z0)), x1), ACTIVE(quote(z0)))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)))
ACTIVE(indx(dbl(0), x1)) → c21(INDX(mark(0), x1))
ACTIVE(indx(dbls(nil), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(indx(indx(nil, z0), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0))))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1))
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0)))
ACTIVE(dbl1(sel(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl1(sel(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl1(sel1(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl1(sel1(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl1(quote(dbl(z0)))) → c22(DBL1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl1(quote(sel(z0, z1)))) → c22(DBL1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl1(dbl(z0))) → c22(DBL1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl1(dbls(z0))) → c22(DBL1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(indx(z0, z1))) → c22(DBL1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl1(dbl1(z0))) → c22(DBL1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl1(s1(z0))) → c22(DBL1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(quote(z0))) → c22(DBL1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(dbl1(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(dbl(0))) → c22(DBL1(mark(0)))
ACTIVE(dbl1(dbls(nil))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(indx(nil, z0))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(dbl1(0))) → c22(DBL1(mark(01)))
ACTIVE(dbl(dbl1(s(z0)))) → c4(DBL(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(DBLS(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(INDX(mark(s1(s1(dbl1(z0)))), x1))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(DBL1(mark(s(s(dbl(z0))))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(ACTIVE(dbl(s(z0))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(DBL1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(DBL1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl1(from(z0))) → c4(DBL1(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl1(from(z0))) → c4(ACTIVE(from(z0)))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(DBL1(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(s1(sel(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(s1(sel(s(z0), cons(z1, z2)))) → c23(S1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(s1(sel1(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(s1(sel1(s(z0), cons(z1, z2)))) → c23(S1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(s1(quote(dbl(z0)))) → c23(S1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(s1(quote(sel(z0, z1)))) → c23(S1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(s1(dbl(z0))) → c23(S1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(s1(dbls(z0))) → c23(S1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(s1(indx(z0, z1))) → c23(S1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(s1(dbl1(z0))) → c23(S1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(s1(s1(z0))) → c23(S1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(quote(z0))) → c23(S1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(s1(dbl(0))) → c23(S1(mark(0)))
ACTIVE(s1(dbls(nil))) → c23(S1(mark(nil)))
ACTIVE(s1(indx(nil, z0))) → c23(S1(mark(nil)))
ACTIVE(s1(dbl1(0))) → c23(S1(mark(01)))
ACTIVE(s1(dbl(s(z0)))) → c6(S1(mark(s(s(dbl(z0))))))
ACTIVE(s1(dbl(s(z0)))) → c6(ACTIVE(dbl(s(z0))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(S1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(S1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(s1(from(z0))) → c6(S1(mark(cons(z0, from(s(z0))))))
ACTIVE(s1(from(z0))) → c6(ACTIVE(from(z0)))
ACTIVE(s1(dbl1(s(z0)))) → c6(S1(mark(s1(s1(dbl1(z0))))))
ACTIVE(s1(dbl1(s(z0)))) → c6(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(sel(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(quote(sel(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(quote(sel1(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(quote(sel1(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(quote(quote(dbl(z0)))) → c26(QUOTE(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(quote(quote(sel(z0, z1)))) → c26(QUOTE(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(quote(dbl(z0))) → c26(QUOTE(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(quote(dbls(z0))) → c26(QUOTE(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(quote(indx(z0, z1))) → c26(QUOTE(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(quote(dbl1(z0))) → c26(QUOTE(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(quote(s1(z0))) → c26(QUOTE(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(quote(z0))) → c26(QUOTE(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(quote(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(quote(0))) → c22(DBL1(mark(01)))
ACTIVE(s1(quote(0))) → c23(S1(mark(01)))
ACTIVE(quote(dbl(0))) → c26(QUOTE(mark(0)))
ACTIVE(quote(dbls(nil))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(indx(nil, z0))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(dbl1(0))) → c26(QUOTE(mark(01)))
ACTIVE(quote(quote(0))) → c26(QUOTE(mark(01)))
ACTIVE(dbl(quote(s(z0)))) → c7(DBL(mark(s1(quote(z0)))))
ACTIVE(dbl(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(s(z0)))) → c7(DBLS(mark(s1(quote(z0)))))
ACTIVE(dbls(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(indx(quote(s(z0)), x1)) → c7(INDX(mark(s1(quote(z0))), x1))
ACTIVE(indx(quote(s(z0)), x1)) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbl1(quote(s(z0)))) → c7(DBL1(mark(s1(quote(z0)))))
ACTIVE(dbl1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(s1(quote(s(z0)))) → c7(S1(mark(s1(quote(z0)))))
ACTIVE(s1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(quote(dbl(s(z0)))) → c7(QUOTE(mark(s(s(dbl(z0))))))
ACTIVE(quote(dbl(s(z0)))) → c7(ACTIVE(dbl(s(z0))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(QUOTE(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(QUOTE(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(quote(from(z0))) → c7(QUOTE(mark(cons(z0, from(s(z0))))))
ACTIVE(quote(from(z0))) → c7(ACTIVE(from(z0)))
ACTIVE(quote(dbl1(s(z0)))) → c7(QUOTE(mark(s1(s1(dbl1(z0))))))
ACTIVE(quote(dbl1(s(z0)))) → c7(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(quote(s(z0)))) → c7(QUOTE(mark(s1(quote(z0)))))
ACTIVE(quote(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
PROPER(dbl(dbl(z0))) → c45(DBL(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbl(s(z0))) → c45(DBL(s(proper(z0))), PROPER(s(z0)))
PROPER(dbl(dbls(z0))) → c45(DBL(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbl(cons(z0, z1))) → c45(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbl(sel(z0, z1))) → c45(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbl(indx(z0, z1))) → c45(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbl(from(z0))) → c45(DBL(from(proper(z0))), PROPER(from(z0)))
PROPER(dbl(dbl1(z0))) → c45(DBL(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbl(s1(z0))) → c45(DBL(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbl(sel1(z0, z1))) → c45(DBL(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbl(quote(z0))) → c45(DBL(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbl(0)) → c45(DBL(ok(0)))
PROPER(dbl(nil)) → c45(DBL(ok(nil)))
PROPER(dbl(01)) → c45(DBL(ok(01)))
PROPER(s(dbl(z0))) → c47(S(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(s(s(z0))) → c47(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(dbls(z0))) → c47(S(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(s(cons(z0, z1))) → c47(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(sel(z0, z1))) → c47(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(s(indx(z0, z1))) → c47(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(s(from(z0))) → c47(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(dbl1(z0))) → c47(S(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(s(s1(z0))) → c47(S(s1(proper(z0))), PROPER(s1(z0)))
PROPER(s(sel1(z0, z1))) → c47(S(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(s(quote(z0))) → c47(S(quote(proper(z0))), PROPER(quote(z0)))
PROPER(s(0)) → c47(S(ok(0)))
PROPER(s(nil)) → c47(S(ok(nil)))
PROPER(s(01)) → c47(S(ok(01)))
PROPER(dbls(dbl(z0))) → c48(DBLS(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbls(0)) → c48(DBLS(ok(0)), PROPER(0))
PROPER(dbls(s(z0))) → c48(DBLS(s(proper(z0))), PROPER(s(z0)))
PROPER(dbls(dbls(z0))) → c48(DBLS(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbls(nil)) → c48(DBLS(ok(nil)), PROPER(nil))
PROPER(dbls(cons(z0, z1))) → c48(DBLS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbls(sel(z0, z1))) → c48(DBLS(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbls(indx(z0, z1))) → c48(DBLS(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbls(from(z0))) → c48(DBLS(from(proper(z0))), PROPER(from(z0)))
PROPER(dbls(dbl1(z0))) → c48(DBLS(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbls(01)) → c48(DBLS(ok(01)), PROPER(01))
PROPER(dbls(s1(z0))) → c48(DBLS(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbls(sel1(z0, z1))) → c48(DBLS(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbls(quote(z0))) → c48(DBLS(quote(proper(z0))), PROPER(quote(z0)))
K tuples:none
Defined Rule Symbols:
active, s, dbl, cons, dbls, sel, indx, s1, dbl1, sel1, quote, proper, from
Defined Pair Symbols:
ACTIVE, DBL, DBLS, SEL, INDX, DBL1, S1, SEL1, QUOTE, PROPER, S, CONS, FROM, TOP
Compound Symbols:
c5, c12, c15, c16, c19, c20, c24, c25, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c50, c51, c52, c53, c54, c56, c57, c58, c59, c60, c61, c62, c63, c8, c, c17, c17, c1, c18, c18, c2, c21, c21, c3, c22, c22, c4, c23, c23, c6, c26, c26, c7, c45, c45, c47, c47, c48
(57) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 3 trailing tuple parts
(58) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(dbl(0)) → mark(0)
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
active(dbls(nil)) → mark(nil)
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1)))
active(sel(0, cons(z0, z1))) → mark(z0)
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
active(indx(nil, z0)) → mark(nil)
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2)))
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(dbl1(0)) → mark(01)
active(dbl1(s(z0))) → mark(s1(s1(dbl1(z0))))
active(sel1(0, cons(z0, z1))) → mark(z0)
active(sel1(s(z0), cons(z1, z2))) → mark(sel1(z0, z2))
active(quote(0)) → mark(01)
active(quote(s(z0))) → mark(s1(quote(z0)))
active(quote(dbl(z0))) → mark(dbl1(z0))
active(quote(sel(z0, z1))) → mark(sel1(z0, z1))
active(dbl(z0)) → dbl(active(z0))
active(dbls(z0)) → dbls(active(z0))
active(sel(z0, z1)) → sel(active(z0), z1)
active(sel(z0, z1)) → sel(z0, active(z1))
active(indx(z0, z1)) → indx(active(z0), z1)
active(dbl1(z0)) → dbl1(active(z0))
active(s1(z0)) → s1(active(z0))
active(sel1(z0, z1)) → sel1(active(z0), z1)
active(sel1(z0, z1)) → sel1(z0, active(z1))
active(quote(z0)) → quote(active(z0))
s(ok(z0)) → ok(s(z0))
dbl(mark(z0)) → mark(dbl(z0))
dbl(ok(z0)) → ok(dbl(z0))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
dbls(mark(z0)) → mark(dbls(z0))
dbls(ok(z0)) → ok(dbls(z0))
sel(mark(z0), z1) → mark(sel(z0, z1))
sel(z0, mark(z1)) → mark(sel(z0, z1))
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
indx(mark(z0), z1) → mark(indx(z0, z1))
indx(ok(z0), ok(z1)) → ok(indx(z0, z1))
s1(mark(z0)) → mark(s1(z0))
s1(ok(z0)) → ok(s1(z0))
dbl1(mark(z0)) → mark(dbl1(z0))
dbl1(ok(z0)) → ok(dbl1(z0))
sel1(mark(z0), z1) → mark(sel1(z0, z1))
sel1(z0, mark(z1)) → mark(sel1(z0, z1))
sel1(ok(z0), ok(z1)) → ok(sel1(z0, z1))
quote(mark(z0)) → mark(quote(z0))
quote(ok(z0)) → ok(quote(z0))
proper(dbl(z0)) → dbl(proper(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(dbls(z0)) → dbls(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
proper(indx(z0, z1)) → indx(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(dbl1(z0)) → dbl1(proper(z0))
proper(01) → ok(01)
proper(s1(z0)) → s1(proper(z0))
proper(sel1(z0, z1)) → sel1(proper(z0), proper(z1))
proper(quote(z0)) → quote(proper(z0))
from(ok(z0)) → ok(from(z0))
Tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(cons(z0, z1)) → c50(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(sel(z0, z1)) → c51(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(indx(z0, z1)) → c52(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c53(FROM(proper(z0)), PROPER(z0))
PROPER(dbl1(z0)) → c54(DBL1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c56(S1(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c57(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)))
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0))))))
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0))))))
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0)))
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(indx(sel1(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(indx(sel1(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel1(z0, z2)), x1), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(indx(quote(dbl(z0)), x1)) → c21(INDX(mark(dbl1(z0)), x1), ACTIVE(quote(dbl(z0))))
ACTIVE(indx(quote(sel(z0, z1)), x1)) → c21(INDX(mark(sel1(z0, z1)), x1), ACTIVE(quote(sel(z0, z1))))
ACTIVE(indx(dbl(z0), x1)) → c21(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
ACTIVE(indx(dbls(z0), x1)) → c21(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(indx(z0, z1), x1)) → c21(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1)))
ACTIVE(indx(dbl1(z0), x1)) → c21(INDX(dbl1(active(z0)), x1), ACTIVE(dbl1(z0)))
ACTIVE(indx(s1(z0), x1)) → c21(INDX(s1(active(z0)), x1), ACTIVE(s1(z0)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(active(z0), z1), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(z0, active(z1)), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(quote(z0), x1)) → c21(INDX(quote(active(z0)), x1), ACTIVE(quote(z0)))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)))
ACTIVE(indx(dbl(0), x1)) → c21(INDX(mark(0), x1))
ACTIVE(indx(dbls(nil), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(indx(indx(nil, z0), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0))))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1))
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0)))
ACTIVE(dbl1(sel(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl1(sel(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl1(sel1(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl1(sel1(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl1(quote(dbl(z0)))) → c22(DBL1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl1(quote(sel(z0, z1)))) → c22(DBL1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl1(dbl(z0))) → c22(DBL1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl1(dbls(z0))) → c22(DBL1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(indx(z0, z1))) → c22(DBL1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl1(dbl1(z0))) → c22(DBL1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl1(s1(z0))) → c22(DBL1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(quote(z0))) → c22(DBL1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(dbl1(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(dbl(0))) → c22(DBL1(mark(0)))
ACTIVE(dbl1(dbls(nil))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(indx(nil, z0))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(dbl1(0))) → c22(DBL1(mark(01)))
ACTIVE(dbl(dbl1(s(z0)))) → c4(DBL(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(DBLS(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(INDX(mark(s1(s1(dbl1(z0)))), x1))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(DBL1(mark(s(s(dbl(z0))))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(ACTIVE(dbl(s(z0))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(DBL1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(DBL1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl1(from(z0))) → c4(DBL1(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl1(from(z0))) → c4(ACTIVE(from(z0)))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(DBL1(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(s1(sel(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(s1(sel(s(z0), cons(z1, z2)))) → c23(S1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(s1(sel1(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(s1(sel1(s(z0), cons(z1, z2)))) → c23(S1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(s1(quote(dbl(z0)))) → c23(S1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(s1(quote(sel(z0, z1)))) → c23(S1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(s1(dbl(z0))) → c23(S1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(s1(dbls(z0))) → c23(S1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(s1(indx(z0, z1))) → c23(S1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(s1(dbl1(z0))) → c23(S1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(s1(s1(z0))) → c23(S1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(quote(z0))) → c23(S1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(s1(dbl(0))) → c23(S1(mark(0)))
ACTIVE(s1(dbls(nil))) → c23(S1(mark(nil)))
ACTIVE(s1(indx(nil, z0))) → c23(S1(mark(nil)))
ACTIVE(s1(dbl1(0))) → c23(S1(mark(01)))
ACTIVE(s1(dbl(s(z0)))) → c6(S1(mark(s(s(dbl(z0))))))
ACTIVE(s1(dbl(s(z0)))) → c6(ACTIVE(dbl(s(z0))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(S1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(S1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(s1(from(z0))) → c6(S1(mark(cons(z0, from(s(z0))))))
ACTIVE(s1(from(z0))) → c6(ACTIVE(from(z0)))
ACTIVE(s1(dbl1(s(z0)))) → c6(S1(mark(s1(s1(dbl1(z0))))))
ACTIVE(s1(dbl1(s(z0)))) → c6(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(sel(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(quote(sel(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(quote(sel1(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(quote(sel1(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(quote(quote(dbl(z0)))) → c26(QUOTE(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(quote(quote(sel(z0, z1)))) → c26(QUOTE(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(quote(dbl(z0))) → c26(QUOTE(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(quote(dbls(z0))) → c26(QUOTE(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(quote(indx(z0, z1))) → c26(QUOTE(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(quote(dbl1(z0))) → c26(QUOTE(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(quote(s1(z0))) → c26(QUOTE(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(quote(z0))) → c26(QUOTE(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(quote(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(quote(0))) → c22(DBL1(mark(01)))
ACTIVE(s1(quote(0))) → c23(S1(mark(01)))
ACTIVE(quote(dbl(0))) → c26(QUOTE(mark(0)))
ACTIVE(quote(dbls(nil))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(indx(nil, z0))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(dbl1(0))) → c26(QUOTE(mark(01)))
ACTIVE(quote(quote(0))) → c26(QUOTE(mark(01)))
ACTIVE(dbl(quote(s(z0)))) → c7(DBL(mark(s1(quote(z0)))))
ACTIVE(dbl(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(s(z0)))) → c7(DBLS(mark(s1(quote(z0)))))
ACTIVE(dbls(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(indx(quote(s(z0)), x1)) → c7(INDX(mark(s1(quote(z0))), x1))
ACTIVE(indx(quote(s(z0)), x1)) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbl1(quote(s(z0)))) → c7(DBL1(mark(s1(quote(z0)))))
ACTIVE(dbl1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(s1(quote(s(z0)))) → c7(S1(mark(s1(quote(z0)))))
ACTIVE(s1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(quote(dbl(s(z0)))) → c7(QUOTE(mark(s(s(dbl(z0))))))
ACTIVE(quote(dbl(s(z0)))) → c7(ACTIVE(dbl(s(z0))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(QUOTE(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(QUOTE(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(quote(from(z0))) → c7(QUOTE(mark(cons(z0, from(s(z0))))))
ACTIVE(quote(from(z0))) → c7(ACTIVE(from(z0)))
ACTIVE(quote(dbl1(s(z0)))) → c7(QUOTE(mark(s1(s1(dbl1(z0))))))
ACTIVE(quote(dbl1(s(z0)))) → c7(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(quote(s(z0)))) → c7(QUOTE(mark(s1(quote(z0)))))
ACTIVE(quote(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
PROPER(dbl(dbl(z0))) → c45(DBL(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbl(s(z0))) → c45(DBL(s(proper(z0))), PROPER(s(z0)))
PROPER(dbl(dbls(z0))) → c45(DBL(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbl(cons(z0, z1))) → c45(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbl(sel(z0, z1))) → c45(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbl(indx(z0, z1))) → c45(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbl(from(z0))) → c45(DBL(from(proper(z0))), PROPER(from(z0)))
PROPER(dbl(dbl1(z0))) → c45(DBL(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbl(s1(z0))) → c45(DBL(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbl(sel1(z0, z1))) → c45(DBL(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbl(quote(z0))) → c45(DBL(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbl(0)) → c45(DBL(ok(0)))
PROPER(dbl(nil)) → c45(DBL(ok(nil)))
PROPER(dbl(01)) → c45(DBL(ok(01)))
PROPER(s(dbl(z0))) → c47(S(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(s(s(z0))) → c47(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(dbls(z0))) → c47(S(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(s(cons(z0, z1))) → c47(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(sel(z0, z1))) → c47(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(s(indx(z0, z1))) → c47(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(s(from(z0))) → c47(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(dbl1(z0))) → c47(S(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(s(s1(z0))) → c47(S(s1(proper(z0))), PROPER(s1(z0)))
PROPER(s(sel1(z0, z1))) → c47(S(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(s(quote(z0))) → c47(S(quote(proper(z0))), PROPER(quote(z0)))
PROPER(s(0)) → c47(S(ok(0)))
PROPER(s(nil)) → c47(S(ok(nil)))
PROPER(s(01)) → c47(S(ok(01)))
PROPER(dbls(dbl(z0))) → c48(DBLS(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbls(s(z0))) → c48(DBLS(s(proper(z0))), PROPER(s(z0)))
PROPER(dbls(dbls(z0))) → c48(DBLS(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbls(cons(z0, z1))) → c48(DBLS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbls(sel(z0, z1))) → c48(DBLS(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbls(indx(z0, z1))) → c48(DBLS(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbls(from(z0))) → c48(DBLS(from(proper(z0))), PROPER(from(z0)))
PROPER(dbls(dbl1(z0))) → c48(DBLS(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbls(s1(z0))) → c48(DBLS(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbls(sel1(z0, z1))) → c48(DBLS(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbls(quote(z0))) → c48(DBLS(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbls(0)) → c48(DBLS(ok(0)))
PROPER(dbls(nil)) → c48(DBLS(ok(nil)))
PROPER(dbls(01)) → c48(DBLS(ok(01)))
S tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(cons(z0, z1)) → c50(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(sel(z0, z1)) → c51(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(indx(z0, z1)) → c52(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c53(FROM(proper(z0)), PROPER(z0))
PROPER(dbl1(z0)) → c54(DBL1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c56(S1(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c57(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)))
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0))))))
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0))))))
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0)))
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(indx(sel1(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(indx(sel1(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel1(z0, z2)), x1), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(indx(quote(dbl(z0)), x1)) → c21(INDX(mark(dbl1(z0)), x1), ACTIVE(quote(dbl(z0))))
ACTIVE(indx(quote(sel(z0, z1)), x1)) → c21(INDX(mark(sel1(z0, z1)), x1), ACTIVE(quote(sel(z0, z1))))
ACTIVE(indx(dbl(z0), x1)) → c21(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
ACTIVE(indx(dbls(z0), x1)) → c21(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(indx(z0, z1), x1)) → c21(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1)))
ACTIVE(indx(dbl1(z0), x1)) → c21(INDX(dbl1(active(z0)), x1), ACTIVE(dbl1(z0)))
ACTIVE(indx(s1(z0), x1)) → c21(INDX(s1(active(z0)), x1), ACTIVE(s1(z0)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(active(z0), z1), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(z0, active(z1)), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(quote(z0), x1)) → c21(INDX(quote(active(z0)), x1), ACTIVE(quote(z0)))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)))
ACTIVE(indx(dbl(0), x1)) → c21(INDX(mark(0), x1))
ACTIVE(indx(dbls(nil), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(indx(indx(nil, z0), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0))))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1))
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0)))
ACTIVE(dbl1(sel(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl1(sel(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl1(sel1(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl1(sel1(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl1(quote(dbl(z0)))) → c22(DBL1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl1(quote(sel(z0, z1)))) → c22(DBL1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl1(dbl(z0))) → c22(DBL1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl1(dbls(z0))) → c22(DBL1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(indx(z0, z1))) → c22(DBL1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl1(dbl1(z0))) → c22(DBL1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl1(s1(z0))) → c22(DBL1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(quote(z0))) → c22(DBL1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(dbl1(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(dbl(0))) → c22(DBL1(mark(0)))
ACTIVE(dbl1(dbls(nil))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(indx(nil, z0))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(dbl1(0))) → c22(DBL1(mark(01)))
ACTIVE(dbl(dbl1(s(z0)))) → c4(DBL(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(DBLS(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(INDX(mark(s1(s1(dbl1(z0)))), x1))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(DBL1(mark(s(s(dbl(z0))))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(ACTIVE(dbl(s(z0))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(DBL1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(DBL1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl1(from(z0))) → c4(DBL1(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl1(from(z0))) → c4(ACTIVE(from(z0)))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(DBL1(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(s1(sel(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(s1(sel(s(z0), cons(z1, z2)))) → c23(S1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(s1(sel1(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(s1(sel1(s(z0), cons(z1, z2)))) → c23(S1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(s1(quote(dbl(z0)))) → c23(S1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(s1(quote(sel(z0, z1)))) → c23(S1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(s1(dbl(z0))) → c23(S1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(s1(dbls(z0))) → c23(S1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(s1(indx(z0, z1))) → c23(S1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(s1(dbl1(z0))) → c23(S1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(s1(s1(z0))) → c23(S1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(quote(z0))) → c23(S1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(s1(dbl(0))) → c23(S1(mark(0)))
ACTIVE(s1(dbls(nil))) → c23(S1(mark(nil)))
ACTIVE(s1(indx(nil, z0))) → c23(S1(mark(nil)))
ACTIVE(s1(dbl1(0))) → c23(S1(mark(01)))
ACTIVE(s1(dbl(s(z0)))) → c6(S1(mark(s(s(dbl(z0))))))
ACTIVE(s1(dbl(s(z0)))) → c6(ACTIVE(dbl(s(z0))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(S1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(S1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(s1(from(z0))) → c6(S1(mark(cons(z0, from(s(z0))))))
ACTIVE(s1(from(z0))) → c6(ACTIVE(from(z0)))
ACTIVE(s1(dbl1(s(z0)))) → c6(S1(mark(s1(s1(dbl1(z0))))))
ACTIVE(s1(dbl1(s(z0)))) → c6(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(sel(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(quote(sel(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(quote(sel1(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(quote(sel1(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(quote(quote(dbl(z0)))) → c26(QUOTE(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(quote(quote(sel(z0, z1)))) → c26(QUOTE(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(quote(dbl(z0))) → c26(QUOTE(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(quote(dbls(z0))) → c26(QUOTE(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(quote(indx(z0, z1))) → c26(QUOTE(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(quote(dbl1(z0))) → c26(QUOTE(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(quote(s1(z0))) → c26(QUOTE(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(quote(z0))) → c26(QUOTE(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(quote(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(quote(0))) → c22(DBL1(mark(01)))
ACTIVE(s1(quote(0))) → c23(S1(mark(01)))
ACTIVE(quote(dbl(0))) → c26(QUOTE(mark(0)))
ACTIVE(quote(dbls(nil))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(indx(nil, z0))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(dbl1(0))) → c26(QUOTE(mark(01)))
ACTIVE(quote(quote(0))) → c26(QUOTE(mark(01)))
ACTIVE(dbl(quote(s(z0)))) → c7(DBL(mark(s1(quote(z0)))))
ACTIVE(dbl(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(s(z0)))) → c7(DBLS(mark(s1(quote(z0)))))
ACTIVE(dbls(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(indx(quote(s(z0)), x1)) → c7(INDX(mark(s1(quote(z0))), x1))
ACTIVE(indx(quote(s(z0)), x1)) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbl1(quote(s(z0)))) → c7(DBL1(mark(s1(quote(z0)))))
ACTIVE(dbl1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(s1(quote(s(z0)))) → c7(S1(mark(s1(quote(z0)))))
ACTIVE(s1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(quote(dbl(s(z0)))) → c7(QUOTE(mark(s(s(dbl(z0))))))
ACTIVE(quote(dbl(s(z0)))) → c7(ACTIVE(dbl(s(z0))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(QUOTE(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(QUOTE(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(quote(from(z0))) → c7(QUOTE(mark(cons(z0, from(s(z0))))))
ACTIVE(quote(from(z0))) → c7(ACTIVE(from(z0)))
ACTIVE(quote(dbl1(s(z0)))) → c7(QUOTE(mark(s1(s1(dbl1(z0))))))
ACTIVE(quote(dbl1(s(z0)))) → c7(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(quote(s(z0)))) → c7(QUOTE(mark(s1(quote(z0)))))
ACTIVE(quote(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
PROPER(dbl(dbl(z0))) → c45(DBL(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbl(s(z0))) → c45(DBL(s(proper(z0))), PROPER(s(z0)))
PROPER(dbl(dbls(z0))) → c45(DBL(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbl(cons(z0, z1))) → c45(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbl(sel(z0, z1))) → c45(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbl(indx(z0, z1))) → c45(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbl(from(z0))) → c45(DBL(from(proper(z0))), PROPER(from(z0)))
PROPER(dbl(dbl1(z0))) → c45(DBL(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbl(s1(z0))) → c45(DBL(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbl(sel1(z0, z1))) → c45(DBL(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbl(quote(z0))) → c45(DBL(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbl(0)) → c45(DBL(ok(0)))
PROPER(dbl(nil)) → c45(DBL(ok(nil)))
PROPER(dbl(01)) → c45(DBL(ok(01)))
PROPER(s(dbl(z0))) → c47(S(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(s(s(z0))) → c47(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(dbls(z0))) → c47(S(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(s(cons(z0, z1))) → c47(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(sel(z0, z1))) → c47(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(s(indx(z0, z1))) → c47(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(s(from(z0))) → c47(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(dbl1(z0))) → c47(S(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(s(s1(z0))) → c47(S(s1(proper(z0))), PROPER(s1(z0)))
PROPER(s(sel1(z0, z1))) → c47(S(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(s(quote(z0))) → c47(S(quote(proper(z0))), PROPER(quote(z0)))
PROPER(s(0)) → c47(S(ok(0)))
PROPER(s(nil)) → c47(S(ok(nil)))
PROPER(s(01)) → c47(S(ok(01)))
PROPER(dbls(dbl(z0))) → c48(DBLS(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbls(s(z0))) → c48(DBLS(s(proper(z0))), PROPER(s(z0)))
PROPER(dbls(dbls(z0))) → c48(DBLS(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbls(cons(z0, z1))) → c48(DBLS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbls(sel(z0, z1))) → c48(DBLS(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbls(indx(z0, z1))) → c48(DBLS(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbls(from(z0))) → c48(DBLS(from(proper(z0))), PROPER(from(z0)))
PROPER(dbls(dbl1(z0))) → c48(DBLS(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbls(s1(z0))) → c48(DBLS(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbls(sel1(z0, z1))) → c48(DBLS(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbls(quote(z0))) → c48(DBLS(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbls(0)) → c48(DBLS(ok(0)))
PROPER(dbls(nil)) → c48(DBLS(ok(nil)))
PROPER(dbls(01)) → c48(DBLS(ok(01)))
K tuples:none
Defined Rule Symbols:
active, s, dbl, cons, dbls, sel, indx, s1, dbl1, sel1, quote, proper, from
Defined Pair Symbols:
ACTIVE, DBL, DBLS, SEL, INDX, DBL1, S1, SEL1, QUOTE, PROPER, S, CONS, FROM, TOP
Compound Symbols:
c5, c12, c15, c16, c19, c20, c24, c25, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c50, c51, c52, c53, c54, c56, c57, c58, c59, c60, c61, c62, c63, c8, c, c17, c17, c1, c18, c18, c2, c21, c21, c3, c22, c22, c4, c23, c23, c6, c26, c26, c7, c45, c45, c47, c47, c48, c48
(59) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
PROPER(
cons(
z0,
z1)) →
c50(
CONS(
proper(
z0),
proper(
z1)),
PROPER(
z0),
PROPER(
z1)) by
PROPER(cons(x0, dbl(z0))) → c50(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(cons(x0, 0)) → c50(CONS(proper(x0), ok(0)), PROPER(x0), PROPER(0))
PROPER(cons(x0, s(z0))) → c50(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, dbls(z0))) → c50(CONS(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(cons(x0, nil)) → c50(CONS(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
PROPER(cons(x0, cons(z0, z1))) → c50(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, sel(z0, z1))) → c50(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(cons(x0, indx(z0, z1))) → c50(CONS(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(cons(x0, from(z0))) → c50(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, dbl1(z0))) → c50(CONS(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(cons(x0, 01)) → c50(CONS(proper(x0), ok(01)), PROPER(x0), PROPER(01))
PROPER(cons(x0, s1(z0))) → c50(CONS(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(cons(x0, sel1(z0, z1))) → c50(CONS(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(cons(x0, quote(z0))) → c50(CONS(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(cons(dbl(z0), x1)) → c50(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(cons(0, x1)) → c50(CONS(ok(0), proper(x1)), PROPER(0), PROPER(x1))
PROPER(cons(s(z0), x1)) → c50(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(dbls(z0), x1)) → c50(CONS(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(cons(nil, x1)) → c50(CONS(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c50(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(sel(z0, z1), x1)) → c50(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(cons(indx(z0, z1), x1)) → c50(CONS(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c50(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(dbl1(z0), x1)) → c50(CONS(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(cons(01, x1)) → c50(CONS(ok(01), proper(x1)), PROPER(01), PROPER(x1))
PROPER(cons(s1(z0), x1)) → c50(CONS(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(cons(sel1(z0, z1), x1)) → c50(CONS(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(cons(quote(z0), x1)) → c50(CONS(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
(60) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(dbl(0)) → mark(0)
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
active(dbls(nil)) → mark(nil)
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1)))
active(sel(0, cons(z0, z1))) → mark(z0)
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
active(indx(nil, z0)) → mark(nil)
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2)))
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(dbl1(0)) → mark(01)
active(dbl1(s(z0))) → mark(s1(s1(dbl1(z0))))
active(sel1(0, cons(z0, z1))) → mark(z0)
active(sel1(s(z0), cons(z1, z2))) → mark(sel1(z0, z2))
active(quote(0)) → mark(01)
active(quote(s(z0))) → mark(s1(quote(z0)))
active(quote(dbl(z0))) → mark(dbl1(z0))
active(quote(sel(z0, z1))) → mark(sel1(z0, z1))
active(dbl(z0)) → dbl(active(z0))
active(dbls(z0)) → dbls(active(z0))
active(sel(z0, z1)) → sel(active(z0), z1)
active(sel(z0, z1)) → sel(z0, active(z1))
active(indx(z0, z1)) → indx(active(z0), z1)
active(dbl1(z0)) → dbl1(active(z0))
active(s1(z0)) → s1(active(z0))
active(sel1(z0, z1)) → sel1(active(z0), z1)
active(sel1(z0, z1)) → sel1(z0, active(z1))
active(quote(z0)) → quote(active(z0))
s(ok(z0)) → ok(s(z0))
dbl(mark(z0)) → mark(dbl(z0))
dbl(ok(z0)) → ok(dbl(z0))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
dbls(mark(z0)) → mark(dbls(z0))
dbls(ok(z0)) → ok(dbls(z0))
sel(mark(z0), z1) → mark(sel(z0, z1))
sel(z0, mark(z1)) → mark(sel(z0, z1))
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
indx(mark(z0), z1) → mark(indx(z0, z1))
indx(ok(z0), ok(z1)) → ok(indx(z0, z1))
s1(mark(z0)) → mark(s1(z0))
s1(ok(z0)) → ok(s1(z0))
dbl1(mark(z0)) → mark(dbl1(z0))
dbl1(ok(z0)) → ok(dbl1(z0))
sel1(mark(z0), z1) → mark(sel1(z0, z1))
sel1(z0, mark(z1)) → mark(sel1(z0, z1))
sel1(ok(z0), ok(z1)) → ok(sel1(z0, z1))
quote(mark(z0)) → mark(quote(z0))
quote(ok(z0)) → ok(quote(z0))
proper(dbl(z0)) → dbl(proper(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(dbls(z0)) → dbls(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
proper(indx(z0, z1)) → indx(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(dbl1(z0)) → dbl1(proper(z0))
proper(01) → ok(01)
proper(s1(z0)) → s1(proper(z0))
proper(sel1(z0, z1)) → sel1(proper(z0), proper(z1))
proper(quote(z0)) → quote(proper(z0))
from(ok(z0)) → ok(from(z0))
Tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(sel(z0, z1)) → c51(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(indx(z0, z1)) → c52(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c53(FROM(proper(z0)), PROPER(z0))
PROPER(dbl1(z0)) → c54(DBL1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c56(S1(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c57(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)))
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0))))))
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0))))))
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0)))
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(indx(sel1(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(indx(sel1(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel1(z0, z2)), x1), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(indx(quote(dbl(z0)), x1)) → c21(INDX(mark(dbl1(z0)), x1), ACTIVE(quote(dbl(z0))))
ACTIVE(indx(quote(sel(z0, z1)), x1)) → c21(INDX(mark(sel1(z0, z1)), x1), ACTIVE(quote(sel(z0, z1))))
ACTIVE(indx(dbl(z0), x1)) → c21(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
ACTIVE(indx(dbls(z0), x1)) → c21(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(indx(z0, z1), x1)) → c21(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1)))
ACTIVE(indx(dbl1(z0), x1)) → c21(INDX(dbl1(active(z0)), x1), ACTIVE(dbl1(z0)))
ACTIVE(indx(s1(z0), x1)) → c21(INDX(s1(active(z0)), x1), ACTIVE(s1(z0)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(active(z0), z1), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(z0, active(z1)), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(quote(z0), x1)) → c21(INDX(quote(active(z0)), x1), ACTIVE(quote(z0)))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)))
ACTIVE(indx(dbl(0), x1)) → c21(INDX(mark(0), x1))
ACTIVE(indx(dbls(nil), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(indx(indx(nil, z0), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0))))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1))
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0)))
ACTIVE(dbl1(sel(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl1(sel(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl1(sel1(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl1(sel1(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl1(quote(dbl(z0)))) → c22(DBL1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl1(quote(sel(z0, z1)))) → c22(DBL1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl1(dbl(z0))) → c22(DBL1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl1(dbls(z0))) → c22(DBL1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(indx(z0, z1))) → c22(DBL1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl1(dbl1(z0))) → c22(DBL1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl1(s1(z0))) → c22(DBL1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(quote(z0))) → c22(DBL1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(dbl1(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(dbl(0))) → c22(DBL1(mark(0)))
ACTIVE(dbl1(dbls(nil))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(indx(nil, z0))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(dbl1(0))) → c22(DBL1(mark(01)))
ACTIVE(dbl(dbl1(s(z0)))) → c4(DBL(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(DBLS(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(INDX(mark(s1(s1(dbl1(z0)))), x1))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(DBL1(mark(s(s(dbl(z0))))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(ACTIVE(dbl(s(z0))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(DBL1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(DBL1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl1(from(z0))) → c4(DBL1(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl1(from(z0))) → c4(ACTIVE(from(z0)))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(DBL1(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(s1(sel(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(s1(sel(s(z0), cons(z1, z2)))) → c23(S1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(s1(sel1(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(s1(sel1(s(z0), cons(z1, z2)))) → c23(S1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(s1(quote(dbl(z0)))) → c23(S1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(s1(quote(sel(z0, z1)))) → c23(S1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(s1(dbl(z0))) → c23(S1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(s1(dbls(z0))) → c23(S1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(s1(indx(z0, z1))) → c23(S1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(s1(dbl1(z0))) → c23(S1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(s1(s1(z0))) → c23(S1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(quote(z0))) → c23(S1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(s1(dbl(0))) → c23(S1(mark(0)))
ACTIVE(s1(dbls(nil))) → c23(S1(mark(nil)))
ACTIVE(s1(indx(nil, z0))) → c23(S1(mark(nil)))
ACTIVE(s1(dbl1(0))) → c23(S1(mark(01)))
ACTIVE(s1(dbl(s(z0)))) → c6(S1(mark(s(s(dbl(z0))))))
ACTIVE(s1(dbl(s(z0)))) → c6(ACTIVE(dbl(s(z0))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(S1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(S1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(s1(from(z0))) → c6(S1(mark(cons(z0, from(s(z0))))))
ACTIVE(s1(from(z0))) → c6(ACTIVE(from(z0)))
ACTIVE(s1(dbl1(s(z0)))) → c6(S1(mark(s1(s1(dbl1(z0))))))
ACTIVE(s1(dbl1(s(z0)))) → c6(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(sel(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(quote(sel(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(quote(sel1(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(quote(sel1(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(quote(quote(dbl(z0)))) → c26(QUOTE(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(quote(quote(sel(z0, z1)))) → c26(QUOTE(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(quote(dbl(z0))) → c26(QUOTE(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(quote(dbls(z0))) → c26(QUOTE(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(quote(indx(z0, z1))) → c26(QUOTE(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(quote(dbl1(z0))) → c26(QUOTE(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(quote(s1(z0))) → c26(QUOTE(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(quote(z0))) → c26(QUOTE(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(quote(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(quote(0))) → c22(DBL1(mark(01)))
ACTIVE(s1(quote(0))) → c23(S1(mark(01)))
ACTIVE(quote(dbl(0))) → c26(QUOTE(mark(0)))
ACTIVE(quote(dbls(nil))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(indx(nil, z0))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(dbl1(0))) → c26(QUOTE(mark(01)))
ACTIVE(quote(quote(0))) → c26(QUOTE(mark(01)))
ACTIVE(dbl(quote(s(z0)))) → c7(DBL(mark(s1(quote(z0)))))
ACTIVE(dbl(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(s(z0)))) → c7(DBLS(mark(s1(quote(z0)))))
ACTIVE(dbls(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(indx(quote(s(z0)), x1)) → c7(INDX(mark(s1(quote(z0))), x1))
ACTIVE(indx(quote(s(z0)), x1)) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbl1(quote(s(z0)))) → c7(DBL1(mark(s1(quote(z0)))))
ACTIVE(dbl1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(s1(quote(s(z0)))) → c7(S1(mark(s1(quote(z0)))))
ACTIVE(s1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(quote(dbl(s(z0)))) → c7(QUOTE(mark(s(s(dbl(z0))))))
ACTIVE(quote(dbl(s(z0)))) → c7(ACTIVE(dbl(s(z0))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(QUOTE(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(QUOTE(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(quote(from(z0))) → c7(QUOTE(mark(cons(z0, from(s(z0))))))
ACTIVE(quote(from(z0))) → c7(ACTIVE(from(z0)))
ACTIVE(quote(dbl1(s(z0)))) → c7(QUOTE(mark(s1(s1(dbl1(z0))))))
ACTIVE(quote(dbl1(s(z0)))) → c7(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(quote(s(z0)))) → c7(QUOTE(mark(s1(quote(z0)))))
ACTIVE(quote(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
PROPER(dbl(dbl(z0))) → c45(DBL(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbl(s(z0))) → c45(DBL(s(proper(z0))), PROPER(s(z0)))
PROPER(dbl(dbls(z0))) → c45(DBL(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbl(cons(z0, z1))) → c45(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbl(sel(z0, z1))) → c45(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbl(indx(z0, z1))) → c45(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbl(from(z0))) → c45(DBL(from(proper(z0))), PROPER(from(z0)))
PROPER(dbl(dbl1(z0))) → c45(DBL(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbl(s1(z0))) → c45(DBL(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbl(sel1(z0, z1))) → c45(DBL(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbl(quote(z0))) → c45(DBL(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbl(0)) → c45(DBL(ok(0)))
PROPER(dbl(nil)) → c45(DBL(ok(nil)))
PROPER(dbl(01)) → c45(DBL(ok(01)))
PROPER(s(dbl(z0))) → c47(S(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(s(s(z0))) → c47(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(dbls(z0))) → c47(S(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(s(cons(z0, z1))) → c47(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(sel(z0, z1))) → c47(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(s(indx(z0, z1))) → c47(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(s(from(z0))) → c47(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(dbl1(z0))) → c47(S(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(s(s1(z0))) → c47(S(s1(proper(z0))), PROPER(s1(z0)))
PROPER(s(sel1(z0, z1))) → c47(S(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(s(quote(z0))) → c47(S(quote(proper(z0))), PROPER(quote(z0)))
PROPER(s(0)) → c47(S(ok(0)))
PROPER(s(nil)) → c47(S(ok(nil)))
PROPER(s(01)) → c47(S(ok(01)))
PROPER(dbls(dbl(z0))) → c48(DBLS(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbls(s(z0))) → c48(DBLS(s(proper(z0))), PROPER(s(z0)))
PROPER(dbls(dbls(z0))) → c48(DBLS(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbls(cons(z0, z1))) → c48(DBLS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbls(sel(z0, z1))) → c48(DBLS(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbls(indx(z0, z1))) → c48(DBLS(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbls(from(z0))) → c48(DBLS(from(proper(z0))), PROPER(from(z0)))
PROPER(dbls(dbl1(z0))) → c48(DBLS(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbls(s1(z0))) → c48(DBLS(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbls(sel1(z0, z1))) → c48(DBLS(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbls(quote(z0))) → c48(DBLS(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbls(0)) → c48(DBLS(ok(0)))
PROPER(dbls(nil)) → c48(DBLS(ok(nil)))
PROPER(dbls(01)) → c48(DBLS(ok(01)))
PROPER(cons(x0, dbl(z0))) → c50(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(cons(x0, 0)) → c50(CONS(proper(x0), ok(0)), PROPER(x0), PROPER(0))
PROPER(cons(x0, s(z0))) → c50(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, dbls(z0))) → c50(CONS(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(cons(x0, nil)) → c50(CONS(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
PROPER(cons(x0, cons(z0, z1))) → c50(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, sel(z0, z1))) → c50(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(cons(x0, indx(z0, z1))) → c50(CONS(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(cons(x0, from(z0))) → c50(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, dbl1(z0))) → c50(CONS(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(cons(x0, 01)) → c50(CONS(proper(x0), ok(01)), PROPER(x0), PROPER(01))
PROPER(cons(x0, s1(z0))) → c50(CONS(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(cons(x0, sel1(z0, z1))) → c50(CONS(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(cons(x0, quote(z0))) → c50(CONS(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(cons(dbl(z0), x1)) → c50(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(cons(0, x1)) → c50(CONS(ok(0), proper(x1)), PROPER(0), PROPER(x1))
PROPER(cons(s(z0), x1)) → c50(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(dbls(z0), x1)) → c50(CONS(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(cons(nil, x1)) → c50(CONS(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c50(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(sel(z0, z1), x1)) → c50(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(cons(indx(z0, z1), x1)) → c50(CONS(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c50(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(dbl1(z0), x1)) → c50(CONS(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(cons(01, x1)) → c50(CONS(ok(01), proper(x1)), PROPER(01), PROPER(x1))
PROPER(cons(s1(z0), x1)) → c50(CONS(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(cons(sel1(z0, z1), x1)) → c50(CONS(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(cons(quote(z0), x1)) → c50(CONS(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
S tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(sel(z0, z1)) → c51(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(indx(z0, z1)) → c52(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c53(FROM(proper(z0)), PROPER(z0))
PROPER(dbl1(z0)) → c54(DBL1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c56(S1(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c57(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)))
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0))))))
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0))))))
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0)))
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(indx(sel1(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(indx(sel1(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel1(z0, z2)), x1), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(indx(quote(dbl(z0)), x1)) → c21(INDX(mark(dbl1(z0)), x1), ACTIVE(quote(dbl(z0))))
ACTIVE(indx(quote(sel(z0, z1)), x1)) → c21(INDX(mark(sel1(z0, z1)), x1), ACTIVE(quote(sel(z0, z1))))
ACTIVE(indx(dbl(z0), x1)) → c21(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
ACTIVE(indx(dbls(z0), x1)) → c21(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(indx(z0, z1), x1)) → c21(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1)))
ACTIVE(indx(dbl1(z0), x1)) → c21(INDX(dbl1(active(z0)), x1), ACTIVE(dbl1(z0)))
ACTIVE(indx(s1(z0), x1)) → c21(INDX(s1(active(z0)), x1), ACTIVE(s1(z0)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(active(z0), z1), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(z0, active(z1)), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(quote(z0), x1)) → c21(INDX(quote(active(z0)), x1), ACTIVE(quote(z0)))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)))
ACTIVE(indx(dbl(0), x1)) → c21(INDX(mark(0), x1))
ACTIVE(indx(dbls(nil), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(indx(indx(nil, z0), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0))))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1))
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0)))
ACTIVE(dbl1(sel(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl1(sel(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl1(sel1(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl1(sel1(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl1(quote(dbl(z0)))) → c22(DBL1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl1(quote(sel(z0, z1)))) → c22(DBL1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl1(dbl(z0))) → c22(DBL1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl1(dbls(z0))) → c22(DBL1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(indx(z0, z1))) → c22(DBL1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl1(dbl1(z0))) → c22(DBL1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl1(s1(z0))) → c22(DBL1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(quote(z0))) → c22(DBL1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(dbl1(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(dbl(0))) → c22(DBL1(mark(0)))
ACTIVE(dbl1(dbls(nil))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(indx(nil, z0))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(dbl1(0))) → c22(DBL1(mark(01)))
ACTIVE(dbl(dbl1(s(z0)))) → c4(DBL(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(DBLS(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(INDX(mark(s1(s1(dbl1(z0)))), x1))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(DBL1(mark(s(s(dbl(z0))))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(ACTIVE(dbl(s(z0))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(DBL1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(DBL1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl1(from(z0))) → c4(DBL1(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl1(from(z0))) → c4(ACTIVE(from(z0)))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(DBL1(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(s1(sel(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(s1(sel(s(z0), cons(z1, z2)))) → c23(S1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(s1(sel1(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(s1(sel1(s(z0), cons(z1, z2)))) → c23(S1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(s1(quote(dbl(z0)))) → c23(S1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(s1(quote(sel(z0, z1)))) → c23(S1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(s1(dbl(z0))) → c23(S1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(s1(dbls(z0))) → c23(S1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(s1(indx(z0, z1))) → c23(S1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(s1(dbl1(z0))) → c23(S1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(s1(s1(z0))) → c23(S1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(quote(z0))) → c23(S1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(s1(dbl(0))) → c23(S1(mark(0)))
ACTIVE(s1(dbls(nil))) → c23(S1(mark(nil)))
ACTIVE(s1(indx(nil, z0))) → c23(S1(mark(nil)))
ACTIVE(s1(dbl1(0))) → c23(S1(mark(01)))
ACTIVE(s1(dbl(s(z0)))) → c6(S1(mark(s(s(dbl(z0))))))
ACTIVE(s1(dbl(s(z0)))) → c6(ACTIVE(dbl(s(z0))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(S1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(S1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(s1(from(z0))) → c6(S1(mark(cons(z0, from(s(z0))))))
ACTIVE(s1(from(z0))) → c6(ACTIVE(from(z0)))
ACTIVE(s1(dbl1(s(z0)))) → c6(S1(mark(s1(s1(dbl1(z0))))))
ACTIVE(s1(dbl1(s(z0)))) → c6(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(sel(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(quote(sel(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(quote(sel1(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(quote(sel1(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(quote(quote(dbl(z0)))) → c26(QUOTE(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(quote(quote(sel(z0, z1)))) → c26(QUOTE(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(quote(dbl(z0))) → c26(QUOTE(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(quote(dbls(z0))) → c26(QUOTE(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(quote(indx(z0, z1))) → c26(QUOTE(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(quote(dbl1(z0))) → c26(QUOTE(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(quote(s1(z0))) → c26(QUOTE(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(quote(z0))) → c26(QUOTE(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(quote(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(quote(0))) → c22(DBL1(mark(01)))
ACTIVE(s1(quote(0))) → c23(S1(mark(01)))
ACTIVE(quote(dbl(0))) → c26(QUOTE(mark(0)))
ACTIVE(quote(dbls(nil))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(indx(nil, z0))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(dbl1(0))) → c26(QUOTE(mark(01)))
ACTIVE(quote(quote(0))) → c26(QUOTE(mark(01)))
ACTIVE(dbl(quote(s(z0)))) → c7(DBL(mark(s1(quote(z0)))))
ACTIVE(dbl(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(s(z0)))) → c7(DBLS(mark(s1(quote(z0)))))
ACTIVE(dbls(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(indx(quote(s(z0)), x1)) → c7(INDX(mark(s1(quote(z0))), x1))
ACTIVE(indx(quote(s(z0)), x1)) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbl1(quote(s(z0)))) → c7(DBL1(mark(s1(quote(z0)))))
ACTIVE(dbl1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(s1(quote(s(z0)))) → c7(S1(mark(s1(quote(z0)))))
ACTIVE(s1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(quote(dbl(s(z0)))) → c7(QUOTE(mark(s(s(dbl(z0))))))
ACTIVE(quote(dbl(s(z0)))) → c7(ACTIVE(dbl(s(z0))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(QUOTE(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(QUOTE(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(quote(from(z0))) → c7(QUOTE(mark(cons(z0, from(s(z0))))))
ACTIVE(quote(from(z0))) → c7(ACTIVE(from(z0)))
ACTIVE(quote(dbl1(s(z0)))) → c7(QUOTE(mark(s1(s1(dbl1(z0))))))
ACTIVE(quote(dbl1(s(z0)))) → c7(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(quote(s(z0)))) → c7(QUOTE(mark(s1(quote(z0)))))
ACTIVE(quote(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
PROPER(dbl(dbl(z0))) → c45(DBL(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbl(s(z0))) → c45(DBL(s(proper(z0))), PROPER(s(z0)))
PROPER(dbl(dbls(z0))) → c45(DBL(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbl(cons(z0, z1))) → c45(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbl(sel(z0, z1))) → c45(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbl(indx(z0, z1))) → c45(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbl(from(z0))) → c45(DBL(from(proper(z0))), PROPER(from(z0)))
PROPER(dbl(dbl1(z0))) → c45(DBL(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbl(s1(z0))) → c45(DBL(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbl(sel1(z0, z1))) → c45(DBL(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbl(quote(z0))) → c45(DBL(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbl(0)) → c45(DBL(ok(0)))
PROPER(dbl(nil)) → c45(DBL(ok(nil)))
PROPER(dbl(01)) → c45(DBL(ok(01)))
PROPER(s(dbl(z0))) → c47(S(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(s(s(z0))) → c47(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(dbls(z0))) → c47(S(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(s(cons(z0, z1))) → c47(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(sel(z0, z1))) → c47(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(s(indx(z0, z1))) → c47(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(s(from(z0))) → c47(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(dbl1(z0))) → c47(S(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(s(s1(z0))) → c47(S(s1(proper(z0))), PROPER(s1(z0)))
PROPER(s(sel1(z0, z1))) → c47(S(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(s(quote(z0))) → c47(S(quote(proper(z0))), PROPER(quote(z0)))
PROPER(s(0)) → c47(S(ok(0)))
PROPER(s(nil)) → c47(S(ok(nil)))
PROPER(s(01)) → c47(S(ok(01)))
PROPER(dbls(dbl(z0))) → c48(DBLS(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbls(s(z0))) → c48(DBLS(s(proper(z0))), PROPER(s(z0)))
PROPER(dbls(dbls(z0))) → c48(DBLS(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbls(cons(z0, z1))) → c48(DBLS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbls(sel(z0, z1))) → c48(DBLS(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbls(indx(z0, z1))) → c48(DBLS(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbls(from(z0))) → c48(DBLS(from(proper(z0))), PROPER(from(z0)))
PROPER(dbls(dbl1(z0))) → c48(DBLS(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbls(s1(z0))) → c48(DBLS(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbls(sel1(z0, z1))) → c48(DBLS(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbls(quote(z0))) → c48(DBLS(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbls(0)) → c48(DBLS(ok(0)))
PROPER(dbls(nil)) → c48(DBLS(ok(nil)))
PROPER(dbls(01)) → c48(DBLS(ok(01)))
PROPER(cons(x0, dbl(z0))) → c50(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(cons(x0, 0)) → c50(CONS(proper(x0), ok(0)), PROPER(x0), PROPER(0))
PROPER(cons(x0, s(z0))) → c50(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, dbls(z0))) → c50(CONS(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(cons(x0, nil)) → c50(CONS(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
PROPER(cons(x0, cons(z0, z1))) → c50(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, sel(z0, z1))) → c50(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(cons(x0, indx(z0, z1))) → c50(CONS(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(cons(x0, from(z0))) → c50(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, dbl1(z0))) → c50(CONS(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(cons(x0, 01)) → c50(CONS(proper(x0), ok(01)), PROPER(x0), PROPER(01))
PROPER(cons(x0, s1(z0))) → c50(CONS(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(cons(x0, sel1(z0, z1))) → c50(CONS(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(cons(x0, quote(z0))) → c50(CONS(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(cons(dbl(z0), x1)) → c50(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(cons(0, x1)) → c50(CONS(ok(0), proper(x1)), PROPER(0), PROPER(x1))
PROPER(cons(s(z0), x1)) → c50(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(dbls(z0), x1)) → c50(CONS(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(cons(nil, x1)) → c50(CONS(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c50(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(sel(z0, z1), x1)) → c50(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(cons(indx(z0, z1), x1)) → c50(CONS(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c50(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(dbl1(z0), x1)) → c50(CONS(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(cons(01, x1)) → c50(CONS(ok(01), proper(x1)), PROPER(01), PROPER(x1))
PROPER(cons(s1(z0), x1)) → c50(CONS(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(cons(sel1(z0, z1), x1)) → c50(CONS(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(cons(quote(z0), x1)) → c50(CONS(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
K tuples:none
Defined Rule Symbols:
active, s, dbl, cons, dbls, sel, indx, s1, dbl1, sel1, quote, proper, from
Defined Pair Symbols:
ACTIVE, DBL, DBLS, SEL, INDX, DBL1, S1, SEL1, QUOTE, PROPER, S, CONS, FROM, TOP
Compound Symbols:
c5, c12, c15, c16, c19, c20, c24, c25, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c51, c52, c53, c54, c56, c57, c58, c59, c60, c61, c62, c63, c8, c, c17, c17, c1, c18, c18, c2, c21, c21, c3, c22, c22, c4, c23, c23, c6, c26, c26, c7, c45, c45, c47, c47, c48, c48, c50
(61) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 6 trailing tuple parts
(62) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(dbl(0)) → mark(0)
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
active(dbls(nil)) → mark(nil)
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1)))
active(sel(0, cons(z0, z1))) → mark(z0)
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
active(indx(nil, z0)) → mark(nil)
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2)))
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(dbl1(0)) → mark(01)
active(dbl1(s(z0))) → mark(s1(s1(dbl1(z0))))
active(sel1(0, cons(z0, z1))) → mark(z0)
active(sel1(s(z0), cons(z1, z2))) → mark(sel1(z0, z2))
active(quote(0)) → mark(01)
active(quote(s(z0))) → mark(s1(quote(z0)))
active(quote(dbl(z0))) → mark(dbl1(z0))
active(quote(sel(z0, z1))) → mark(sel1(z0, z1))
active(dbl(z0)) → dbl(active(z0))
active(dbls(z0)) → dbls(active(z0))
active(sel(z0, z1)) → sel(active(z0), z1)
active(sel(z0, z1)) → sel(z0, active(z1))
active(indx(z0, z1)) → indx(active(z0), z1)
active(dbl1(z0)) → dbl1(active(z0))
active(s1(z0)) → s1(active(z0))
active(sel1(z0, z1)) → sel1(active(z0), z1)
active(sel1(z0, z1)) → sel1(z0, active(z1))
active(quote(z0)) → quote(active(z0))
s(ok(z0)) → ok(s(z0))
dbl(mark(z0)) → mark(dbl(z0))
dbl(ok(z0)) → ok(dbl(z0))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
dbls(mark(z0)) → mark(dbls(z0))
dbls(ok(z0)) → ok(dbls(z0))
sel(mark(z0), z1) → mark(sel(z0, z1))
sel(z0, mark(z1)) → mark(sel(z0, z1))
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
indx(mark(z0), z1) → mark(indx(z0, z1))
indx(ok(z0), ok(z1)) → ok(indx(z0, z1))
s1(mark(z0)) → mark(s1(z0))
s1(ok(z0)) → ok(s1(z0))
dbl1(mark(z0)) → mark(dbl1(z0))
dbl1(ok(z0)) → ok(dbl1(z0))
sel1(mark(z0), z1) → mark(sel1(z0, z1))
sel1(z0, mark(z1)) → mark(sel1(z0, z1))
sel1(ok(z0), ok(z1)) → ok(sel1(z0, z1))
quote(mark(z0)) → mark(quote(z0))
quote(ok(z0)) → ok(quote(z0))
proper(dbl(z0)) → dbl(proper(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(dbls(z0)) → dbls(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
proper(indx(z0, z1)) → indx(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(dbl1(z0)) → dbl1(proper(z0))
proper(01) → ok(01)
proper(s1(z0)) → s1(proper(z0))
proper(sel1(z0, z1)) → sel1(proper(z0), proper(z1))
proper(quote(z0)) → quote(proper(z0))
from(ok(z0)) → ok(from(z0))
Tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(sel(z0, z1)) → c51(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(indx(z0, z1)) → c52(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c53(FROM(proper(z0)), PROPER(z0))
PROPER(dbl1(z0)) → c54(DBL1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c56(S1(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c57(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)))
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0))))))
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0))))))
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0)))
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(indx(sel1(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(indx(sel1(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel1(z0, z2)), x1), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(indx(quote(dbl(z0)), x1)) → c21(INDX(mark(dbl1(z0)), x1), ACTIVE(quote(dbl(z0))))
ACTIVE(indx(quote(sel(z0, z1)), x1)) → c21(INDX(mark(sel1(z0, z1)), x1), ACTIVE(quote(sel(z0, z1))))
ACTIVE(indx(dbl(z0), x1)) → c21(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
ACTIVE(indx(dbls(z0), x1)) → c21(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(indx(z0, z1), x1)) → c21(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1)))
ACTIVE(indx(dbl1(z0), x1)) → c21(INDX(dbl1(active(z0)), x1), ACTIVE(dbl1(z0)))
ACTIVE(indx(s1(z0), x1)) → c21(INDX(s1(active(z0)), x1), ACTIVE(s1(z0)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(active(z0), z1), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(z0, active(z1)), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(quote(z0), x1)) → c21(INDX(quote(active(z0)), x1), ACTIVE(quote(z0)))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)))
ACTIVE(indx(dbl(0), x1)) → c21(INDX(mark(0), x1))
ACTIVE(indx(dbls(nil), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(indx(indx(nil, z0), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0))))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1))
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0)))
ACTIVE(dbl1(sel(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl1(sel(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl1(sel1(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl1(sel1(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl1(quote(dbl(z0)))) → c22(DBL1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl1(quote(sel(z0, z1)))) → c22(DBL1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl1(dbl(z0))) → c22(DBL1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl1(dbls(z0))) → c22(DBL1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(indx(z0, z1))) → c22(DBL1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl1(dbl1(z0))) → c22(DBL1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl1(s1(z0))) → c22(DBL1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(quote(z0))) → c22(DBL1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(dbl1(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(dbl(0))) → c22(DBL1(mark(0)))
ACTIVE(dbl1(dbls(nil))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(indx(nil, z0))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(dbl1(0))) → c22(DBL1(mark(01)))
ACTIVE(dbl(dbl1(s(z0)))) → c4(DBL(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(DBLS(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(INDX(mark(s1(s1(dbl1(z0)))), x1))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(DBL1(mark(s(s(dbl(z0))))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(ACTIVE(dbl(s(z0))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(DBL1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(DBL1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl1(from(z0))) → c4(DBL1(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl1(from(z0))) → c4(ACTIVE(from(z0)))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(DBL1(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(s1(sel(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(s1(sel(s(z0), cons(z1, z2)))) → c23(S1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(s1(sel1(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(s1(sel1(s(z0), cons(z1, z2)))) → c23(S1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(s1(quote(dbl(z0)))) → c23(S1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(s1(quote(sel(z0, z1)))) → c23(S1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(s1(dbl(z0))) → c23(S1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(s1(dbls(z0))) → c23(S1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(s1(indx(z0, z1))) → c23(S1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(s1(dbl1(z0))) → c23(S1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(s1(s1(z0))) → c23(S1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(quote(z0))) → c23(S1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(s1(dbl(0))) → c23(S1(mark(0)))
ACTIVE(s1(dbls(nil))) → c23(S1(mark(nil)))
ACTIVE(s1(indx(nil, z0))) → c23(S1(mark(nil)))
ACTIVE(s1(dbl1(0))) → c23(S1(mark(01)))
ACTIVE(s1(dbl(s(z0)))) → c6(S1(mark(s(s(dbl(z0))))))
ACTIVE(s1(dbl(s(z0)))) → c6(ACTIVE(dbl(s(z0))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(S1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(S1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(s1(from(z0))) → c6(S1(mark(cons(z0, from(s(z0))))))
ACTIVE(s1(from(z0))) → c6(ACTIVE(from(z0)))
ACTIVE(s1(dbl1(s(z0)))) → c6(S1(mark(s1(s1(dbl1(z0))))))
ACTIVE(s1(dbl1(s(z0)))) → c6(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(sel(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(quote(sel(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(quote(sel1(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(quote(sel1(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(quote(quote(dbl(z0)))) → c26(QUOTE(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(quote(quote(sel(z0, z1)))) → c26(QUOTE(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(quote(dbl(z0))) → c26(QUOTE(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(quote(dbls(z0))) → c26(QUOTE(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(quote(indx(z0, z1))) → c26(QUOTE(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(quote(dbl1(z0))) → c26(QUOTE(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(quote(s1(z0))) → c26(QUOTE(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(quote(z0))) → c26(QUOTE(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(quote(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(quote(0))) → c22(DBL1(mark(01)))
ACTIVE(s1(quote(0))) → c23(S1(mark(01)))
ACTIVE(quote(dbl(0))) → c26(QUOTE(mark(0)))
ACTIVE(quote(dbls(nil))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(indx(nil, z0))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(dbl1(0))) → c26(QUOTE(mark(01)))
ACTIVE(quote(quote(0))) → c26(QUOTE(mark(01)))
ACTIVE(dbl(quote(s(z0)))) → c7(DBL(mark(s1(quote(z0)))))
ACTIVE(dbl(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(s(z0)))) → c7(DBLS(mark(s1(quote(z0)))))
ACTIVE(dbls(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(indx(quote(s(z0)), x1)) → c7(INDX(mark(s1(quote(z0))), x1))
ACTIVE(indx(quote(s(z0)), x1)) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbl1(quote(s(z0)))) → c7(DBL1(mark(s1(quote(z0)))))
ACTIVE(dbl1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(s1(quote(s(z0)))) → c7(S1(mark(s1(quote(z0)))))
ACTIVE(s1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(quote(dbl(s(z0)))) → c7(QUOTE(mark(s(s(dbl(z0))))))
ACTIVE(quote(dbl(s(z0)))) → c7(ACTIVE(dbl(s(z0))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(QUOTE(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(QUOTE(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(quote(from(z0))) → c7(QUOTE(mark(cons(z0, from(s(z0))))))
ACTIVE(quote(from(z0))) → c7(ACTIVE(from(z0)))
ACTIVE(quote(dbl1(s(z0)))) → c7(QUOTE(mark(s1(s1(dbl1(z0))))))
ACTIVE(quote(dbl1(s(z0)))) → c7(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(quote(s(z0)))) → c7(QUOTE(mark(s1(quote(z0)))))
ACTIVE(quote(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
PROPER(dbl(dbl(z0))) → c45(DBL(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbl(s(z0))) → c45(DBL(s(proper(z0))), PROPER(s(z0)))
PROPER(dbl(dbls(z0))) → c45(DBL(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbl(cons(z0, z1))) → c45(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbl(sel(z0, z1))) → c45(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbl(indx(z0, z1))) → c45(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbl(from(z0))) → c45(DBL(from(proper(z0))), PROPER(from(z0)))
PROPER(dbl(dbl1(z0))) → c45(DBL(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbl(s1(z0))) → c45(DBL(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbl(sel1(z0, z1))) → c45(DBL(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbl(quote(z0))) → c45(DBL(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbl(0)) → c45(DBL(ok(0)))
PROPER(dbl(nil)) → c45(DBL(ok(nil)))
PROPER(dbl(01)) → c45(DBL(ok(01)))
PROPER(s(dbl(z0))) → c47(S(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(s(s(z0))) → c47(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(dbls(z0))) → c47(S(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(s(cons(z0, z1))) → c47(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(sel(z0, z1))) → c47(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(s(indx(z0, z1))) → c47(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(s(from(z0))) → c47(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(dbl1(z0))) → c47(S(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(s(s1(z0))) → c47(S(s1(proper(z0))), PROPER(s1(z0)))
PROPER(s(sel1(z0, z1))) → c47(S(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(s(quote(z0))) → c47(S(quote(proper(z0))), PROPER(quote(z0)))
PROPER(s(0)) → c47(S(ok(0)))
PROPER(s(nil)) → c47(S(ok(nil)))
PROPER(s(01)) → c47(S(ok(01)))
PROPER(dbls(dbl(z0))) → c48(DBLS(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbls(s(z0))) → c48(DBLS(s(proper(z0))), PROPER(s(z0)))
PROPER(dbls(dbls(z0))) → c48(DBLS(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbls(cons(z0, z1))) → c48(DBLS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbls(sel(z0, z1))) → c48(DBLS(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbls(indx(z0, z1))) → c48(DBLS(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbls(from(z0))) → c48(DBLS(from(proper(z0))), PROPER(from(z0)))
PROPER(dbls(dbl1(z0))) → c48(DBLS(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbls(s1(z0))) → c48(DBLS(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbls(sel1(z0, z1))) → c48(DBLS(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbls(quote(z0))) → c48(DBLS(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbls(0)) → c48(DBLS(ok(0)))
PROPER(dbls(nil)) → c48(DBLS(ok(nil)))
PROPER(dbls(01)) → c48(DBLS(ok(01)))
PROPER(cons(x0, dbl(z0))) → c50(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(cons(x0, s(z0))) → c50(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, dbls(z0))) → c50(CONS(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(cons(x0, cons(z0, z1))) → c50(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, sel(z0, z1))) → c50(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(cons(x0, indx(z0, z1))) → c50(CONS(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(cons(x0, from(z0))) → c50(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, dbl1(z0))) → c50(CONS(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(cons(x0, s1(z0))) → c50(CONS(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(cons(x0, sel1(z0, z1))) → c50(CONS(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(cons(x0, quote(z0))) → c50(CONS(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(cons(dbl(z0), x1)) → c50(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(cons(s(z0), x1)) → c50(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(dbls(z0), x1)) → c50(CONS(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c50(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(sel(z0, z1), x1)) → c50(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(cons(indx(z0, z1), x1)) → c50(CONS(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c50(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(dbl1(z0), x1)) → c50(CONS(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(cons(s1(z0), x1)) → c50(CONS(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(cons(sel1(z0, z1), x1)) → c50(CONS(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(cons(quote(z0), x1)) → c50(CONS(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c50(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c50(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, 01)) → c50(CONS(proper(x0), ok(01)), PROPER(x0))
PROPER(cons(0, x1)) → c50(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c50(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(01, x1)) → c50(CONS(ok(01), proper(x1)), PROPER(x1))
S tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(sel(z0, z1)) → c51(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(indx(z0, z1)) → c52(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c53(FROM(proper(z0)), PROPER(z0))
PROPER(dbl1(z0)) → c54(DBL1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c56(S1(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c57(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)))
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0))))))
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0))))))
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0)))
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(indx(sel1(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(indx(sel1(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel1(z0, z2)), x1), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(indx(quote(dbl(z0)), x1)) → c21(INDX(mark(dbl1(z0)), x1), ACTIVE(quote(dbl(z0))))
ACTIVE(indx(quote(sel(z0, z1)), x1)) → c21(INDX(mark(sel1(z0, z1)), x1), ACTIVE(quote(sel(z0, z1))))
ACTIVE(indx(dbl(z0), x1)) → c21(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
ACTIVE(indx(dbls(z0), x1)) → c21(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(indx(z0, z1), x1)) → c21(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1)))
ACTIVE(indx(dbl1(z0), x1)) → c21(INDX(dbl1(active(z0)), x1), ACTIVE(dbl1(z0)))
ACTIVE(indx(s1(z0), x1)) → c21(INDX(s1(active(z0)), x1), ACTIVE(s1(z0)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(active(z0), z1), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(z0, active(z1)), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(quote(z0), x1)) → c21(INDX(quote(active(z0)), x1), ACTIVE(quote(z0)))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)))
ACTIVE(indx(dbl(0), x1)) → c21(INDX(mark(0), x1))
ACTIVE(indx(dbls(nil), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(indx(indx(nil, z0), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0))))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1))
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0)))
ACTIVE(dbl1(sel(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl1(sel(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl1(sel1(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl1(sel1(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl1(quote(dbl(z0)))) → c22(DBL1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl1(quote(sel(z0, z1)))) → c22(DBL1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl1(dbl(z0))) → c22(DBL1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl1(dbls(z0))) → c22(DBL1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(indx(z0, z1))) → c22(DBL1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl1(dbl1(z0))) → c22(DBL1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl1(s1(z0))) → c22(DBL1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(quote(z0))) → c22(DBL1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(dbl1(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(dbl(0))) → c22(DBL1(mark(0)))
ACTIVE(dbl1(dbls(nil))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(indx(nil, z0))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(dbl1(0))) → c22(DBL1(mark(01)))
ACTIVE(dbl(dbl1(s(z0)))) → c4(DBL(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(DBLS(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(INDX(mark(s1(s1(dbl1(z0)))), x1))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(DBL1(mark(s(s(dbl(z0))))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(ACTIVE(dbl(s(z0))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(DBL1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(DBL1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl1(from(z0))) → c4(DBL1(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl1(from(z0))) → c4(ACTIVE(from(z0)))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(DBL1(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(s1(sel(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(s1(sel(s(z0), cons(z1, z2)))) → c23(S1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(s1(sel1(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(s1(sel1(s(z0), cons(z1, z2)))) → c23(S1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(s1(quote(dbl(z0)))) → c23(S1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(s1(quote(sel(z0, z1)))) → c23(S1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(s1(dbl(z0))) → c23(S1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(s1(dbls(z0))) → c23(S1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(s1(indx(z0, z1))) → c23(S1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(s1(dbl1(z0))) → c23(S1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(s1(s1(z0))) → c23(S1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(quote(z0))) → c23(S1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(s1(dbl(0))) → c23(S1(mark(0)))
ACTIVE(s1(dbls(nil))) → c23(S1(mark(nil)))
ACTIVE(s1(indx(nil, z0))) → c23(S1(mark(nil)))
ACTIVE(s1(dbl1(0))) → c23(S1(mark(01)))
ACTIVE(s1(dbl(s(z0)))) → c6(S1(mark(s(s(dbl(z0))))))
ACTIVE(s1(dbl(s(z0)))) → c6(ACTIVE(dbl(s(z0))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(S1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(S1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(s1(from(z0))) → c6(S1(mark(cons(z0, from(s(z0))))))
ACTIVE(s1(from(z0))) → c6(ACTIVE(from(z0)))
ACTIVE(s1(dbl1(s(z0)))) → c6(S1(mark(s1(s1(dbl1(z0))))))
ACTIVE(s1(dbl1(s(z0)))) → c6(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(sel(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(quote(sel(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(quote(sel1(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(quote(sel1(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(quote(quote(dbl(z0)))) → c26(QUOTE(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(quote(quote(sel(z0, z1)))) → c26(QUOTE(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(quote(dbl(z0))) → c26(QUOTE(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(quote(dbls(z0))) → c26(QUOTE(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(quote(indx(z0, z1))) → c26(QUOTE(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(quote(dbl1(z0))) → c26(QUOTE(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(quote(s1(z0))) → c26(QUOTE(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(quote(z0))) → c26(QUOTE(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(quote(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(quote(0))) → c22(DBL1(mark(01)))
ACTIVE(s1(quote(0))) → c23(S1(mark(01)))
ACTIVE(quote(dbl(0))) → c26(QUOTE(mark(0)))
ACTIVE(quote(dbls(nil))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(indx(nil, z0))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(dbl1(0))) → c26(QUOTE(mark(01)))
ACTIVE(quote(quote(0))) → c26(QUOTE(mark(01)))
ACTIVE(dbl(quote(s(z0)))) → c7(DBL(mark(s1(quote(z0)))))
ACTIVE(dbl(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(s(z0)))) → c7(DBLS(mark(s1(quote(z0)))))
ACTIVE(dbls(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(indx(quote(s(z0)), x1)) → c7(INDX(mark(s1(quote(z0))), x1))
ACTIVE(indx(quote(s(z0)), x1)) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbl1(quote(s(z0)))) → c7(DBL1(mark(s1(quote(z0)))))
ACTIVE(dbl1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(s1(quote(s(z0)))) → c7(S1(mark(s1(quote(z0)))))
ACTIVE(s1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(quote(dbl(s(z0)))) → c7(QUOTE(mark(s(s(dbl(z0))))))
ACTIVE(quote(dbl(s(z0)))) → c7(ACTIVE(dbl(s(z0))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(QUOTE(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(QUOTE(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(quote(from(z0))) → c7(QUOTE(mark(cons(z0, from(s(z0))))))
ACTIVE(quote(from(z0))) → c7(ACTIVE(from(z0)))
ACTIVE(quote(dbl1(s(z0)))) → c7(QUOTE(mark(s1(s1(dbl1(z0))))))
ACTIVE(quote(dbl1(s(z0)))) → c7(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(quote(s(z0)))) → c7(QUOTE(mark(s1(quote(z0)))))
ACTIVE(quote(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
PROPER(dbl(dbl(z0))) → c45(DBL(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbl(s(z0))) → c45(DBL(s(proper(z0))), PROPER(s(z0)))
PROPER(dbl(dbls(z0))) → c45(DBL(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbl(cons(z0, z1))) → c45(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbl(sel(z0, z1))) → c45(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbl(indx(z0, z1))) → c45(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbl(from(z0))) → c45(DBL(from(proper(z0))), PROPER(from(z0)))
PROPER(dbl(dbl1(z0))) → c45(DBL(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbl(s1(z0))) → c45(DBL(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbl(sel1(z0, z1))) → c45(DBL(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbl(quote(z0))) → c45(DBL(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbl(0)) → c45(DBL(ok(0)))
PROPER(dbl(nil)) → c45(DBL(ok(nil)))
PROPER(dbl(01)) → c45(DBL(ok(01)))
PROPER(s(dbl(z0))) → c47(S(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(s(s(z0))) → c47(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(dbls(z0))) → c47(S(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(s(cons(z0, z1))) → c47(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(sel(z0, z1))) → c47(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(s(indx(z0, z1))) → c47(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(s(from(z0))) → c47(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(dbl1(z0))) → c47(S(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(s(s1(z0))) → c47(S(s1(proper(z0))), PROPER(s1(z0)))
PROPER(s(sel1(z0, z1))) → c47(S(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(s(quote(z0))) → c47(S(quote(proper(z0))), PROPER(quote(z0)))
PROPER(s(0)) → c47(S(ok(0)))
PROPER(s(nil)) → c47(S(ok(nil)))
PROPER(s(01)) → c47(S(ok(01)))
PROPER(dbls(dbl(z0))) → c48(DBLS(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbls(s(z0))) → c48(DBLS(s(proper(z0))), PROPER(s(z0)))
PROPER(dbls(dbls(z0))) → c48(DBLS(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbls(cons(z0, z1))) → c48(DBLS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbls(sel(z0, z1))) → c48(DBLS(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbls(indx(z0, z1))) → c48(DBLS(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbls(from(z0))) → c48(DBLS(from(proper(z0))), PROPER(from(z0)))
PROPER(dbls(dbl1(z0))) → c48(DBLS(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbls(s1(z0))) → c48(DBLS(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbls(sel1(z0, z1))) → c48(DBLS(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbls(quote(z0))) → c48(DBLS(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbls(0)) → c48(DBLS(ok(0)))
PROPER(dbls(nil)) → c48(DBLS(ok(nil)))
PROPER(dbls(01)) → c48(DBLS(ok(01)))
PROPER(cons(x0, dbl(z0))) → c50(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(cons(x0, s(z0))) → c50(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, dbls(z0))) → c50(CONS(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(cons(x0, cons(z0, z1))) → c50(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, sel(z0, z1))) → c50(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(cons(x0, indx(z0, z1))) → c50(CONS(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(cons(x0, from(z0))) → c50(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, dbl1(z0))) → c50(CONS(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(cons(x0, s1(z0))) → c50(CONS(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(cons(x0, sel1(z0, z1))) → c50(CONS(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(cons(x0, quote(z0))) → c50(CONS(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(cons(dbl(z0), x1)) → c50(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(cons(s(z0), x1)) → c50(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(dbls(z0), x1)) → c50(CONS(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c50(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(sel(z0, z1), x1)) → c50(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(cons(indx(z0, z1), x1)) → c50(CONS(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c50(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(dbl1(z0), x1)) → c50(CONS(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(cons(s1(z0), x1)) → c50(CONS(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(cons(sel1(z0, z1), x1)) → c50(CONS(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(cons(quote(z0), x1)) → c50(CONS(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c50(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c50(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, 01)) → c50(CONS(proper(x0), ok(01)), PROPER(x0))
PROPER(cons(0, x1)) → c50(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c50(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(01, x1)) → c50(CONS(ok(01), proper(x1)), PROPER(x1))
K tuples:none
Defined Rule Symbols:
active, s, dbl, cons, dbls, sel, indx, s1, dbl1, sel1, quote, proper, from
Defined Pair Symbols:
ACTIVE, DBL, DBLS, SEL, INDX, DBL1, S1, SEL1, QUOTE, PROPER, S, CONS, FROM, TOP
Compound Symbols:
c5, c12, c15, c16, c19, c20, c24, c25, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c51, c52, c53, c54, c56, c57, c58, c59, c60, c61, c62, c63, c8, c, c17, c17, c1, c18, c18, c2, c21, c21, c3, c22, c22, c4, c23, c23, c6, c26, c26, c7, c45, c45, c47, c47, c48, c48, c50, c50
(63) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
PROPER(
sel(
z0,
z1)) →
c51(
SEL(
proper(
z0),
proper(
z1)),
PROPER(
z0),
PROPER(
z1)) by
PROPER(sel(x0, dbl(z0))) → c51(SEL(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(sel(x0, 0)) → c51(SEL(proper(x0), ok(0)), PROPER(x0), PROPER(0))
PROPER(sel(x0, s(z0))) → c51(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(sel(x0, dbls(z0))) → c51(SEL(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(sel(x0, nil)) → c51(SEL(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
PROPER(sel(x0, cons(z0, z1))) → c51(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(sel(x0, sel(z0, z1))) → c51(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(sel(x0, indx(z0, z1))) → c51(SEL(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(sel(x0, from(z0))) → c51(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(sel(x0, dbl1(z0))) → c51(SEL(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(sel(x0, 01)) → c51(SEL(proper(x0), ok(01)), PROPER(x0), PROPER(01))
PROPER(sel(x0, s1(z0))) → c51(SEL(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(sel(x0, sel1(z0, z1))) → c51(SEL(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(sel(x0, quote(z0))) → c51(SEL(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(sel(dbl(z0), x1)) → c51(SEL(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(sel(0, x1)) → c51(SEL(ok(0), proper(x1)), PROPER(0), PROPER(x1))
PROPER(sel(s(z0), x1)) → c51(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(sel(dbls(z0), x1)) → c51(SEL(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(sel(nil, x1)) → c51(SEL(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
PROPER(sel(cons(z0, z1), x1)) → c51(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(sel(sel(z0, z1), x1)) → c51(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(sel(indx(z0, z1), x1)) → c51(SEL(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(sel(from(z0), x1)) → c51(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(sel(dbl1(z0), x1)) → c51(SEL(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(sel(01, x1)) → c51(SEL(ok(01), proper(x1)), PROPER(01), PROPER(x1))
PROPER(sel(s1(z0), x1)) → c51(SEL(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(sel(sel1(z0, z1), x1)) → c51(SEL(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(sel(quote(z0), x1)) → c51(SEL(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
(64) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(dbl(0)) → mark(0)
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
active(dbls(nil)) → mark(nil)
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1)))
active(sel(0, cons(z0, z1))) → mark(z0)
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
active(indx(nil, z0)) → mark(nil)
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2)))
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(dbl1(0)) → mark(01)
active(dbl1(s(z0))) → mark(s1(s1(dbl1(z0))))
active(sel1(0, cons(z0, z1))) → mark(z0)
active(sel1(s(z0), cons(z1, z2))) → mark(sel1(z0, z2))
active(quote(0)) → mark(01)
active(quote(s(z0))) → mark(s1(quote(z0)))
active(quote(dbl(z0))) → mark(dbl1(z0))
active(quote(sel(z0, z1))) → mark(sel1(z0, z1))
active(dbl(z0)) → dbl(active(z0))
active(dbls(z0)) → dbls(active(z0))
active(sel(z0, z1)) → sel(active(z0), z1)
active(sel(z0, z1)) → sel(z0, active(z1))
active(indx(z0, z1)) → indx(active(z0), z1)
active(dbl1(z0)) → dbl1(active(z0))
active(s1(z0)) → s1(active(z0))
active(sel1(z0, z1)) → sel1(active(z0), z1)
active(sel1(z0, z1)) → sel1(z0, active(z1))
active(quote(z0)) → quote(active(z0))
s(ok(z0)) → ok(s(z0))
dbl(mark(z0)) → mark(dbl(z0))
dbl(ok(z0)) → ok(dbl(z0))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
dbls(mark(z0)) → mark(dbls(z0))
dbls(ok(z0)) → ok(dbls(z0))
sel(mark(z0), z1) → mark(sel(z0, z1))
sel(z0, mark(z1)) → mark(sel(z0, z1))
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
indx(mark(z0), z1) → mark(indx(z0, z1))
indx(ok(z0), ok(z1)) → ok(indx(z0, z1))
s1(mark(z0)) → mark(s1(z0))
s1(ok(z0)) → ok(s1(z0))
dbl1(mark(z0)) → mark(dbl1(z0))
dbl1(ok(z0)) → ok(dbl1(z0))
sel1(mark(z0), z1) → mark(sel1(z0, z1))
sel1(z0, mark(z1)) → mark(sel1(z0, z1))
sel1(ok(z0), ok(z1)) → ok(sel1(z0, z1))
quote(mark(z0)) → mark(quote(z0))
quote(ok(z0)) → ok(quote(z0))
proper(dbl(z0)) → dbl(proper(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(dbls(z0)) → dbls(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
proper(indx(z0, z1)) → indx(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(dbl1(z0)) → dbl1(proper(z0))
proper(01) → ok(01)
proper(s1(z0)) → s1(proper(z0))
proper(sel1(z0, z1)) → sel1(proper(z0), proper(z1))
proper(quote(z0)) → quote(proper(z0))
from(ok(z0)) → ok(from(z0))
Tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(indx(z0, z1)) → c52(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c53(FROM(proper(z0)), PROPER(z0))
PROPER(dbl1(z0)) → c54(DBL1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c56(S1(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c57(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)))
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0))))))
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0))))))
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0)))
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(indx(sel1(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(indx(sel1(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel1(z0, z2)), x1), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(indx(quote(dbl(z0)), x1)) → c21(INDX(mark(dbl1(z0)), x1), ACTIVE(quote(dbl(z0))))
ACTIVE(indx(quote(sel(z0, z1)), x1)) → c21(INDX(mark(sel1(z0, z1)), x1), ACTIVE(quote(sel(z0, z1))))
ACTIVE(indx(dbl(z0), x1)) → c21(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
ACTIVE(indx(dbls(z0), x1)) → c21(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(indx(z0, z1), x1)) → c21(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1)))
ACTIVE(indx(dbl1(z0), x1)) → c21(INDX(dbl1(active(z0)), x1), ACTIVE(dbl1(z0)))
ACTIVE(indx(s1(z0), x1)) → c21(INDX(s1(active(z0)), x1), ACTIVE(s1(z0)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(active(z0), z1), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(z0, active(z1)), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(quote(z0), x1)) → c21(INDX(quote(active(z0)), x1), ACTIVE(quote(z0)))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)))
ACTIVE(indx(dbl(0), x1)) → c21(INDX(mark(0), x1))
ACTIVE(indx(dbls(nil), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(indx(indx(nil, z0), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0))))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1))
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0)))
ACTIVE(dbl1(sel(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl1(sel(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl1(sel1(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl1(sel1(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl1(quote(dbl(z0)))) → c22(DBL1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl1(quote(sel(z0, z1)))) → c22(DBL1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl1(dbl(z0))) → c22(DBL1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl1(dbls(z0))) → c22(DBL1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(indx(z0, z1))) → c22(DBL1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl1(dbl1(z0))) → c22(DBL1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl1(s1(z0))) → c22(DBL1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(quote(z0))) → c22(DBL1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(dbl1(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(dbl(0))) → c22(DBL1(mark(0)))
ACTIVE(dbl1(dbls(nil))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(indx(nil, z0))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(dbl1(0))) → c22(DBL1(mark(01)))
ACTIVE(dbl(dbl1(s(z0)))) → c4(DBL(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(DBLS(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(INDX(mark(s1(s1(dbl1(z0)))), x1))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(DBL1(mark(s(s(dbl(z0))))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(ACTIVE(dbl(s(z0))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(DBL1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(DBL1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl1(from(z0))) → c4(DBL1(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl1(from(z0))) → c4(ACTIVE(from(z0)))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(DBL1(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(s1(sel(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(s1(sel(s(z0), cons(z1, z2)))) → c23(S1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(s1(sel1(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(s1(sel1(s(z0), cons(z1, z2)))) → c23(S1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(s1(quote(dbl(z0)))) → c23(S1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(s1(quote(sel(z0, z1)))) → c23(S1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(s1(dbl(z0))) → c23(S1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(s1(dbls(z0))) → c23(S1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(s1(indx(z0, z1))) → c23(S1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(s1(dbl1(z0))) → c23(S1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(s1(s1(z0))) → c23(S1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(quote(z0))) → c23(S1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(s1(dbl(0))) → c23(S1(mark(0)))
ACTIVE(s1(dbls(nil))) → c23(S1(mark(nil)))
ACTIVE(s1(indx(nil, z0))) → c23(S1(mark(nil)))
ACTIVE(s1(dbl1(0))) → c23(S1(mark(01)))
ACTIVE(s1(dbl(s(z0)))) → c6(S1(mark(s(s(dbl(z0))))))
ACTIVE(s1(dbl(s(z0)))) → c6(ACTIVE(dbl(s(z0))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(S1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(S1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(s1(from(z0))) → c6(S1(mark(cons(z0, from(s(z0))))))
ACTIVE(s1(from(z0))) → c6(ACTIVE(from(z0)))
ACTIVE(s1(dbl1(s(z0)))) → c6(S1(mark(s1(s1(dbl1(z0))))))
ACTIVE(s1(dbl1(s(z0)))) → c6(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(sel(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(quote(sel(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(quote(sel1(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(quote(sel1(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(quote(quote(dbl(z0)))) → c26(QUOTE(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(quote(quote(sel(z0, z1)))) → c26(QUOTE(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(quote(dbl(z0))) → c26(QUOTE(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(quote(dbls(z0))) → c26(QUOTE(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(quote(indx(z0, z1))) → c26(QUOTE(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(quote(dbl1(z0))) → c26(QUOTE(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(quote(s1(z0))) → c26(QUOTE(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(quote(z0))) → c26(QUOTE(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(quote(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(quote(0))) → c22(DBL1(mark(01)))
ACTIVE(s1(quote(0))) → c23(S1(mark(01)))
ACTIVE(quote(dbl(0))) → c26(QUOTE(mark(0)))
ACTIVE(quote(dbls(nil))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(indx(nil, z0))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(dbl1(0))) → c26(QUOTE(mark(01)))
ACTIVE(quote(quote(0))) → c26(QUOTE(mark(01)))
ACTIVE(dbl(quote(s(z0)))) → c7(DBL(mark(s1(quote(z0)))))
ACTIVE(dbl(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(s(z0)))) → c7(DBLS(mark(s1(quote(z0)))))
ACTIVE(dbls(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(indx(quote(s(z0)), x1)) → c7(INDX(mark(s1(quote(z0))), x1))
ACTIVE(indx(quote(s(z0)), x1)) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbl1(quote(s(z0)))) → c7(DBL1(mark(s1(quote(z0)))))
ACTIVE(dbl1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(s1(quote(s(z0)))) → c7(S1(mark(s1(quote(z0)))))
ACTIVE(s1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(quote(dbl(s(z0)))) → c7(QUOTE(mark(s(s(dbl(z0))))))
ACTIVE(quote(dbl(s(z0)))) → c7(ACTIVE(dbl(s(z0))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(QUOTE(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(QUOTE(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(quote(from(z0))) → c7(QUOTE(mark(cons(z0, from(s(z0))))))
ACTIVE(quote(from(z0))) → c7(ACTIVE(from(z0)))
ACTIVE(quote(dbl1(s(z0)))) → c7(QUOTE(mark(s1(s1(dbl1(z0))))))
ACTIVE(quote(dbl1(s(z0)))) → c7(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(quote(s(z0)))) → c7(QUOTE(mark(s1(quote(z0)))))
ACTIVE(quote(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
PROPER(dbl(dbl(z0))) → c45(DBL(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbl(s(z0))) → c45(DBL(s(proper(z0))), PROPER(s(z0)))
PROPER(dbl(dbls(z0))) → c45(DBL(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbl(cons(z0, z1))) → c45(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbl(sel(z0, z1))) → c45(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbl(indx(z0, z1))) → c45(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbl(from(z0))) → c45(DBL(from(proper(z0))), PROPER(from(z0)))
PROPER(dbl(dbl1(z0))) → c45(DBL(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbl(s1(z0))) → c45(DBL(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbl(sel1(z0, z1))) → c45(DBL(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbl(quote(z0))) → c45(DBL(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbl(0)) → c45(DBL(ok(0)))
PROPER(dbl(nil)) → c45(DBL(ok(nil)))
PROPER(dbl(01)) → c45(DBL(ok(01)))
PROPER(s(dbl(z0))) → c47(S(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(s(s(z0))) → c47(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(dbls(z0))) → c47(S(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(s(cons(z0, z1))) → c47(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(sel(z0, z1))) → c47(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(s(indx(z0, z1))) → c47(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(s(from(z0))) → c47(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(dbl1(z0))) → c47(S(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(s(s1(z0))) → c47(S(s1(proper(z0))), PROPER(s1(z0)))
PROPER(s(sel1(z0, z1))) → c47(S(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(s(quote(z0))) → c47(S(quote(proper(z0))), PROPER(quote(z0)))
PROPER(s(0)) → c47(S(ok(0)))
PROPER(s(nil)) → c47(S(ok(nil)))
PROPER(s(01)) → c47(S(ok(01)))
PROPER(dbls(dbl(z0))) → c48(DBLS(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbls(s(z0))) → c48(DBLS(s(proper(z0))), PROPER(s(z0)))
PROPER(dbls(dbls(z0))) → c48(DBLS(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbls(cons(z0, z1))) → c48(DBLS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbls(sel(z0, z1))) → c48(DBLS(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbls(indx(z0, z1))) → c48(DBLS(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbls(from(z0))) → c48(DBLS(from(proper(z0))), PROPER(from(z0)))
PROPER(dbls(dbl1(z0))) → c48(DBLS(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbls(s1(z0))) → c48(DBLS(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbls(sel1(z0, z1))) → c48(DBLS(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbls(quote(z0))) → c48(DBLS(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbls(0)) → c48(DBLS(ok(0)))
PROPER(dbls(nil)) → c48(DBLS(ok(nil)))
PROPER(dbls(01)) → c48(DBLS(ok(01)))
PROPER(cons(x0, dbl(z0))) → c50(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(cons(x0, s(z0))) → c50(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, dbls(z0))) → c50(CONS(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(cons(x0, cons(z0, z1))) → c50(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, sel(z0, z1))) → c50(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(cons(x0, indx(z0, z1))) → c50(CONS(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(cons(x0, from(z0))) → c50(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, dbl1(z0))) → c50(CONS(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(cons(x0, s1(z0))) → c50(CONS(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(cons(x0, sel1(z0, z1))) → c50(CONS(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(cons(x0, quote(z0))) → c50(CONS(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(cons(dbl(z0), x1)) → c50(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(cons(s(z0), x1)) → c50(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(dbls(z0), x1)) → c50(CONS(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c50(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(sel(z0, z1), x1)) → c50(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(cons(indx(z0, z1), x1)) → c50(CONS(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c50(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(dbl1(z0), x1)) → c50(CONS(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(cons(s1(z0), x1)) → c50(CONS(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(cons(sel1(z0, z1), x1)) → c50(CONS(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(cons(quote(z0), x1)) → c50(CONS(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c50(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c50(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, 01)) → c50(CONS(proper(x0), ok(01)), PROPER(x0))
PROPER(cons(0, x1)) → c50(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c50(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(01, x1)) → c50(CONS(ok(01), proper(x1)), PROPER(x1))
PROPER(sel(x0, dbl(z0))) → c51(SEL(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(sel(x0, 0)) → c51(SEL(proper(x0), ok(0)), PROPER(x0), PROPER(0))
PROPER(sel(x0, s(z0))) → c51(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(sel(x0, dbls(z0))) → c51(SEL(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(sel(x0, nil)) → c51(SEL(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
PROPER(sel(x0, cons(z0, z1))) → c51(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(sel(x0, sel(z0, z1))) → c51(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(sel(x0, indx(z0, z1))) → c51(SEL(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(sel(x0, from(z0))) → c51(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(sel(x0, dbl1(z0))) → c51(SEL(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(sel(x0, 01)) → c51(SEL(proper(x0), ok(01)), PROPER(x0), PROPER(01))
PROPER(sel(x0, s1(z0))) → c51(SEL(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(sel(x0, sel1(z0, z1))) → c51(SEL(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(sel(x0, quote(z0))) → c51(SEL(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(sel(dbl(z0), x1)) → c51(SEL(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(sel(0, x1)) → c51(SEL(ok(0), proper(x1)), PROPER(0), PROPER(x1))
PROPER(sel(s(z0), x1)) → c51(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(sel(dbls(z0), x1)) → c51(SEL(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(sel(nil, x1)) → c51(SEL(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
PROPER(sel(cons(z0, z1), x1)) → c51(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(sel(sel(z0, z1), x1)) → c51(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(sel(indx(z0, z1), x1)) → c51(SEL(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(sel(from(z0), x1)) → c51(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(sel(dbl1(z0), x1)) → c51(SEL(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(sel(01, x1)) → c51(SEL(ok(01), proper(x1)), PROPER(01), PROPER(x1))
PROPER(sel(s1(z0), x1)) → c51(SEL(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(sel(sel1(z0, z1), x1)) → c51(SEL(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(sel(quote(z0), x1)) → c51(SEL(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
S tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(indx(z0, z1)) → c52(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c53(FROM(proper(z0)), PROPER(z0))
PROPER(dbl1(z0)) → c54(DBL1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c56(S1(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c57(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)))
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0))))))
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0))))))
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0)))
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(indx(sel1(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(indx(sel1(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel1(z0, z2)), x1), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(indx(quote(dbl(z0)), x1)) → c21(INDX(mark(dbl1(z0)), x1), ACTIVE(quote(dbl(z0))))
ACTIVE(indx(quote(sel(z0, z1)), x1)) → c21(INDX(mark(sel1(z0, z1)), x1), ACTIVE(quote(sel(z0, z1))))
ACTIVE(indx(dbl(z0), x1)) → c21(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
ACTIVE(indx(dbls(z0), x1)) → c21(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(indx(z0, z1), x1)) → c21(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1)))
ACTIVE(indx(dbl1(z0), x1)) → c21(INDX(dbl1(active(z0)), x1), ACTIVE(dbl1(z0)))
ACTIVE(indx(s1(z0), x1)) → c21(INDX(s1(active(z0)), x1), ACTIVE(s1(z0)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(active(z0), z1), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(z0, active(z1)), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(quote(z0), x1)) → c21(INDX(quote(active(z0)), x1), ACTIVE(quote(z0)))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)))
ACTIVE(indx(dbl(0), x1)) → c21(INDX(mark(0), x1))
ACTIVE(indx(dbls(nil), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(indx(indx(nil, z0), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0))))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1))
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0)))
ACTIVE(dbl1(sel(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl1(sel(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl1(sel1(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl1(sel1(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl1(quote(dbl(z0)))) → c22(DBL1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl1(quote(sel(z0, z1)))) → c22(DBL1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl1(dbl(z0))) → c22(DBL1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl1(dbls(z0))) → c22(DBL1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(indx(z0, z1))) → c22(DBL1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl1(dbl1(z0))) → c22(DBL1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl1(s1(z0))) → c22(DBL1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(quote(z0))) → c22(DBL1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(dbl1(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(dbl(0))) → c22(DBL1(mark(0)))
ACTIVE(dbl1(dbls(nil))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(indx(nil, z0))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(dbl1(0))) → c22(DBL1(mark(01)))
ACTIVE(dbl(dbl1(s(z0)))) → c4(DBL(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(DBLS(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(INDX(mark(s1(s1(dbl1(z0)))), x1))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(DBL1(mark(s(s(dbl(z0))))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(ACTIVE(dbl(s(z0))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(DBL1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(DBL1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl1(from(z0))) → c4(DBL1(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl1(from(z0))) → c4(ACTIVE(from(z0)))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(DBL1(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(s1(sel(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(s1(sel(s(z0), cons(z1, z2)))) → c23(S1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(s1(sel1(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(s1(sel1(s(z0), cons(z1, z2)))) → c23(S1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(s1(quote(dbl(z0)))) → c23(S1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(s1(quote(sel(z0, z1)))) → c23(S1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(s1(dbl(z0))) → c23(S1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(s1(dbls(z0))) → c23(S1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(s1(indx(z0, z1))) → c23(S1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(s1(dbl1(z0))) → c23(S1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(s1(s1(z0))) → c23(S1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(quote(z0))) → c23(S1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(s1(dbl(0))) → c23(S1(mark(0)))
ACTIVE(s1(dbls(nil))) → c23(S1(mark(nil)))
ACTIVE(s1(indx(nil, z0))) → c23(S1(mark(nil)))
ACTIVE(s1(dbl1(0))) → c23(S1(mark(01)))
ACTIVE(s1(dbl(s(z0)))) → c6(S1(mark(s(s(dbl(z0))))))
ACTIVE(s1(dbl(s(z0)))) → c6(ACTIVE(dbl(s(z0))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(S1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(S1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(s1(from(z0))) → c6(S1(mark(cons(z0, from(s(z0))))))
ACTIVE(s1(from(z0))) → c6(ACTIVE(from(z0)))
ACTIVE(s1(dbl1(s(z0)))) → c6(S1(mark(s1(s1(dbl1(z0))))))
ACTIVE(s1(dbl1(s(z0)))) → c6(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(sel(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(quote(sel(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(quote(sel1(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(quote(sel1(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(quote(quote(dbl(z0)))) → c26(QUOTE(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(quote(quote(sel(z0, z1)))) → c26(QUOTE(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(quote(dbl(z0))) → c26(QUOTE(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(quote(dbls(z0))) → c26(QUOTE(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(quote(indx(z0, z1))) → c26(QUOTE(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(quote(dbl1(z0))) → c26(QUOTE(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(quote(s1(z0))) → c26(QUOTE(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(quote(z0))) → c26(QUOTE(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(quote(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(quote(0))) → c22(DBL1(mark(01)))
ACTIVE(s1(quote(0))) → c23(S1(mark(01)))
ACTIVE(quote(dbl(0))) → c26(QUOTE(mark(0)))
ACTIVE(quote(dbls(nil))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(indx(nil, z0))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(dbl1(0))) → c26(QUOTE(mark(01)))
ACTIVE(quote(quote(0))) → c26(QUOTE(mark(01)))
ACTIVE(dbl(quote(s(z0)))) → c7(DBL(mark(s1(quote(z0)))))
ACTIVE(dbl(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(s(z0)))) → c7(DBLS(mark(s1(quote(z0)))))
ACTIVE(dbls(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(indx(quote(s(z0)), x1)) → c7(INDX(mark(s1(quote(z0))), x1))
ACTIVE(indx(quote(s(z0)), x1)) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbl1(quote(s(z0)))) → c7(DBL1(mark(s1(quote(z0)))))
ACTIVE(dbl1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(s1(quote(s(z0)))) → c7(S1(mark(s1(quote(z0)))))
ACTIVE(s1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(quote(dbl(s(z0)))) → c7(QUOTE(mark(s(s(dbl(z0))))))
ACTIVE(quote(dbl(s(z0)))) → c7(ACTIVE(dbl(s(z0))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(QUOTE(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(QUOTE(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(quote(from(z0))) → c7(QUOTE(mark(cons(z0, from(s(z0))))))
ACTIVE(quote(from(z0))) → c7(ACTIVE(from(z0)))
ACTIVE(quote(dbl1(s(z0)))) → c7(QUOTE(mark(s1(s1(dbl1(z0))))))
ACTIVE(quote(dbl1(s(z0)))) → c7(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(quote(s(z0)))) → c7(QUOTE(mark(s1(quote(z0)))))
ACTIVE(quote(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
PROPER(dbl(dbl(z0))) → c45(DBL(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbl(s(z0))) → c45(DBL(s(proper(z0))), PROPER(s(z0)))
PROPER(dbl(dbls(z0))) → c45(DBL(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbl(cons(z0, z1))) → c45(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbl(sel(z0, z1))) → c45(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbl(indx(z0, z1))) → c45(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbl(from(z0))) → c45(DBL(from(proper(z0))), PROPER(from(z0)))
PROPER(dbl(dbl1(z0))) → c45(DBL(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbl(s1(z0))) → c45(DBL(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbl(sel1(z0, z1))) → c45(DBL(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbl(quote(z0))) → c45(DBL(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbl(0)) → c45(DBL(ok(0)))
PROPER(dbl(nil)) → c45(DBL(ok(nil)))
PROPER(dbl(01)) → c45(DBL(ok(01)))
PROPER(s(dbl(z0))) → c47(S(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(s(s(z0))) → c47(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(dbls(z0))) → c47(S(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(s(cons(z0, z1))) → c47(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(sel(z0, z1))) → c47(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(s(indx(z0, z1))) → c47(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(s(from(z0))) → c47(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(dbl1(z0))) → c47(S(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(s(s1(z0))) → c47(S(s1(proper(z0))), PROPER(s1(z0)))
PROPER(s(sel1(z0, z1))) → c47(S(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(s(quote(z0))) → c47(S(quote(proper(z0))), PROPER(quote(z0)))
PROPER(s(0)) → c47(S(ok(0)))
PROPER(s(nil)) → c47(S(ok(nil)))
PROPER(s(01)) → c47(S(ok(01)))
PROPER(dbls(dbl(z0))) → c48(DBLS(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbls(s(z0))) → c48(DBLS(s(proper(z0))), PROPER(s(z0)))
PROPER(dbls(dbls(z0))) → c48(DBLS(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbls(cons(z0, z1))) → c48(DBLS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbls(sel(z0, z1))) → c48(DBLS(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbls(indx(z0, z1))) → c48(DBLS(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbls(from(z0))) → c48(DBLS(from(proper(z0))), PROPER(from(z0)))
PROPER(dbls(dbl1(z0))) → c48(DBLS(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbls(s1(z0))) → c48(DBLS(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbls(sel1(z0, z1))) → c48(DBLS(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbls(quote(z0))) → c48(DBLS(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbls(0)) → c48(DBLS(ok(0)))
PROPER(dbls(nil)) → c48(DBLS(ok(nil)))
PROPER(dbls(01)) → c48(DBLS(ok(01)))
PROPER(cons(x0, dbl(z0))) → c50(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(cons(x0, s(z0))) → c50(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, dbls(z0))) → c50(CONS(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(cons(x0, cons(z0, z1))) → c50(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, sel(z0, z1))) → c50(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(cons(x0, indx(z0, z1))) → c50(CONS(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(cons(x0, from(z0))) → c50(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, dbl1(z0))) → c50(CONS(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(cons(x0, s1(z0))) → c50(CONS(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(cons(x0, sel1(z0, z1))) → c50(CONS(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(cons(x0, quote(z0))) → c50(CONS(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(cons(dbl(z0), x1)) → c50(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(cons(s(z0), x1)) → c50(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(dbls(z0), x1)) → c50(CONS(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c50(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(sel(z0, z1), x1)) → c50(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(cons(indx(z0, z1), x1)) → c50(CONS(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c50(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(dbl1(z0), x1)) → c50(CONS(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(cons(s1(z0), x1)) → c50(CONS(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(cons(sel1(z0, z1), x1)) → c50(CONS(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(cons(quote(z0), x1)) → c50(CONS(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c50(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c50(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, 01)) → c50(CONS(proper(x0), ok(01)), PROPER(x0))
PROPER(cons(0, x1)) → c50(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c50(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(01, x1)) → c50(CONS(ok(01), proper(x1)), PROPER(x1))
PROPER(sel(x0, dbl(z0))) → c51(SEL(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(sel(x0, 0)) → c51(SEL(proper(x0), ok(0)), PROPER(x0), PROPER(0))
PROPER(sel(x0, s(z0))) → c51(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(sel(x0, dbls(z0))) → c51(SEL(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(sel(x0, nil)) → c51(SEL(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
PROPER(sel(x0, cons(z0, z1))) → c51(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(sel(x0, sel(z0, z1))) → c51(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(sel(x0, indx(z0, z1))) → c51(SEL(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(sel(x0, from(z0))) → c51(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(sel(x0, dbl1(z0))) → c51(SEL(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(sel(x0, 01)) → c51(SEL(proper(x0), ok(01)), PROPER(x0), PROPER(01))
PROPER(sel(x0, s1(z0))) → c51(SEL(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(sel(x0, sel1(z0, z1))) → c51(SEL(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(sel(x0, quote(z0))) → c51(SEL(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(sel(dbl(z0), x1)) → c51(SEL(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(sel(0, x1)) → c51(SEL(ok(0), proper(x1)), PROPER(0), PROPER(x1))
PROPER(sel(s(z0), x1)) → c51(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(sel(dbls(z0), x1)) → c51(SEL(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(sel(nil, x1)) → c51(SEL(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
PROPER(sel(cons(z0, z1), x1)) → c51(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(sel(sel(z0, z1), x1)) → c51(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(sel(indx(z0, z1), x1)) → c51(SEL(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(sel(from(z0), x1)) → c51(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(sel(dbl1(z0), x1)) → c51(SEL(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(sel(01, x1)) → c51(SEL(ok(01), proper(x1)), PROPER(01), PROPER(x1))
PROPER(sel(s1(z0), x1)) → c51(SEL(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(sel(sel1(z0, z1), x1)) → c51(SEL(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(sel(quote(z0), x1)) → c51(SEL(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
K tuples:none
Defined Rule Symbols:
active, s, dbl, cons, dbls, sel, indx, s1, dbl1, sel1, quote, proper, from
Defined Pair Symbols:
ACTIVE, DBL, DBLS, SEL, INDX, DBL1, S1, SEL1, QUOTE, PROPER, S, CONS, FROM, TOP
Compound Symbols:
c5, c12, c15, c16, c19, c20, c24, c25, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c52, c53, c54, c56, c57, c58, c59, c60, c61, c62, c63, c8, c, c17, c17, c1, c18, c18, c2, c21, c21, c3, c22, c22, c4, c23, c23, c6, c26, c26, c7, c45, c45, c47, c47, c48, c48, c50, c50, c51
(65) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 6 trailing tuple parts
(66) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(dbl(0)) → mark(0)
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
active(dbls(nil)) → mark(nil)
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1)))
active(sel(0, cons(z0, z1))) → mark(z0)
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
active(indx(nil, z0)) → mark(nil)
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2)))
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(dbl1(0)) → mark(01)
active(dbl1(s(z0))) → mark(s1(s1(dbl1(z0))))
active(sel1(0, cons(z0, z1))) → mark(z0)
active(sel1(s(z0), cons(z1, z2))) → mark(sel1(z0, z2))
active(quote(0)) → mark(01)
active(quote(s(z0))) → mark(s1(quote(z0)))
active(quote(dbl(z0))) → mark(dbl1(z0))
active(quote(sel(z0, z1))) → mark(sel1(z0, z1))
active(dbl(z0)) → dbl(active(z0))
active(dbls(z0)) → dbls(active(z0))
active(sel(z0, z1)) → sel(active(z0), z1)
active(sel(z0, z1)) → sel(z0, active(z1))
active(indx(z0, z1)) → indx(active(z0), z1)
active(dbl1(z0)) → dbl1(active(z0))
active(s1(z0)) → s1(active(z0))
active(sel1(z0, z1)) → sel1(active(z0), z1)
active(sel1(z0, z1)) → sel1(z0, active(z1))
active(quote(z0)) → quote(active(z0))
s(ok(z0)) → ok(s(z0))
dbl(mark(z0)) → mark(dbl(z0))
dbl(ok(z0)) → ok(dbl(z0))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
dbls(mark(z0)) → mark(dbls(z0))
dbls(ok(z0)) → ok(dbls(z0))
sel(mark(z0), z1) → mark(sel(z0, z1))
sel(z0, mark(z1)) → mark(sel(z0, z1))
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
indx(mark(z0), z1) → mark(indx(z0, z1))
indx(ok(z0), ok(z1)) → ok(indx(z0, z1))
s1(mark(z0)) → mark(s1(z0))
s1(ok(z0)) → ok(s1(z0))
dbl1(mark(z0)) → mark(dbl1(z0))
dbl1(ok(z0)) → ok(dbl1(z0))
sel1(mark(z0), z1) → mark(sel1(z0, z1))
sel1(z0, mark(z1)) → mark(sel1(z0, z1))
sel1(ok(z0), ok(z1)) → ok(sel1(z0, z1))
quote(mark(z0)) → mark(quote(z0))
quote(ok(z0)) → ok(quote(z0))
proper(dbl(z0)) → dbl(proper(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(dbls(z0)) → dbls(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
proper(indx(z0, z1)) → indx(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(dbl1(z0)) → dbl1(proper(z0))
proper(01) → ok(01)
proper(s1(z0)) → s1(proper(z0))
proper(sel1(z0, z1)) → sel1(proper(z0), proper(z1))
proper(quote(z0)) → quote(proper(z0))
from(ok(z0)) → ok(from(z0))
Tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(indx(z0, z1)) → c52(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c53(FROM(proper(z0)), PROPER(z0))
PROPER(dbl1(z0)) → c54(DBL1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c56(S1(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c57(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)))
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0))))))
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0))))))
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0)))
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(indx(sel1(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(indx(sel1(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel1(z0, z2)), x1), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(indx(quote(dbl(z0)), x1)) → c21(INDX(mark(dbl1(z0)), x1), ACTIVE(quote(dbl(z0))))
ACTIVE(indx(quote(sel(z0, z1)), x1)) → c21(INDX(mark(sel1(z0, z1)), x1), ACTIVE(quote(sel(z0, z1))))
ACTIVE(indx(dbl(z0), x1)) → c21(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
ACTIVE(indx(dbls(z0), x1)) → c21(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(indx(z0, z1), x1)) → c21(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1)))
ACTIVE(indx(dbl1(z0), x1)) → c21(INDX(dbl1(active(z0)), x1), ACTIVE(dbl1(z0)))
ACTIVE(indx(s1(z0), x1)) → c21(INDX(s1(active(z0)), x1), ACTIVE(s1(z0)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(active(z0), z1), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(z0, active(z1)), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(quote(z0), x1)) → c21(INDX(quote(active(z0)), x1), ACTIVE(quote(z0)))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)))
ACTIVE(indx(dbl(0), x1)) → c21(INDX(mark(0), x1))
ACTIVE(indx(dbls(nil), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(indx(indx(nil, z0), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0))))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1))
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0)))
ACTIVE(dbl1(sel(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl1(sel(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl1(sel1(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl1(sel1(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl1(quote(dbl(z0)))) → c22(DBL1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl1(quote(sel(z0, z1)))) → c22(DBL1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl1(dbl(z0))) → c22(DBL1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl1(dbls(z0))) → c22(DBL1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(indx(z0, z1))) → c22(DBL1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl1(dbl1(z0))) → c22(DBL1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl1(s1(z0))) → c22(DBL1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(quote(z0))) → c22(DBL1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(dbl1(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(dbl(0))) → c22(DBL1(mark(0)))
ACTIVE(dbl1(dbls(nil))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(indx(nil, z0))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(dbl1(0))) → c22(DBL1(mark(01)))
ACTIVE(dbl(dbl1(s(z0)))) → c4(DBL(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(DBLS(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(INDX(mark(s1(s1(dbl1(z0)))), x1))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(DBL1(mark(s(s(dbl(z0))))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(ACTIVE(dbl(s(z0))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(DBL1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(DBL1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl1(from(z0))) → c4(DBL1(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl1(from(z0))) → c4(ACTIVE(from(z0)))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(DBL1(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(s1(sel(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(s1(sel(s(z0), cons(z1, z2)))) → c23(S1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(s1(sel1(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(s1(sel1(s(z0), cons(z1, z2)))) → c23(S1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(s1(quote(dbl(z0)))) → c23(S1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(s1(quote(sel(z0, z1)))) → c23(S1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(s1(dbl(z0))) → c23(S1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(s1(dbls(z0))) → c23(S1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(s1(indx(z0, z1))) → c23(S1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(s1(dbl1(z0))) → c23(S1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(s1(s1(z0))) → c23(S1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(quote(z0))) → c23(S1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(s1(dbl(0))) → c23(S1(mark(0)))
ACTIVE(s1(dbls(nil))) → c23(S1(mark(nil)))
ACTIVE(s1(indx(nil, z0))) → c23(S1(mark(nil)))
ACTIVE(s1(dbl1(0))) → c23(S1(mark(01)))
ACTIVE(s1(dbl(s(z0)))) → c6(S1(mark(s(s(dbl(z0))))))
ACTIVE(s1(dbl(s(z0)))) → c6(ACTIVE(dbl(s(z0))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(S1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(S1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(s1(from(z0))) → c6(S1(mark(cons(z0, from(s(z0))))))
ACTIVE(s1(from(z0))) → c6(ACTIVE(from(z0)))
ACTIVE(s1(dbl1(s(z0)))) → c6(S1(mark(s1(s1(dbl1(z0))))))
ACTIVE(s1(dbl1(s(z0)))) → c6(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(sel(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(quote(sel(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(quote(sel1(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(quote(sel1(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(quote(quote(dbl(z0)))) → c26(QUOTE(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(quote(quote(sel(z0, z1)))) → c26(QUOTE(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(quote(dbl(z0))) → c26(QUOTE(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(quote(dbls(z0))) → c26(QUOTE(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(quote(indx(z0, z1))) → c26(QUOTE(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(quote(dbl1(z0))) → c26(QUOTE(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(quote(s1(z0))) → c26(QUOTE(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(quote(z0))) → c26(QUOTE(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(quote(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(quote(0))) → c22(DBL1(mark(01)))
ACTIVE(s1(quote(0))) → c23(S1(mark(01)))
ACTIVE(quote(dbl(0))) → c26(QUOTE(mark(0)))
ACTIVE(quote(dbls(nil))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(indx(nil, z0))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(dbl1(0))) → c26(QUOTE(mark(01)))
ACTIVE(quote(quote(0))) → c26(QUOTE(mark(01)))
ACTIVE(dbl(quote(s(z0)))) → c7(DBL(mark(s1(quote(z0)))))
ACTIVE(dbl(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(s(z0)))) → c7(DBLS(mark(s1(quote(z0)))))
ACTIVE(dbls(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(indx(quote(s(z0)), x1)) → c7(INDX(mark(s1(quote(z0))), x1))
ACTIVE(indx(quote(s(z0)), x1)) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbl1(quote(s(z0)))) → c7(DBL1(mark(s1(quote(z0)))))
ACTIVE(dbl1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(s1(quote(s(z0)))) → c7(S1(mark(s1(quote(z0)))))
ACTIVE(s1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(quote(dbl(s(z0)))) → c7(QUOTE(mark(s(s(dbl(z0))))))
ACTIVE(quote(dbl(s(z0)))) → c7(ACTIVE(dbl(s(z0))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(QUOTE(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(QUOTE(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(quote(from(z0))) → c7(QUOTE(mark(cons(z0, from(s(z0))))))
ACTIVE(quote(from(z0))) → c7(ACTIVE(from(z0)))
ACTIVE(quote(dbl1(s(z0)))) → c7(QUOTE(mark(s1(s1(dbl1(z0))))))
ACTIVE(quote(dbl1(s(z0)))) → c7(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(quote(s(z0)))) → c7(QUOTE(mark(s1(quote(z0)))))
ACTIVE(quote(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
PROPER(dbl(dbl(z0))) → c45(DBL(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbl(s(z0))) → c45(DBL(s(proper(z0))), PROPER(s(z0)))
PROPER(dbl(dbls(z0))) → c45(DBL(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbl(cons(z0, z1))) → c45(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbl(sel(z0, z1))) → c45(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbl(indx(z0, z1))) → c45(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbl(from(z0))) → c45(DBL(from(proper(z0))), PROPER(from(z0)))
PROPER(dbl(dbl1(z0))) → c45(DBL(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbl(s1(z0))) → c45(DBL(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbl(sel1(z0, z1))) → c45(DBL(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbl(quote(z0))) → c45(DBL(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbl(0)) → c45(DBL(ok(0)))
PROPER(dbl(nil)) → c45(DBL(ok(nil)))
PROPER(dbl(01)) → c45(DBL(ok(01)))
PROPER(s(dbl(z0))) → c47(S(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(s(s(z0))) → c47(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(dbls(z0))) → c47(S(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(s(cons(z0, z1))) → c47(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(sel(z0, z1))) → c47(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(s(indx(z0, z1))) → c47(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(s(from(z0))) → c47(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(dbl1(z0))) → c47(S(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(s(s1(z0))) → c47(S(s1(proper(z0))), PROPER(s1(z0)))
PROPER(s(sel1(z0, z1))) → c47(S(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(s(quote(z0))) → c47(S(quote(proper(z0))), PROPER(quote(z0)))
PROPER(s(0)) → c47(S(ok(0)))
PROPER(s(nil)) → c47(S(ok(nil)))
PROPER(s(01)) → c47(S(ok(01)))
PROPER(dbls(dbl(z0))) → c48(DBLS(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbls(s(z0))) → c48(DBLS(s(proper(z0))), PROPER(s(z0)))
PROPER(dbls(dbls(z0))) → c48(DBLS(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbls(cons(z0, z1))) → c48(DBLS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbls(sel(z0, z1))) → c48(DBLS(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbls(indx(z0, z1))) → c48(DBLS(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbls(from(z0))) → c48(DBLS(from(proper(z0))), PROPER(from(z0)))
PROPER(dbls(dbl1(z0))) → c48(DBLS(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbls(s1(z0))) → c48(DBLS(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbls(sel1(z0, z1))) → c48(DBLS(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbls(quote(z0))) → c48(DBLS(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbls(0)) → c48(DBLS(ok(0)))
PROPER(dbls(nil)) → c48(DBLS(ok(nil)))
PROPER(dbls(01)) → c48(DBLS(ok(01)))
PROPER(cons(x0, dbl(z0))) → c50(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(cons(x0, s(z0))) → c50(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, dbls(z0))) → c50(CONS(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(cons(x0, cons(z0, z1))) → c50(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, sel(z0, z1))) → c50(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(cons(x0, indx(z0, z1))) → c50(CONS(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(cons(x0, from(z0))) → c50(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, dbl1(z0))) → c50(CONS(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(cons(x0, s1(z0))) → c50(CONS(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(cons(x0, sel1(z0, z1))) → c50(CONS(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(cons(x0, quote(z0))) → c50(CONS(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(cons(dbl(z0), x1)) → c50(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(cons(s(z0), x1)) → c50(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(dbls(z0), x1)) → c50(CONS(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c50(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(sel(z0, z1), x1)) → c50(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(cons(indx(z0, z1), x1)) → c50(CONS(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c50(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(dbl1(z0), x1)) → c50(CONS(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(cons(s1(z0), x1)) → c50(CONS(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(cons(sel1(z0, z1), x1)) → c50(CONS(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(cons(quote(z0), x1)) → c50(CONS(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c50(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c50(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, 01)) → c50(CONS(proper(x0), ok(01)), PROPER(x0))
PROPER(cons(0, x1)) → c50(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c50(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(01, x1)) → c50(CONS(ok(01), proper(x1)), PROPER(x1))
PROPER(sel(x0, dbl(z0))) → c51(SEL(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(sel(x0, s(z0))) → c51(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(sel(x0, dbls(z0))) → c51(SEL(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(sel(x0, cons(z0, z1))) → c51(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(sel(x0, sel(z0, z1))) → c51(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(sel(x0, indx(z0, z1))) → c51(SEL(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(sel(x0, from(z0))) → c51(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(sel(x0, dbl1(z0))) → c51(SEL(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(sel(x0, s1(z0))) → c51(SEL(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(sel(x0, sel1(z0, z1))) → c51(SEL(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(sel(x0, quote(z0))) → c51(SEL(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(sel(dbl(z0), x1)) → c51(SEL(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(sel(s(z0), x1)) → c51(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(sel(dbls(z0), x1)) → c51(SEL(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(sel(cons(z0, z1), x1)) → c51(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(sel(sel(z0, z1), x1)) → c51(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(sel(indx(z0, z1), x1)) → c51(SEL(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(sel(from(z0), x1)) → c51(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(sel(dbl1(z0), x1)) → c51(SEL(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(sel(s1(z0), x1)) → c51(SEL(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(sel(sel1(z0, z1), x1)) → c51(SEL(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(sel(quote(z0), x1)) → c51(SEL(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(sel(x0, 0)) → c51(SEL(proper(x0), ok(0)), PROPER(x0))
PROPER(sel(x0, nil)) → c51(SEL(proper(x0), ok(nil)), PROPER(x0))
PROPER(sel(x0, 01)) → c51(SEL(proper(x0), ok(01)), PROPER(x0))
PROPER(sel(0, x1)) → c51(SEL(ok(0), proper(x1)), PROPER(x1))
PROPER(sel(nil, x1)) → c51(SEL(ok(nil), proper(x1)), PROPER(x1))
PROPER(sel(01, x1)) → c51(SEL(ok(01), proper(x1)), PROPER(x1))
S tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(indx(z0, z1)) → c52(INDX(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c53(FROM(proper(z0)), PROPER(z0))
PROPER(dbl1(z0)) → c54(DBL1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c56(S1(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c57(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)))
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0))))))
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0))))))
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0)))
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(indx(sel1(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(indx(sel1(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel1(z0, z2)), x1), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(indx(quote(dbl(z0)), x1)) → c21(INDX(mark(dbl1(z0)), x1), ACTIVE(quote(dbl(z0))))
ACTIVE(indx(quote(sel(z0, z1)), x1)) → c21(INDX(mark(sel1(z0, z1)), x1), ACTIVE(quote(sel(z0, z1))))
ACTIVE(indx(dbl(z0), x1)) → c21(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
ACTIVE(indx(dbls(z0), x1)) → c21(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(indx(z0, z1), x1)) → c21(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1)))
ACTIVE(indx(dbl1(z0), x1)) → c21(INDX(dbl1(active(z0)), x1), ACTIVE(dbl1(z0)))
ACTIVE(indx(s1(z0), x1)) → c21(INDX(s1(active(z0)), x1), ACTIVE(s1(z0)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(active(z0), z1), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(z0, active(z1)), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(quote(z0), x1)) → c21(INDX(quote(active(z0)), x1), ACTIVE(quote(z0)))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)))
ACTIVE(indx(dbl(0), x1)) → c21(INDX(mark(0), x1))
ACTIVE(indx(dbls(nil), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(indx(indx(nil, z0), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0))))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1))
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0)))
ACTIVE(dbl1(sel(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl1(sel(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl1(sel1(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl1(sel1(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl1(quote(dbl(z0)))) → c22(DBL1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl1(quote(sel(z0, z1)))) → c22(DBL1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl1(dbl(z0))) → c22(DBL1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl1(dbls(z0))) → c22(DBL1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(indx(z0, z1))) → c22(DBL1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl1(dbl1(z0))) → c22(DBL1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl1(s1(z0))) → c22(DBL1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(quote(z0))) → c22(DBL1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(dbl1(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(dbl(0))) → c22(DBL1(mark(0)))
ACTIVE(dbl1(dbls(nil))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(indx(nil, z0))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(dbl1(0))) → c22(DBL1(mark(01)))
ACTIVE(dbl(dbl1(s(z0)))) → c4(DBL(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(DBLS(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(INDX(mark(s1(s1(dbl1(z0)))), x1))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(DBL1(mark(s(s(dbl(z0))))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(ACTIVE(dbl(s(z0))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(DBL1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(DBL1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl1(from(z0))) → c4(DBL1(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl1(from(z0))) → c4(ACTIVE(from(z0)))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(DBL1(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(s1(sel(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(s1(sel(s(z0), cons(z1, z2)))) → c23(S1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(s1(sel1(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(s1(sel1(s(z0), cons(z1, z2)))) → c23(S1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(s1(quote(dbl(z0)))) → c23(S1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(s1(quote(sel(z0, z1)))) → c23(S1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(s1(dbl(z0))) → c23(S1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(s1(dbls(z0))) → c23(S1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(s1(indx(z0, z1))) → c23(S1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(s1(dbl1(z0))) → c23(S1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(s1(s1(z0))) → c23(S1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(quote(z0))) → c23(S1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(s1(dbl(0))) → c23(S1(mark(0)))
ACTIVE(s1(dbls(nil))) → c23(S1(mark(nil)))
ACTIVE(s1(indx(nil, z0))) → c23(S1(mark(nil)))
ACTIVE(s1(dbl1(0))) → c23(S1(mark(01)))
ACTIVE(s1(dbl(s(z0)))) → c6(S1(mark(s(s(dbl(z0))))))
ACTIVE(s1(dbl(s(z0)))) → c6(ACTIVE(dbl(s(z0))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(S1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(S1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(s1(from(z0))) → c6(S1(mark(cons(z0, from(s(z0))))))
ACTIVE(s1(from(z0))) → c6(ACTIVE(from(z0)))
ACTIVE(s1(dbl1(s(z0)))) → c6(S1(mark(s1(s1(dbl1(z0))))))
ACTIVE(s1(dbl1(s(z0)))) → c6(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(sel(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(quote(sel(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(quote(sel1(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(quote(sel1(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(quote(quote(dbl(z0)))) → c26(QUOTE(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(quote(quote(sel(z0, z1)))) → c26(QUOTE(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(quote(dbl(z0))) → c26(QUOTE(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(quote(dbls(z0))) → c26(QUOTE(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(quote(indx(z0, z1))) → c26(QUOTE(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(quote(dbl1(z0))) → c26(QUOTE(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(quote(s1(z0))) → c26(QUOTE(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(quote(z0))) → c26(QUOTE(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(quote(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(quote(0))) → c22(DBL1(mark(01)))
ACTIVE(s1(quote(0))) → c23(S1(mark(01)))
ACTIVE(quote(dbl(0))) → c26(QUOTE(mark(0)))
ACTIVE(quote(dbls(nil))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(indx(nil, z0))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(dbl1(0))) → c26(QUOTE(mark(01)))
ACTIVE(quote(quote(0))) → c26(QUOTE(mark(01)))
ACTIVE(dbl(quote(s(z0)))) → c7(DBL(mark(s1(quote(z0)))))
ACTIVE(dbl(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(s(z0)))) → c7(DBLS(mark(s1(quote(z0)))))
ACTIVE(dbls(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(indx(quote(s(z0)), x1)) → c7(INDX(mark(s1(quote(z0))), x1))
ACTIVE(indx(quote(s(z0)), x1)) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbl1(quote(s(z0)))) → c7(DBL1(mark(s1(quote(z0)))))
ACTIVE(dbl1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(s1(quote(s(z0)))) → c7(S1(mark(s1(quote(z0)))))
ACTIVE(s1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(quote(dbl(s(z0)))) → c7(QUOTE(mark(s(s(dbl(z0))))))
ACTIVE(quote(dbl(s(z0)))) → c7(ACTIVE(dbl(s(z0))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(QUOTE(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(QUOTE(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(quote(from(z0))) → c7(QUOTE(mark(cons(z0, from(s(z0))))))
ACTIVE(quote(from(z0))) → c7(ACTIVE(from(z0)))
ACTIVE(quote(dbl1(s(z0)))) → c7(QUOTE(mark(s1(s1(dbl1(z0))))))
ACTIVE(quote(dbl1(s(z0)))) → c7(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(quote(s(z0)))) → c7(QUOTE(mark(s1(quote(z0)))))
ACTIVE(quote(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
PROPER(dbl(dbl(z0))) → c45(DBL(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbl(s(z0))) → c45(DBL(s(proper(z0))), PROPER(s(z0)))
PROPER(dbl(dbls(z0))) → c45(DBL(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbl(cons(z0, z1))) → c45(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbl(sel(z0, z1))) → c45(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbl(indx(z0, z1))) → c45(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbl(from(z0))) → c45(DBL(from(proper(z0))), PROPER(from(z0)))
PROPER(dbl(dbl1(z0))) → c45(DBL(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbl(s1(z0))) → c45(DBL(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbl(sel1(z0, z1))) → c45(DBL(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbl(quote(z0))) → c45(DBL(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbl(0)) → c45(DBL(ok(0)))
PROPER(dbl(nil)) → c45(DBL(ok(nil)))
PROPER(dbl(01)) → c45(DBL(ok(01)))
PROPER(s(dbl(z0))) → c47(S(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(s(s(z0))) → c47(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(dbls(z0))) → c47(S(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(s(cons(z0, z1))) → c47(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(sel(z0, z1))) → c47(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(s(indx(z0, z1))) → c47(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(s(from(z0))) → c47(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(dbl1(z0))) → c47(S(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(s(s1(z0))) → c47(S(s1(proper(z0))), PROPER(s1(z0)))
PROPER(s(sel1(z0, z1))) → c47(S(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(s(quote(z0))) → c47(S(quote(proper(z0))), PROPER(quote(z0)))
PROPER(s(0)) → c47(S(ok(0)))
PROPER(s(nil)) → c47(S(ok(nil)))
PROPER(s(01)) → c47(S(ok(01)))
PROPER(dbls(dbl(z0))) → c48(DBLS(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbls(s(z0))) → c48(DBLS(s(proper(z0))), PROPER(s(z0)))
PROPER(dbls(dbls(z0))) → c48(DBLS(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbls(cons(z0, z1))) → c48(DBLS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbls(sel(z0, z1))) → c48(DBLS(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbls(indx(z0, z1))) → c48(DBLS(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbls(from(z0))) → c48(DBLS(from(proper(z0))), PROPER(from(z0)))
PROPER(dbls(dbl1(z0))) → c48(DBLS(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbls(s1(z0))) → c48(DBLS(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbls(sel1(z0, z1))) → c48(DBLS(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbls(quote(z0))) → c48(DBLS(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbls(0)) → c48(DBLS(ok(0)))
PROPER(dbls(nil)) → c48(DBLS(ok(nil)))
PROPER(dbls(01)) → c48(DBLS(ok(01)))
PROPER(cons(x0, dbl(z0))) → c50(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(cons(x0, s(z0))) → c50(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, dbls(z0))) → c50(CONS(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(cons(x0, cons(z0, z1))) → c50(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, sel(z0, z1))) → c50(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(cons(x0, indx(z0, z1))) → c50(CONS(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(cons(x0, from(z0))) → c50(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, dbl1(z0))) → c50(CONS(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(cons(x0, s1(z0))) → c50(CONS(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(cons(x0, sel1(z0, z1))) → c50(CONS(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(cons(x0, quote(z0))) → c50(CONS(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(cons(dbl(z0), x1)) → c50(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(cons(s(z0), x1)) → c50(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(dbls(z0), x1)) → c50(CONS(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c50(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(sel(z0, z1), x1)) → c50(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(cons(indx(z0, z1), x1)) → c50(CONS(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c50(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(dbl1(z0), x1)) → c50(CONS(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(cons(s1(z0), x1)) → c50(CONS(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(cons(sel1(z0, z1), x1)) → c50(CONS(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(cons(quote(z0), x1)) → c50(CONS(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c50(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c50(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, 01)) → c50(CONS(proper(x0), ok(01)), PROPER(x0))
PROPER(cons(0, x1)) → c50(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c50(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(01, x1)) → c50(CONS(ok(01), proper(x1)), PROPER(x1))
PROPER(sel(x0, dbl(z0))) → c51(SEL(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(sel(x0, s(z0))) → c51(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(sel(x0, dbls(z0))) → c51(SEL(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(sel(x0, cons(z0, z1))) → c51(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(sel(x0, sel(z0, z1))) → c51(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(sel(x0, indx(z0, z1))) → c51(SEL(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(sel(x0, from(z0))) → c51(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(sel(x0, dbl1(z0))) → c51(SEL(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(sel(x0, s1(z0))) → c51(SEL(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(sel(x0, sel1(z0, z1))) → c51(SEL(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(sel(x0, quote(z0))) → c51(SEL(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(sel(dbl(z0), x1)) → c51(SEL(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(sel(s(z0), x1)) → c51(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(sel(dbls(z0), x1)) → c51(SEL(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(sel(cons(z0, z1), x1)) → c51(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(sel(sel(z0, z1), x1)) → c51(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(sel(indx(z0, z1), x1)) → c51(SEL(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(sel(from(z0), x1)) → c51(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(sel(dbl1(z0), x1)) → c51(SEL(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(sel(s1(z0), x1)) → c51(SEL(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(sel(sel1(z0, z1), x1)) → c51(SEL(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(sel(quote(z0), x1)) → c51(SEL(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(sel(x0, 0)) → c51(SEL(proper(x0), ok(0)), PROPER(x0))
PROPER(sel(x0, nil)) → c51(SEL(proper(x0), ok(nil)), PROPER(x0))
PROPER(sel(x0, 01)) → c51(SEL(proper(x0), ok(01)), PROPER(x0))
PROPER(sel(0, x1)) → c51(SEL(ok(0), proper(x1)), PROPER(x1))
PROPER(sel(nil, x1)) → c51(SEL(ok(nil), proper(x1)), PROPER(x1))
PROPER(sel(01, x1)) → c51(SEL(ok(01), proper(x1)), PROPER(x1))
K tuples:none
Defined Rule Symbols:
active, s, dbl, cons, dbls, sel, indx, s1, dbl1, sel1, quote, proper, from
Defined Pair Symbols:
ACTIVE, DBL, DBLS, SEL, INDX, DBL1, S1, SEL1, QUOTE, PROPER, S, CONS, FROM, TOP
Compound Symbols:
c5, c12, c15, c16, c19, c20, c24, c25, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c52, c53, c54, c56, c57, c58, c59, c60, c61, c62, c63, c8, c, c17, c17, c1, c18, c18, c2, c21, c21, c3, c22, c22, c4, c23, c23, c6, c26, c26, c7, c45, c45, c47, c47, c48, c48, c50, c50, c51, c51
(67) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
PROPER(
indx(
z0,
z1)) →
c52(
INDX(
proper(
z0),
proper(
z1)),
PROPER(
z0),
PROPER(
z1)) by
PROPER(indx(x0, dbl(z0))) → c52(INDX(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(indx(x0, 0)) → c52(INDX(proper(x0), ok(0)), PROPER(x0), PROPER(0))
PROPER(indx(x0, s(z0))) → c52(INDX(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(indx(x0, dbls(z0))) → c52(INDX(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(indx(x0, nil)) → c52(INDX(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
PROPER(indx(x0, cons(z0, z1))) → c52(INDX(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(indx(x0, sel(z0, z1))) → c52(INDX(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(indx(x0, indx(z0, z1))) → c52(INDX(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(indx(x0, from(z0))) → c52(INDX(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(indx(x0, dbl1(z0))) → c52(INDX(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(indx(x0, 01)) → c52(INDX(proper(x0), ok(01)), PROPER(x0), PROPER(01))
PROPER(indx(x0, s1(z0))) → c52(INDX(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(indx(x0, sel1(z0, z1))) → c52(INDX(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(indx(x0, quote(z0))) → c52(INDX(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(indx(dbl(z0), x1)) → c52(INDX(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(indx(0, x1)) → c52(INDX(ok(0), proper(x1)), PROPER(0), PROPER(x1))
PROPER(indx(s(z0), x1)) → c52(INDX(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(indx(dbls(z0), x1)) → c52(INDX(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(indx(nil, x1)) → c52(INDX(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
PROPER(indx(cons(z0, z1), x1)) → c52(INDX(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(indx(sel(z0, z1), x1)) → c52(INDX(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(indx(indx(z0, z1), x1)) → c52(INDX(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(indx(from(z0), x1)) → c52(INDX(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(indx(dbl1(z0), x1)) → c52(INDX(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(indx(01, x1)) → c52(INDX(ok(01), proper(x1)), PROPER(01), PROPER(x1))
PROPER(indx(s1(z0), x1)) → c52(INDX(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(indx(sel1(z0, z1), x1)) → c52(INDX(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(indx(quote(z0), x1)) → c52(INDX(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
(68) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(dbl(0)) → mark(0)
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
active(dbls(nil)) → mark(nil)
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1)))
active(sel(0, cons(z0, z1))) → mark(z0)
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
active(indx(nil, z0)) → mark(nil)
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2)))
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(dbl1(0)) → mark(01)
active(dbl1(s(z0))) → mark(s1(s1(dbl1(z0))))
active(sel1(0, cons(z0, z1))) → mark(z0)
active(sel1(s(z0), cons(z1, z2))) → mark(sel1(z0, z2))
active(quote(0)) → mark(01)
active(quote(s(z0))) → mark(s1(quote(z0)))
active(quote(dbl(z0))) → mark(dbl1(z0))
active(quote(sel(z0, z1))) → mark(sel1(z0, z1))
active(dbl(z0)) → dbl(active(z0))
active(dbls(z0)) → dbls(active(z0))
active(sel(z0, z1)) → sel(active(z0), z1)
active(sel(z0, z1)) → sel(z0, active(z1))
active(indx(z0, z1)) → indx(active(z0), z1)
active(dbl1(z0)) → dbl1(active(z0))
active(s1(z0)) → s1(active(z0))
active(sel1(z0, z1)) → sel1(active(z0), z1)
active(sel1(z0, z1)) → sel1(z0, active(z1))
active(quote(z0)) → quote(active(z0))
s(ok(z0)) → ok(s(z0))
dbl(mark(z0)) → mark(dbl(z0))
dbl(ok(z0)) → ok(dbl(z0))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
dbls(mark(z0)) → mark(dbls(z0))
dbls(ok(z0)) → ok(dbls(z0))
sel(mark(z0), z1) → mark(sel(z0, z1))
sel(z0, mark(z1)) → mark(sel(z0, z1))
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
indx(mark(z0), z1) → mark(indx(z0, z1))
indx(ok(z0), ok(z1)) → ok(indx(z0, z1))
s1(mark(z0)) → mark(s1(z0))
s1(ok(z0)) → ok(s1(z0))
dbl1(mark(z0)) → mark(dbl1(z0))
dbl1(ok(z0)) → ok(dbl1(z0))
sel1(mark(z0), z1) → mark(sel1(z0, z1))
sel1(z0, mark(z1)) → mark(sel1(z0, z1))
sel1(ok(z0), ok(z1)) → ok(sel1(z0, z1))
quote(mark(z0)) → mark(quote(z0))
quote(ok(z0)) → ok(quote(z0))
proper(dbl(z0)) → dbl(proper(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(dbls(z0)) → dbls(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
proper(indx(z0, z1)) → indx(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(dbl1(z0)) → dbl1(proper(z0))
proper(01) → ok(01)
proper(s1(z0)) → s1(proper(z0))
proper(sel1(z0, z1)) → sel1(proper(z0), proper(z1))
proper(quote(z0)) → quote(proper(z0))
from(ok(z0)) → ok(from(z0))
Tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(from(z0)) → c53(FROM(proper(z0)), PROPER(z0))
PROPER(dbl1(z0)) → c54(DBL1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c56(S1(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c57(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)))
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0))))))
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0))))))
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0)))
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(indx(sel1(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(indx(sel1(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel1(z0, z2)), x1), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(indx(quote(dbl(z0)), x1)) → c21(INDX(mark(dbl1(z0)), x1), ACTIVE(quote(dbl(z0))))
ACTIVE(indx(quote(sel(z0, z1)), x1)) → c21(INDX(mark(sel1(z0, z1)), x1), ACTIVE(quote(sel(z0, z1))))
ACTIVE(indx(dbl(z0), x1)) → c21(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
ACTIVE(indx(dbls(z0), x1)) → c21(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(indx(z0, z1), x1)) → c21(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1)))
ACTIVE(indx(dbl1(z0), x1)) → c21(INDX(dbl1(active(z0)), x1), ACTIVE(dbl1(z0)))
ACTIVE(indx(s1(z0), x1)) → c21(INDX(s1(active(z0)), x1), ACTIVE(s1(z0)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(active(z0), z1), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(z0, active(z1)), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(quote(z0), x1)) → c21(INDX(quote(active(z0)), x1), ACTIVE(quote(z0)))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)))
ACTIVE(indx(dbl(0), x1)) → c21(INDX(mark(0), x1))
ACTIVE(indx(dbls(nil), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(indx(indx(nil, z0), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0))))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1))
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0)))
ACTIVE(dbl1(sel(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl1(sel(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl1(sel1(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl1(sel1(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl1(quote(dbl(z0)))) → c22(DBL1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl1(quote(sel(z0, z1)))) → c22(DBL1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl1(dbl(z0))) → c22(DBL1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl1(dbls(z0))) → c22(DBL1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(indx(z0, z1))) → c22(DBL1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl1(dbl1(z0))) → c22(DBL1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl1(s1(z0))) → c22(DBL1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(quote(z0))) → c22(DBL1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(dbl1(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(dbl(0))) → c22(DBL1(mark(0)))
ACTIVE(dbl1(dbls(nil))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(indx(nil, z0))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(dbl1(0))) → c22(DBL1(mark(01)))
ACTIVE(dbl(dbl1(s(z0)))) → c4(DBL(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(DBLS(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(INDX(mark(s1(s1(dbl1(z0)))), x1))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(DBL1(mark(s(s(dbl(z0))))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(ACTIVE(dbl(s(z0))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(DBL1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(DBL1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl1(from(z0))) → c4(DBL1(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl1(from(z0))) → c4(ACTIVE(from(z0)))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(DBL1(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(s1(sel(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(s1(sel(s(z0), cons(z1, z2)))) → c23(S1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(s1(sel1(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(s1(sel1(s(z0), cons(z1, z2)))) → c23(S1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(s1(quote(dbl(z0)))) → c23(S1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(s1(quote(sel(z0, z1)))) → c23(S1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(s1(dbl(z0))) → c23(S1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(s1(dbls(z0))) → c23(S1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(s1(indx(z0, z1))) → c23(S1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(s1(dbl1(z0))) → c23(S1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(s1(s1(z0))) → c23(S1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(quote(z0))) → c23(S1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(s1(dbl(0))) → c23(S1(mark(0)))
ACTIVE(s1(dbls(nil))) → c23(S1(mark(nil)))
ACTIVE(s1(indx(nil, z0))) → c23(S1(mark(nil)))
ACTIVE(s1(dbl1(0))) → c23(S1(mark(01)))
ACTIVE(s1(dbl(s(z0)))) → c6(S1(mark(s(s(dbl(z0))))))
ACTIVE(s1(dbl(s(z0)))) → c6(ACTIVE(dbl(s(z0))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(S1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(S1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(s1(from(z0))) → c6(S1(mark(cons(z0, from(s(z0))))))
ACTIVE(s1(from(z0))) → c6(ACTIVE(from(z0)))
ACTIVE(s1(dbl1(s(z0)))) → c6(S1(mark(s1(s1(dbl1(z0))))))
ACTIVE(s1(dbl1(s(z0)))) → c6(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(sel(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(quote(sel(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(quote(sel1(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(quote(sel1(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(quote(quote(dbl(z0)))) → c26(QUOTE(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(quote(quote(sel(z0, z1)))) → c26(QUOTE(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(quote(dbl(z0))) → c26(QUOTE(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(quote(dbls(z0))) → c26(QUOTE(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(quote(indx(z0, z1))) → c26(QUOTE(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(quote(dbl1(z0))) → c26(QUOTE(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(quote(s1(z0))) → c26(QUOTE(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(quote(z0))) → c26(QUOTE(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(quote(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(quote(0))) → c22(DBL1(mark(01)))
ACTIVE(s1(quote(0))) → c23(S1(mark(01)))
ACTIVE(quote(dbl(0))) → c26(QUOTE(mark(0)))
ACTIVE(quote(dbls(nil))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(indx(nil, z0))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(dbl1(0))) → c26(QUOTE(mark(01)))
ACTIVE(quote(quote(0))) → c26(QUOTE(mark(01)))
ACTIVE(dbl(quote(s(z0)))) → c7(DBL(mark(s1(quote(z0)))))
ACTIVE(dbl(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(s(z0)))) → c7(DBLS(mark(s1(quote(z0)))))
ACTIVE(dbls(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(indx(quote(s(z0)), x1)) → c7(INDX(mark(s1(quote(z0))), x1))
ACTIVE(indx(quote(s(z0)), x1)) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbl1(quote(s(z0)))) → c7(DBL1(mark(s1(quote(z0)))))
ACTIVE(dbl1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(s1(quote(s(z0)))) → c7(S1(mark(s1(quote(z0)))))
ACTIVE(s1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(quote(dbl(s(z0)))) → c7(QUOTE(mark(s(s(dbl(z0))))))
ACTIVE(quote(dbl(s(z0)))) → c7(ACTIVE(dbl(s(z0))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(QUOTE(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(QUOTE(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(quote(from(z0))) → c7(QUOTE(mark(cons(z0, from(s(z0))))))
ACTIVE(quote(from(z0))) → c7(ACTIVE(from(z0)))
ACTIVE(quote(dbl1(s(z0)))) → c7(QUOTE(mark(s1(s1(dbl1(z0))))))
ACTIVE(quote(dbl1(s(z0)))) → c7(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(quote(s(z0)))) → c7(QUOTE(mark(s1(quote(z0)))))
ACTIVE(quote(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
PROPER(dbl(dbl(z0))) → c45(DBL(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbl(s(z0))) → c45(DBL(s(proper(z0))), PROPER(s(z0)))
PROPER(dbl(dbls(z0))) → c45(DBL(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbl(cons(z0, z1))) → c45(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbl(sel(z0, z1))) → c45(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbl(indx(z0, z1))) → c45(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbl(from(z0))) → c45(DBL(from(proper(z0))), PROPER(from(z0)))
PROPER(dbl(dbl1(z0))) → c45(DBL(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbl(s1(z0))) → c45(DBL(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbl(sel1(z0, z1))) → c45(DBL(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbl(quote(z0))) → c45(DBL(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbl(0)) → c45(DBL(ok(0)))
PROPER(dbl(nil)) → c45(DBL(ok(nil)))
PROPER(dbl(01)) → c45(DBL(ok(01)))
PROPER(s(dbl(z0))) → c47(S(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(s(s(z0))) → c47(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(dbls(z0))) → c47(S(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(s(cons(z0, z1))) → c47(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(sel(z0, z1))) → c47(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(s(indx(z0, z1))) → c47(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(s(from(z0))) → c47(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(dbl1(z0))) → c47(S(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(s(s1(z0))) → c47(S(s1(proper(z0))), PROPER(s1(z0)))
PROPER(s(sel1(z0, z1))) → c47(S(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(s(quote(z0))) → c47(S(quote(proper(z0))), PROPER(quote(z0)))
PROPER(s(0)) → c47(S(ok(0)))
PROPER(s(nil)) → c47(S(ok(nil)))
PROPER(s(01)) → c47(S(ok(01)))
PROPER(dbls(dbl(z0))) → c48(DBLS(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbls(s(z0))) → c48(DBLS(s(proper(z0))), PROPER(s(z0)))
PROPER(dbls(dbls(z0))) → c48(DBLS(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbls(cons(z0, z1))) → c48(DBLS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbls(sel(z0, z1))) → c48(DBLS(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbls(indx(z0, z1))) → c48(DBLS(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbls(from(z0))) → c48(DBLS(from(proper(z0))), PROPER(from(z0)))
PROPER(dbls(dbl1(z0))) → c48(DBLS(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbls(s1(z0))) → c48(DBLS(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbls(sel1(z0, z1))) → c48(DBLS(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbls(quote(z0))) → c48(DBLS(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbls(0)) → c48(DBLS(ok(0)))
PROPER(dbls(nil)) → c48(DBLS(ok(nil)))
PROPER(dbls(01)) → c48(DBLS(ok(01)))
PROPER(cons(x0, dbl(z0))) → c50(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(cons(x0, s(z0))) → c50(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, dbls(z0))) → c50(CONS(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(cons(x0, cons(z0, z1))) → c50(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, sel(z0, z1))) → c50(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(cons(x0, indx(z0, z1))) → c50(CONS(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(cons(x0, from(z0))) → c50(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, dbl1(z0))) → c50(CONS(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(cons(x0, s1(z0))) → c50(CONS(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(cons(x0, sel1(z0, z1))) → c50(CONS(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(cons(x0, quote(z0))) → c50(CONS(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(cons(dbl(z0), x1)) → c50(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(cons(s(z0), x1)) → c50(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(dbls(z0), x1)) → c50(CONS(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c50(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(sel(z0, z1), x1)) → c50(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(cons(indx(z0, z1), x1)) → c50(CONS(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c50(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(dbl1(z0), x1)) → c50(CONS(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(cons(s1(z0), x1)) → c50(CONS(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(cons(sel1(z0, z1), x1)) → c50(CONS(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(cons(quote(z0), x1)) → c50(CONS(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c50(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c50(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, 01)) → c50(CONS(proper(x0), ok(01)), PROPER(x0))
PROPER(cons(0, x1)) → c50(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c50(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(01, x1)) → c50(CONS(ok(01), proper(x1)), PROPER(x1))
PROPER(sel(x0, dbl(z0))) → c51(SEL(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(sel(x0, s(z0))) → c51(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(sel(x0, dbls(z0))) → c51(SEL(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(sel(x0, cons(z0, z1))) → c51(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(sel(x0, sel(z0, z1))) → c51(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(sel(x0, indx(z0, z1))) → c51(SEL(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(sel(x0, from(z0))) → c51(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(sel(x0, dbl1(z0))) → c51(SEL(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(sel(x0, s1(z0))) → c51(SEL(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(sel(x0, sel1(z0, z1))) → c51(SEL(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(sel(x0, quote(z0))) → c51(SEL(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(sel(dbl(z0), x1)) → c51(SEL(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(sel(s(z0), x1)) → c51(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(sel(dbls(z0), x1)) → c51(SEL(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(sel(cons(z0, z1), x1)) → c51(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(sel(sel(z0, z1), x1)) → c51(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(sel(indx(z0, z1), x1)) → c51(SEL(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(sel(from(z0), x1)) → c51(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(sel(dbl1(z0), x1)) → c51(SEL(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(sel(s1(z0), x1)) → c51(SEL(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(sel(sel1(z0, z1), x1)) → c51(SEL(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(sel(quote(z0), x1)) → c51(SEL(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(sel(x0, 0)) → c51(SEL(proper(x0), ok(0)), PROPER(x0))
PROPER(sel(x0, nil)) → c51(SEL(proper(x0), ok(nil)), PROPER(x0))
PROPER(sel(x0, 01)) → c51(SEL(proper(x0), ok(01)), PROPER(x0))
PROPER(sel(0, x1)) → c51(SEL(ok(0), proper(x1)), PROPER(x1))
PROPER(sel(nil, x1)) → c51(SEL(ok(nil), proper(x1)), PROPER(x1))
PROPER(sel(01, x1)) → c51(SEL(ok(01), proper(x1)), PROPER(x1))
PROPER(indx(x0, dbl(z0))) → c52(INDX(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(indx(x0, 0)) → c52(INDX(proper(x0), ok(0)), PROPER(x0), PROPER(0))
PROPER(indx(x0, s(z0))) → c52(INDX(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(indx(x0, dbls(z0))) → c52(INDX(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(indx(x0, nil)) → c52(INDX(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
PROPER(indx(x0, cons(z0, z1))) → c52(INDX(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(indx(x0, sel(z0, z1))) → c52(INDX(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(indx(x0, indx(z0, z1))) → c52(INDX(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(indx(x0, from(z0))) → c52(INDX(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(indx(x0, dbl1(z0))) → c52(INDX(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(indx(x0, 01)) → c52(INDX(proper(x0), ok(01)), PROPER(x0), PROPER(01))
PROPER(indx(x0, s1(z0))) → c52(INDX(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(indx(x0, sel1(z0, z1))) → c52(INDX(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(indx(x0, quote(z0))) → c52(INDX(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(indx(dbl(z0), x1)) → c52(INDX(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(indx(0, x1)) → c52(INDX(ok(0), proper(x1)), PROPER(0), PROPER(x1))
PROPER(indx(s(z0), x1)) → c52(INDX(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(indx(dbls(z0), x1)) → c52(INDX(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(indx(nil, x1)) → c52(INDX(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
PROPER(indx(cons(z0, z1), x1)) → c52(INDX(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(indx(sel(z0, z1), x1)) → c52(INDX(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(indx(indx(z0, z1), x1)) → c52(INDX(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(indx(from(z0), x1)) → c52(INDX(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(indx(dbl1(z0), x1)) → c52(INDX(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(indx(01, x1)) → c52(INDX(ok(01), proper(x1)), PROPER(01), PROPER(x1))
PROPER(indx(s1(z0), x1)) → c52(INDX(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(indx(sel1(z0, z1), x1)) → c52(INDX(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(indx(quote(z0), x1)) → c52(INDX(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
S tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(from(z0)) → c53(FROM(proper(z0)), PROPER(z0))
PROPER(dbl1(z0)) → c54(DBL1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c56(S1(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c57(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)))
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0))))))
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0))))))
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0)))
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(indx(sel1(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(indx(sel1(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel1(z0, z2)), x1), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(indx(quote(dbl(z0)), x1)) → c21(INDX(mark(dbl1(z0)), x1), ACTIVE(quote(dbl(z0))))
ACTIVE(indx(quote(sel(z0, z1)), x1)) → c21(INDX(mark(sel1(z0, z1)), x1), ACTIVE(quote(sel(z0, z1))))
ACTIVE(indx(dbl(z0), x1)) → c21(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
ACTIVE(indx(dbls(z0), x1)) → c21(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(indx(z0, z1), x1)) → c21(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1)))
ACTIVE(indx(dbl1(z0), x1)) → c21(INDX(dbl1(active(z0)), x1), ACTIVE(dbl1(z0)))
ACTIVE(indx(s1(z0), x1)) → c21(INDX(s1(active(z0)), x1), ACTIVE(s1(z0)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(active(z0), z1), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(z0, active(z1)), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(quote(z0), x1)) → c21(INDX(quote(active(z0)), x1), ACTIVE(quote(z0)))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)))
ACTIVE(indx(dbl(0), x1)) → c21(INDX(mark(0), x1))
ACTIVE(indx(dbls(nil), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(indx(indx(nil, z0), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0))))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1))
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0)))
ACTIVE(dbl1(sel(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl1(sel(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl1(sel1(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl1(sel1(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl1(quote(dbl(z0)))) → c22(DBL1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl1(quote(sel(z0, z1)))) → c22(DBL1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl1(dbl(z0))) → c22(DBL1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl1(dbls(z0))) → c22(DBL1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(indx(z0, z1))) → c22(DBL1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl1(dbl1(z0))) → c22(DBL1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl1(s1(z0))) → c22(DBL1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(quote(z0))) → c22(DBL1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(dbl1(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(dbl(0))) → c22(DBL1(mark(0)))
ACTIVE(dbl1(dbls(nil))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(indx(nil, z0))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(dbl1(0))) → c22(DBL1(mark(01)))
ACTIVE(dbl(dbl1(s(z0)))) → c4(DBL(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(DBLS(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(INDX(mark(s1(s1(dbl1(z0)))), x1))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(DBL1(mark(s(s(dbl(z0))))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(ACTIVE(dbl(s(z0))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(DBL1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(DBL1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl1(from(z0))) → c4(DBL1(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl1(from(z0))) → c4(ACTIVE(from(z0)))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(DBL1(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(s1(sel(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(s1(sel(s(z0), cons(z1, z2)))) → c23(S1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(s1(sel1(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(s1(sel1(s(z0), cons(z1, z2)))) → c23(S1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(s1(quote(dbl(z0)))) → c23(S1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(s1(quote(sel(z0, z1)))) → c23(S1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(s1(dbl(z0))) → c23(S1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(s1(dbls(z0))) → c23(S1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(s1(indx(z0, z1))) → c23(S1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(s1(dbl1(z0))) → c23(S1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(s1(s1(z0))) → c23(S1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(quote(z0))) → c23(S1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(s1(dbl(0))) → c23(S1(mark(0)))
ACTIVE(s1(dbls(nil))) → c23(S1(mark(nil)))
ACTIVE(s1(indx(nil, z0))) → c23(S1(mark(nil)))
ACTIVE(s1(dbl1(0))) → c23(S1(mark(01)))
ACTIVE(s1(dbl(s(z0)))) → c6(S1(mark(s(s(dbl(z0))))))
ACTIVE(s1(dbl(s(z0)))) → c6(ACTIVE(dbl(s(z0))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(S1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(S1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(s1(from(z0))) → c6(S1(mark(cons(z0, from(s(z0))))))
ACTIVE(s1(from(z0))) → c6(ACTIVE(from(z0)))
ACTIVE(s1(dbl1(s(z0)))) → c6(S1(mark(s1(s1(dbl1(z0))))))
ACTIVE(s1(dbl1(s(z0)))) → c6(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(sel(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(quote(sel(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(quote(sel1(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(quote(sel1(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(quote(quote(dbl(z0)))) → c26(QUOTE(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(quote(quote(sel(z0, z1)))) → c26(QUOTE(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(quote(dbl(z0))) → c26(QUOTE(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(quote(dbls(z0))) → c26(QUOTE(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(quote(indx(z0, z1))) → c26(QUOTE(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(quote(dbl1(z0))) → c26(QUOTE(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(quote(s1(z0))) → c26(QUOTE(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(quote(z0))) → c26(QUOTE(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(quote(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(quote(0))) → c22(DBL1(mark(01)))
ACTIVE(s1(quote(0))) → c23(S1(mark(01)))
ACTIVE(quote(dbl(0))) → c26(QUOTE(mark(0)))
ACTIVE(quote(dbls(nil))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(indx(nil, z0))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(dbl1(0))) → c26(QUOTE(mark(01)))
ACTIVE(quote(quote(0))) → c26(QUOTE(mark(01)))
ACTIVE(dbl(quote(s(z0)))) → c7(DBL(mark(s1(quote(z0)))))
ACTIVE(dbl(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(s(z0)))) → c7(DBLS(mark(s1(quote(z0)))))
ACTIVE(dbls(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(indx(quote(s(z0)), x1)) → c7(INDX(mark(s1(quote(z0))), x1))
ACTIVE(indx(quote(s(z0)), x1)) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbl1(quote(s(z0)))) → c7(DBL1(mark(s1(quote(z0)))))
ACTIVE(dbl1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(s1(quote(s(z0)))) → c7(S1(mark(s1(quote(z0)))))
ACTIVE(s1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(quote(dbl(s(z0)))) → c7(QUOTE(mark(s(s(dbl(z0))))))
ACTIVE(quote(dbl(s(z0)))) → c7(ACTIVE(dbl(s(z0))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(QUOTE(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(QUOTE(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(quote(from(z0))) → c7(QUOTE(mark(cons(z0, from(s(z0))))))
ACTIVE(quote(from(z0))) → c7(ACTIVE(from(z0)))
ACTIVE(quote(dbl1(s(z0)))) → c7(QUOTE(mark(s1(s1(dbl1(z0))))))
ACTIVE(quote(dbl1(s(z0)))) → c7(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(quote(s(z0)))) → c7(QUOTE(mark(s1(quote(z0)))))
ACTIVE(quote(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
PROPER(dbl(dbl(z0))) → c45(DBL(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbl(s(z0))) → c45(DBL(s(proper(z0))), PROPER(s(z0)))
PROPER(dbl(dbls(z0))) → c45(DBL(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbl(cons(z0, z1))) → c45(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbl(sel(z0, z1))) → c45(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbl(indx(z0, z1))) → c45(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbl(from(z0))) → c45(DBL(from(proper(z0))), PROPER(from(z0)))
PROPER(dbl(dbl1(z0))) → c45(DBL(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbl(s1(z0))) → c45(DBL(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbl(sel1(z0, z1))) → c45(DBL(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbl(quote(z0))) → c45(DBL(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbl(0)) → c45(DBL(ok(0)))
PROPER(dbl(nil)) → c45(DBL(ok(nil)))
PROPER(dbl(01)) → c45(DBL(ok(01)))
PROPER(s(dbl(z0))) → c47(S(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(s(s(z0))) → c47(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(dbls(z0))) → c47(S(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(s(cons(z0, z1))) → c47(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(sel(z0, z1))) → c47(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(s(indx(z0, z1))) → c47(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(s(from(z0))) → c47(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(dbl1(z0))) → c47(S(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(s(s1(z0))) → c47(S(s1(proper(z0))), PROPER(s1(z0)))
PROPER(s(sel1(z0, z1))) → c47(S(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(s(quote(z0))) → c47(S(quote(proper(z0))), PROPER(quote(z0)))
PROPER(s(0)) → c47(S(ok(0)))
PROPER(s(nil)) → c47(S(ok(nil)))
PROPER(s(01)) → c47(S(ok(01)))
PROPER(dbls(dbl(z0))) → c48(DBLS(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbls(s(z0))) → c48(DBLS(s(proper(z0))), PROPER(s(z0)))
PROPER(dbls(dbls(z0))) → c48(DBLS(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbls(cons(z0, z1))) → c48(DBLS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbls(sel(z0, z1))) → c48(DBLS(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbls(indx(z0, z1))) → c48(DBLS(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbls(from(z0))) → c48(DBLS(from(proper(z0))), PROPER(from(z0)))
PROPER(dbls(dbl1(z0))) → c48(DBLS(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbls(s1(z0))) → c48(DBLS(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbls(sel1(z0, z1))) → c48(DBLS(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbls(quote(z0))) → c48(DBLS(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbls(0)) → c48(DBLS(ok(0)))
PROPER(dbls(nil)) → c48(DBLS(ok(nil)))
PROPER(dbls(01)) → c48(DBLS(ok(01)))
PROPER(cons(x0, dbl(z0))) → c50(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(cons(x0, s(z0))) → c50(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, dbls(z0))) → c50(CONS(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(cons(x0, cons(z0, z1))) → c50(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, sel(z0, z1))) → c50(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(cons(x0, indx(z0, z1))) → c50(CONS(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(cons(x0, from(z0))) → c50(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, dbl1(z0))) → c50(CONS(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(cons(x0, s1(z0))) → c50(CONS(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(cons(x0, sel1(z0, z1))) → c50(CONS(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(cons(x0, quote(z0))) → c50(CONS(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(cons(dbl(z0), x1)) → c50(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(cons(s(z0), x1)) → c50(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(dbls(z0), x1)) → c50(CONS(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c50(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(sel(z0, z1), x1)) → c50(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(cons(indx(z0, z1), x1)) → c50(CONS(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c50(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(dbl1(z0), x1)) → c50(CONS(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(cons(s1(z0), x1)) → c50(CONS(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(cons(sel1(z0, z1), x1)) → c50(CONS(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(cons(quote(z0), x1)) → c50(CONS(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c50(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c50(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, 01)) → c50(CONS(proper(x0), ok(01)), PROPER(x0))
PROPER(cons(0, x1)) → c50(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c50(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(01, x1)) → c50(CONS(ok(01), proper(x1)), PROPER(x1))
PROPER(sel(x0, dbl(z0))) → c51(SEL(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(sel(x0, s(z0))) → c51(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(sel(x0, dbls(z0))) → c51(SEL(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(sel(x0, cons(z0, z1))) → c51(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(sel(x0, sel(z0, z1))) → c51(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(sel(x0, indx(z0, z1))) → c51(SEL(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(sel(x0, from(z0))) → c51(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(sel(x0, dbl1(z0))) → c51(SEL(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(sel(x0, s1(z0))) → c51(SEL(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(sel(x0, sel1(z0, z1))) → c51(SEL(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(sel(x0, quote(z0))) → c51(SEL(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(sel(dbl(z0), x1)) → c51(SEL(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(sel(s(z0), x1)) → c51(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(sel(dbls(z0), x1)) → c51(SEL(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(sel(cons(z0, z1), x1)) → c51(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(sel(sel(z0, z1), x1)) → c51(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(sel(indx(z0, z1), x1)) → c51(SEL(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(sel(from(z0), x1)) → c51(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(sel(dbl1(z0), x1)) → c51(SEL(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(sel(s1(z0), x1)) → c51(SEL(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(sel(sel1(z0, z1), x1)) → c51(SEL(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(sel(quote(z0), x1)) → c51(SEL(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(sel(x0, 0)) → c51(SEL(proper(x0), ok(0)), PROPER(x0))
PROPER(sel(x0, nil)) → c51(SEL(proper(x0), ok(nil)), PROPER(x0))
PROPER(sel(x0, 01)) → c51(SEL(proper(x0), ok(01)), PROPER(x0))
PROPER(sel(0, x1)) → c51(SEL(ok(0), proper(x1)), PROPER(x1))
PROPER(sel(nil, x1)) → c51(SEL(ok(nil), proper(x1)), PROPER(x1))
PROPER(sel(01, x1)) → c51(SEL(ok(01), proper(x1)), PROPER(x1))
PROPER(indx(x0, dbl(z0))) → c52(INDX(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(indx(x0, 0)) → c52(INDX(proper(x0), ok(0)), PROPER(x0), PROPER(0))
PROPER(indx(x0, s(z0))) → c52(INDX(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(indx(x0, dbls(z0))) → c52(INDX(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(indx(x0, nil)) → c52(INDX(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
PROPER(indx(x0, cons(z0, z1))) → c52(INDX(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(indx(x0, sel(z0, z1))) → c52(INDX(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(indx(x0, indx(z0, z1))) → c52(INDX(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(indx(x0, from(z0))) → c52(INDX(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(indx(x0, dbl1(z0))) → c52(INDX(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(indx(x0, 01)) → c52(INDX(proper(x0), ok(01)), PROPER(x0), PROPER(01))
PROPER(indx(x0, s1(z0))) → c52(INDX(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(indx(x0, sel1(z0, z1))) → c52(INDX(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(indx(x0, quote(z0))) → c52(INDX(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(indx(dbl(z0), x1)) → c52(INDX(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(indx(0, x1)) → c52(INDX(ok(0), proper(x1)), PROPER(0), PROPER(x1))
PROPER(indx(s(z0), x1)) → c52(INDX(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(indx(dbls(z0), x1)) → c52(INDX(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(indx(nil, x1)) → c52(INDX(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
PROPER(indx(cons(z0, z1), x1)) → c52(INDX(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(indx(sel(z0, z1), x1)) → c52(INDX(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(indx(indx(z0, z1), x1)) → c52(INDX(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(indx(from(z0), x1)) → c52(INDX(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(indx(dbl1(z0), x1)) → c52(INDX(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(indx(01, x1)) → c52(INDX(ok(01), proper(x1)), PROPER(01), PROPER(x1))
PROPER(indx(s1(z0), x1)) → c52(INDX(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(indx(sel1(z0, z1), x1)) → c52(INDX(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(indx(quote(z0), x1)) → c52(INDX(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
K tuples:none
Defined Rule Symbols:
active, s, dbl, cons, dbls, sel, indx, s1, dbl1, sel1, quote, proper, from
Defined Pair Symbols:
ACTIVE, DBL, DBLS, SEL, INDX, DBL1, S1, SEL1, QUOTE, PROPER, S, CONS, FROM, TOP
Compound Symbols:
c5, c12, c15, c16, c19, c20, c24, c25, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c53, c54, c56, c57, c58, c59, c60, c61, c62, c63, c8, c, c17, c17, c1, c18, c18, c2, c21, c21, c3, c22, c22, c4, c23, c23, c6, c26, c26, c7, c45, c45, c47, c47, c48, c48, c50, c50, c51, c51, c52
(69) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 6 trailing tuple parts
(70) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(dbl(0)) → mark(0)
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
active(dbls(nil)) → mark(nil)
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1)))
active(sel(0, cons(z0, z1))) → mark(z0)
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
active(indx(nil, z0)) → mark(nil)
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2)))
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(dbl1(0)) → mark(01)
active(dbl1(s(z0))) → mark(s1(s1(dbl1(z0))))
active(sel1(0, cons(z0, z1))) → mark(z0)
active(sel1(s(z0), cons(z1, z2))) → mark(sel1(z0, z2))
active(quote(0)) → mark(01)
active(quote(s(z0))) → mark(s1(quote(z0)))
active(quote(dbl(z0))) → mark(dbl1(z0))
active(quote(sel(z0, z1))) → mark(sel1(z0, z1))
active(dbl(z0)) → dbl(active(z0))
active(dbls(z0)) → dbls(active(z0))
active(sel(z0, z1)) → sel(active(z0), z1)
active(sel(z0, z1)) → sel(z0, active(z1))
active(indx(z0, z1)) → indx(active(z0), z1)
active(dbl1(z0)) → dbl1(active(z0))
active(s1(z0)) → s1(active(z0))
active(sel1(z0, z1)) → sel1(active(z0), z1)
active(sel1(z0, z1)) → sel1(z0, active(z1))
active(quote(z0)) → quote(active(z0))
s(ok(z0)) → ok(s(z0))
dbl(mark(z0)) → mark(dbl(z0))
dbl(ok(z0)) → ok(dbl(z0))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
dbls(mark(z0)) → mark(dbls(z0))
dbls(ok(z0)) → ok(dbls(z0))
sel(mark(z0), z1) → mark(sel(z0, z1))
sel(z0, mark(z1)) → mark(sel(z0, z1))
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
indx(mark(z0), z1) → mark(indx(z0, z1))
indx(ok(z0), ok(z1)) → ok(indx(z0, z1))
s1(mark(z0)) → mark(s1(z0))
s1(ok(z0)) → ok(s1(z0))
dbl1(mark(z0)) → mark(dbl1(z0))
dbl1(ok(z0)) → ok(dbl1(z0))
sel1(mark(z0), z1) → mark(sel1(z0, z1))
sel1(z0, mark(z1)) → mark(sel1(z0, z1))
sel1(ok(z0), ok(z1)) → ok(sel1(z0, z1))
quote(mark(z0)) → mark(quote(z0))
quote(ok(z0)) → ok(quote(z0))
proper(dbl(z0)) → dbl(proper(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(dbls(z0)) → dbls(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
proper(indx(z0, z1)) → indx(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(dbl1(z0)) → dbl1(proper(z0))
proper(01) → ok(01)
proper(s1(z0)) → s1(proper(z0))
proper(sel1(z0, z1)) → sel1(proper(z0), proper(z1))
proper(quote(z0)) → quote(proper(z0))
from(ok(z0)) → ok(from(z0))
Tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(from(z0)) → c53(FROM(proper(z0)), PROPER(z0))
PROPER(dbl1(z0)) → c54(DBL1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c56(S1(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c57(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)))
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0))))))
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0))))))
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0)))
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(indx(sel1(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(indx(sel1(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel1(z0, z2)), x1), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(indx(quote(dbl(z0)), x1)) → c21(INDX(mark(dbl1(z0)), x1), ACTIVE(quote(dbl(z0))))
ACTIVE(indx(quote(sel(z0, z1)), x1)) → c21(INDX(mark(sel1(z0, z1)), x1), ACTIVE(quote(sel(z0, z1))))
ACTIVE(indx(dbl(z0), x1)) → c21(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
ACTIVE(indx(dbls(z0), x1)) → c21(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(indx(z0, z1), x1)) → c21(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1)))
ACTIVE(indx(dbl1(z0), x1)) → c21(INDX(dbl1(active(z0)), x1), ACTIVE(dbl1(z0)))
ACTIVE(indx(s1(z0), x1)) → c21(INDX(s1(active(z0)), x1), ACTIVE(s1(z0)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(active(z0), z1), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(z0, active(z1)), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(quote(z0), x1)) → c21(INDX(quote(active(z0)), x1), ACTIVE(quote(z0)))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)))
ACTIVE(indx(dbl(0), x1)) → c21(INDX(mark(0), x1))
ACTIVE(indx(dbls(nil), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(indx(indx(nil, z0), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0))))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1))
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0)))
ACTIVE(dbl1(sel(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl1(sel(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl1(sel1(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl1(sel1(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl1(quote(dbl(z0)))) → c22(DBL1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl1(quote(sel(z0, z1)))) → c22(DBL1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl1(dbl(z0))) → c22(DBL1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl1(dbls(z0))) → c22(DBL1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(indx(z0, z1))) → c22(DBL1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl1(dbl1(z0))) → c22(DBL1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl1(s1(z0))) → c22(DBL1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(quote(z0))) → c22(DBL1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(dbl1(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(dbl(0))) → c22(DBL1(mark(0)))
ACTIVE(dbl1(dbls(nil))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(indx(nil, z0))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(dbl1(0))) → c22(DBL1(mark(01)))
ACTIVE(dbl(dbl1(s(z0)))) → c4(DBL(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(DBLS(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(INDX(mark(s1(s1(dbl1(z0)))), x1))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(DBL1(mark(s(s(dbl(z0))))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(ACTIVE(dbl(s(z0))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(DBL1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(DBL1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl1(from(z0))) → c4(DBL1(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl1(from(z0))) → c4(ACTIVE(from(z0)))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(DBL1(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(s1(sel(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(s1(sel(s(z0), cons(z1, z2)))) → c23(S1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(s1(sel1(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(s1(sel1(s(z0), cons(z1, z2)))) → c23(S1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(s1(quote(dbl(z0)))) → c23(S1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(s1(quote(sel(z0, z1)))) → c23(S1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(s1(dbl(z0))) → c23(S1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(s1(dbls(z0))) → c23(S1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(s1(indx(z0, z1))) → c23(S1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(s1(dbl1(z0))) → c23(S1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(s1(s1(z0))) → c23(S1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(quote(z0))) → c23(S1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(s1(dbl(0))) → c23(S1(mark(0)))
ACTIVE(s1(dbls(nil))) → c23(S1(mark(nil)))
ACTIVE(s1(indx(nil, z0))) → c23(S1(mark(nil)))
ACTIVE(s1(dbl1(0))) → c23(S1(mark(01)))
ACTIVE(s1(dbl(s(z0)))) → c6(S1(mark(s(s(dbl(z0))))))
ACTIVE(s1(dbl(s(z0)))) → c6(ACTIVE(dbl(s(z0))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(S1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(S1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(s1(from(z0))) → c6(S1(mark(cons(z0, from(s(z0))))))
ACTIVE(s1(from(z0))) → c6(ACTIVE(from(z0)))
ACTIVE(s1(dbl1(s(z0)))) → c6(S1(mark(s1(s1(dbl1(z0))))))
ACTIVE(s1(dbl1(s(z0)))) → c6(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(sel(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(quote(sel(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(quote(sel1(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(quote(sel1(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(quote(quote(dbl(z0)))) → c26(QUOTE(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(quote(quote(sel(z0, z1)))) → c26(QUOTE(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(quote(dbl(z0))) → c26(QUOTE(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(quote(dbls(z0))) → c26(QUOTE(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(quote(indx(z0, z1))) → c26(QUOTE(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(quote(dbl1(z0))) → c26(QUOTE(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(quote(s1(z0))) → c26(QUOTE(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(quote(z0))) → c26(QUOTE(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(quote(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(quote(0))) → c22(DBL1(mark(01)))
ACTIVE(s1(quote(0))) → c23(S1(mark(01)))
ACTIVE(quote(dbl(0))) → c26(QUOTE(mark(0)))
ACTIVE(quote(dbls(nil))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(indx(nil, z0))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(dbl1(0))) → c26(QUOTE(mark(01)))
ACTIVE(quote(quote(0))) → c26(QUOTE(mark(01)))
ACTIVE(dbl(quote(s(z0)))) → c7(DBL(mark(s1(quote(z0)))))
ACTIVE(dbl(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(s(z0)))) → c7(DBLS(mark(s1(quote(z0)))))
ACTIVE(dbls(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(indx(quote(s(z0)), x1)) → c7(INDX(mark(s1(quote(z0))), x1))
ACTIVE(indx(quote(s(z0)), x1)) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbl1(quote(s(z0)))) → c7(DBL1(mark(s1(quote(z0)))))
ACTIVE(dbl1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(s1(quote(s(z0)))) → c7(S1(mark(s1(quote(z0)))))
ACTIVE(s1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(quote(dbl(s(z0)))) → c7(QUOTE(mark(s(s(dbl(z0))))))
ACTIVE(quote(dbl(s(z0)))) → c7(ACTIVE(dbl(s(z0))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(QUOTE(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(QUOTE(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(quote(from(z0))) → c7(QUOTE(mark(cons(z0, from(s(z0))))))
ACTIVE(quote(from(z0))) → c7(ACTIVE(from(z0)))
ACTIVE(quote(dbl1(s(z0)))) → c7(QUOTE(mark(s1(s1(dbl1(z0))))))
ACTIVE(quote(dbl1(s(z0)))) → c7(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(quote(s(z0)))) → c7(QUOTE(mark(s1(quote(z0)))))
ACTIVE(quote(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
PROPER(dbl(dbl(z0))) → c45(DBL(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbl(s(z0))) → c45(DBL(s(proper(z0))), PROPER(s(z0)))
PROPER(dbl(dbls(z0))) → c45(DBL(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbl(cons(z0, z1))) → c45(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbl(sel(z0, z1))) → c45(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbl(indx(z0, z1))) → c45(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbl(from(z0))) → c45(DBL(from(proper(z0))), PROPER(from(z0)))
PROPER(dbl(dbl1(z0))) → c45(DBL(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbl(s1(z0))) → c45(DBL(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbl(sel1(z0, z1))) → c45(DBL(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbl(quote(z0))) → c45(DBL(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbl(0)) → c45(DBL(ok(0)))
PROPER(dbl(nil)) → c45(DBL(ok(nil)))
PROPER(dbl(01)) → c45(DBL(ok(01)))
PROPER(s(dbl(z0))) → c47(S(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(s(s(z0))) → c47(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(dbls(z0))) → c47(S(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(s(cons(z0, z1))) → c47(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(sel(z0, z1))) → c47(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(s(indx(z0, z1))) → c47(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(s(from(z0))) → c47(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(dbl1(z0))) → c47(S(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(s(s1(z0))) → c47(S(s1(proper(z0))), PROPER(s1(z0)))
PROPER(s(sel1(z0, z1))) → c47(S(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(s(quote(z0))) → c47(S(quote(proper(z0))), PROPER(quote(z0)))
PROPER(s(0)) → c47(S(ok(0)))
PROPER(s(nil)) → c47(S(ok(nil)))
PROPER(s(01)) → c47(S(ok(01)))
PROPER(dbls(dbl(z0))) → c48(DBLS(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbls(s(z0))) → c48(DBLS(s(proper(z0))), PROPER(s(z0)))
PROPER(dbls(dbls(z0))) → c48(DBLS(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbls(cons(z0, z1))) → c48(DBLS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbls(sel(z0, z1))) → c48(DBLS(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbls(indx(z0, z1))) → c48(DBLS(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbls(from(z0))) → c48(DBLS(from(proper(z0))), PROPER(from(z0)))
PROPER(dbls(dbl1(z0))) → c48(DBLS(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbls(s1(z0))) → c48(DBLS(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbls(sel1(z0, z1))) → c48(DBLS(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbls(quote(z0))) → c48(DBLS(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbls(0)) → c48(DBLS(ok(0)))
PROPER(dbls(nil)) → c48(DBLS(ok(nil)))
PROPER(dbls(01)) → c48(DBLS(ok(01)))
PROPER(cons(x0, dbl(z0))) → c50(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(cons(x0, s(z0))) → c50(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, dbls(z0))) → c50(CONS(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(cons(x0, cons(z0, z1))) → c50(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, sel(z0, z1))) → c50(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(cons(x0, indx(z0, z1))) → c50(CONS(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(cons(x0, from(z0))) → c50(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, dbl1(z0))) → c50(CONS(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(cons(x0, s1(z0))) → c50(CONS(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(cons(x0, sel1(z0, z1))) → c50(CONS(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(cons(x0, quote(z0))) → c50(CONS(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(cons(dbl(z0), x1)) → c50(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(cons(s(z0), x1)) → c50(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(dbls(z0), x1)) → c50(CONS(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c50(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(sel(z0, z1), x1)) → c50(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(cons(indx(z0, z1), x1)) → c50(CONS(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c50(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(dbl1(z0), x1)) → c50(CONS(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(cons(s1(z0), x1)) → c50(CONS(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(cons(sel1(z0, z1), x1)) → c50(CONS(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(cons(quote(z0), x1)) → c50(CONS(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c50(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c50(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, 01)) → c50(CONS(proper(x0), ok(01)), PROPER(x0))
PROPER(cons(0, x1)) → c50(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c50(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(01, x1)) → c50(CONS(ok(01), proper(x1)), PROPER(x1))
PROPER(sel(x0, dbl(z0))) → c51(SEL(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(sel(x0, s(z0))) → c51(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(sel(x0, dbls(z0))) → c51(SEL(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(sel(x0, cons(z0, z1))) → c51(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(sel(x0, sel(z0, z1))) → c51(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(sel(x0, indx(z0, z1))) → c51(SEL(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(sel(x0, from(z0))) → c51(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(sel(x0, dbl1(z0))) → c51(SEL(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(sel(x0, s1(z0))) → c51(SEL(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(sel(x0, sel1(z0, z1))) → c51(SEL(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(sel(x0, quote(z0))) → c51(SEL(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(sel(dbl(z0), x1)) → c51(SEL(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(sel(s(z0), x1)) → c51(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(sel(dbls(z0), x1)) → c51(SEL(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(sel(cons(z0, z1), x1)) → c51(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(sel(sel(z0, z1), x1)) → c51(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(sel(indx(z0, z1), x1)) → c51(SEL(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(sel(from(z0), x1)) → c51(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(sel(dbl1(z0), x1)) → c51(SEL(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(sel(s1(z0), x1)) → c51(SEL(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(sel(sel1(z0, z1), x1)) → c51(SEL(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(sel(quote(z0), x1)) → c51(SEL(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(sel(x0, 0)) → c51(SEL(proper(x0), ok(0)), PROPER(x0))
PROPER(sel(x0, nil)) → c51(SEL(proper(x0), ok(nil)), PROPER(x0))
PROPER(sel(x0, 01)) → c51(SEL(proper(x0), ok(01)), PROPER(x0))
PROPER(sel(0, x1)) → c51(SEL(ok(0), proper(x1)), PROPER(x1))
PROPER(sel(nil, x1)) → c51(SEL(ok(nil), proper(x1)), PROPER(x1))
PROPER(sel(01, x1)) → c51(SEL(ok(01), proper(x1)), PROPER(x1))
PROPER(indx(x0, dbl(z0))) → c52(INDX(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(indx(x0, s(z0))) → c52(INDX(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(indx(x0, dbls(z0))) → c52(INDX(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(indx(x0, cons(z0, z1))) → c52(INDX(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(indx(x0, sel(z0, z1))) → c52(INDX(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(indx(x0, indx(z0, z1))) → c52(INDX(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(indx(x0, from(z0))) → c52(INDX(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(indx(x0, dbl1(z0))) → c52(INDX(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(indx(x0, s1(z0))) → c52(INDX(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(indx(x0, sel1(z0, z1))) → c52(INDX(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(indx(x0, quote(z0))) → c52(INDX(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(indx(dbl(z0), x1)) → c52(INDX(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(indx(s(z0), x1)) → c52(INDX(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(indx(dbls(z0), x1)) → c52(INDX(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(indx(cons(z0, z1), x1)) → c52(INDX(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(indx(sel(z0, z1), x1)) → c52(INDX(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(indx(indx(z0, z1), x1)) → c52(INDX(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(indx(from(z0), x1)) → c52(INDX(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(indx(dbl1(z0), x1)) → c52(INDX(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(indx(s1(z0), x1)) → c52(INDX(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(indx(sel1(z0, z1), x1)) → c52(INDX(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(indx(quote(z0), x1)) → c52(INDX(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(indx(x0, 0)) → c52(INDX(proper(x0), ok(0)), PROPER(x0))
PROPER(indx(x0, nil)) → c52(INDX(proper(x0), ok(nil)), PROPER(x0))
PROPER(indx(x0, 01)) → c52(INDX(proper(x0), ok(01)), PROPER(x0))
PROPER(indx(0, x1)) → c52(INDX(ok(0), proper(x1)), PROPER(x1))
PROPER(indx(nil, x1)) → c52(INDX(ok(nil), proper(x1)), PROPER(x1))
PROPER(indx(01, x1)) → c52(INDX(ok(01), proper(x1)), PROPER(x1))
S tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(from(z0)) → c53(FROM(proper(z0)), PROPER(z0))
PROPER(dbl1(z0)) → c54(DBL1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c56(S1(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c57(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)))
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0))))))
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0))))))
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0)))
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(indx(sel1(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(indx(sel1(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel1(z0, z2)), x1), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(indx(quote(dbl(z0)), x1)) → c21(INDX(mark(dbl1(z0)), x1), ACTIVE(quote(dbl(z0))))
ACTIVE(indx(quote(sel(z0, z1)), x1)) → c21(INDX(mark(sel1(z0, z1)), x1), ACTIVE(quote(sel(z0, z1))))
ACTIVE(indx(dbl(z0), x1)) → c21(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
ACTIVE(indx(dbls(z0), x1)) → c21(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(indx(z0, z1), x1)) → c21(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1)))
ACTIVE(indx(dbl1(z0), x1)) → c21(INDX(dbl1(active(z0)), x1), ACTIVE(dbl1(z0)))
ACTIVE(indx(s1(z0), x1)) → c21(INDX(s1(active(z0)), x1), ACTIVE(s1(z0)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(active(z0), z1), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(z0, active(z1)), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(quote(z0), x1)) → c21(INDX(quote(active(z0)), x1), ACTIVE(quote(z0)))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)))
ACTIVE(indx(dbl(0), x1)) → c21(INDX(mark(0), x1))
ACTIVE(indx(dbls(nil), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(indx(indx(nil, z0), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0))))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1))
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0)))
ACTIVE(dbl1(sel(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl1(sel(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl1(sel1(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl1(sel1(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl1(quote(dbl(z0)))) → c22(DBL1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl1(quote(sel(z0, z1)))) → c22(DBL1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl1(dbl(z0))) → c22(DBL1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl1(dbls(z0))) → c22(DBL1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(indx(z0, z1))) → c22(DBL1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl1(dbl1(z0))) → c22(DBL1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl1(s1(z0))) → c22(DBL1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(quote(z0))) → c22(DBL1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(dbl1(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(dbl(0))) → c22(DBL1(mark(0)))
ACTIVE(dbl1(dbls(nil))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(indx(nil, z0))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(dbl1(0))) → c22(DBL1(mark(01)))
ACTIVE(dbl(dbl1(s(z0)))) → c4(DBL(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(DBLS(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(INDX(mark(s1(s1(dbl1(z0)))), x1))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(DBL1(mark(s(s(dbl(z0))))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(ACTIVE(dbl(s(z0))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(DBL1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(DBL1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl1(from(z0))) → c4(DBL1(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl1(from(z0))) → c4(ACTIVE(from(z0)))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(DBL1(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(s1(sel(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(s1(sel(s(z0), cons(z1, z2)))) → c23(S1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(s1(sel1(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(s1(sel1(s(z0), cons(z1, z2)))) → c23(S1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(s1(quote(dbl(z0)))) → c23(S1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(s1(quote(sel(z0, z1)))) → c23(S1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(s1(dbl(z0))) → c23(S1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(s1(dbls(z0))) → c23(S1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(s1(indx(z0, z1))) → c23(S1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(s1(dbl1(z0))) → c23(S1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(s1(s1(z0))) → c23(S1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(quote(z0))) → c23(S1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(s1(dbl(0))) → c23(S1(mark(0)))
ACTIVE(s1(dbls(nil))) → c23(S1(mark(nil)))
ACTIVE(s1(indx(nil, z0))) → c23(S1(mark(nil)))
ACTIVE(s1(dbl1(0))) → c23(S1(mark(01)))
ACTIVE(s1(dbl(s(z0)))) → c6(S1(mark(s(s(dbl(z0))))))
ACTIVE(s1(dbl(s(z0)))) → c6(ACTIVE(dbl(s(z0))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(S1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(S1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(s1(from(z0))) → c6(S1(mark(cons(z0, from(s(z0))))))
ACTIVE(s1(from(z0))) → c6(ACTIVE(from(z0)))
ACTIVE(s1(dbl1(s(z0)))) → c6(S1(mark(s1(s1(dbl1(z0))))))
ACTIVE(s1(dbl1(s(z0)))) → c6(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(sel(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(quote(sel(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(quote(sel1(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(quote(sel1(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(quote(quote(dbl(z0)))) → c26(QUOTE(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(quote(quote(sel(z0, z1)))) → c26(QUOTE(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(quote(dbl(z0))) → c26(QUOTE(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(quote(dbls(z0))) → c26(QUOTE(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(quote(indx(z0, z1))) → c26(QUOTE(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(quote(dbl1(z0))) → c26(QUOTE(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(quote(s1(z0))) → c26(QUOTE(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(quote(z0))) → c26(QUOTE(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(quote(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(quote(0))) → c22(DBL1(mark(01)))
ACTIVE(s1(quote(0))) → c23(S1(mark(01)))
ACTIVE(quote(dbl(0))) → c26(QUOTE(mark(0)))
ACTIVE(quote(dbls(nil))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(indx(nil, z0))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(dbl1(0))) → c26(QUOTE(mark(01)))
ACTIVE(quote(quote(0))) → c26(QUOTE(mark(01)))
ACTIVE(dbl(quote(s(z0)))) → c7(DBL(mark(s1(quote(z0)))))
ACTIVE(dbl(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(s(z0)))) → c7(DBLS(mark(s1(quote(z0)))))
ACTIVE(dbls(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(indx(quote(s(z0)), x1)) → c7(INDX(mark(s1(quote(z0))), x1))
ACTIVE(indx(quote(s(z0)), x1)) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbl1(quote(s(z0)))) → c7(DBL1(mark(s1(quote(z0)))))
ACTIVE(dbl1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(s1(quote(s(z0)))) → c7(S1(mark(s1(quote(z0)))))
ACTIVE(s1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(quote(dbl(s(z0)))) → c7(QUOTE(mark(s(s(dbl(z0))))))
ACTIVE(quote(dbl(s(z0)))) → c7(ACTIVE(dbl(s(z0))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(QUOTE(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(QUOTE(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(quote(from(z0))) → c7(QUOTE(mark(cons(z0, from(s(z0))))))
ACTIVE(quote(from(z0))) → c7(ACTIVE(from(z0)))
ACTIVE(quote(dbl1(s(z0)))) → c7(QUOTE(mark(s1(s1(dbl1(z0))))))
ACTIVE(quote(dbl1(s(z0)))) → c7(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(quote(s(z0)))) → c7(QUOTE(mark(s1(quote(z0)))))
ACTIVE(quote(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
PROPER(dbl(dbl(z0))) → c45(DBL(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbl(s(z0))) → c45(DBL(s(proper(z0))), PROPER(s(z0)))
PROPER(dbl(dbls(z0))) → c45(DBL(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbl(cons(z0, z1))) → c45(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbl(sel(z0, z1))) → c45(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbl(indx(z0, z1))) → c45(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbl(from(z0))) → c45(DBL(from(proper(z0))), PROPER(from(z0)))
PROPER(dbl(dbl1(z0))) → c45(DBL(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbl(s1(z0))) → c45(DBL(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbl(sel1(z0, z1))) → c45(DBL(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbl(quote(z0))) → c45(DBL(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbl(0)) → c45(DBL(ok(0)))
PROPER(dbl(nil)) → c45(DBL(ok(nil)))
PROPER(dbl(01)) → c45(DBL(ok(01)))
PROPER(s(dbl(z0))) → c47(S(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(s(s(z0))) → c47(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(dbls(z0))) → c47(S(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(s(cons(z0, z1))) → c47(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(sel(z0, z1))) → c47(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(s(indx(z0, z1))) → c47(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(s(from(z0))) → c47(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(dbl1(z0))) → c47(S(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(s(s1(z0))) → c47(S(s1(proper(z0))), PROPER(s1(z0)))
PROPER(s(sel1(z0, z1))) → c47(S(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(s(quote(z0))) → c47(S(quote(proper(z0))), PROPER(quote(z0)))
PROPER(s(0)) → c47(S(ok(0)))
PROPER(s(nil)) → c47(S(ok(nil)))
PROPER(s(01)) → c47(S(ok(01)))
PROPER(dbls(dbl(z0))) → c48(DBLS(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbls(s(z0))) → c48(DBLS(s(proper(z0))), PROPER(s(z0)))
PROPER(dbls(dbls(z0))) → c48(DBLS(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbls(cons(z0, z1))) → c48(DBLS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbls(sel(z0, z1))) → c48(DBLS(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbls(indx(z0, z1))) → c48(DBLS(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbls(from(z0))) → c48(DBLS(from(proper(z0))), PROPER(from(z0)))
PROPER(dbls(dbl1(z0))) → c48(DBLS(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbls(s1(z0))) → c48(DBLS(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbls(sel1(z0, z1))) → c48(DBLS(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbls(quote(z0))) → c48(DBLS(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbls(0)) → c48(DBLS(ok(0)))
PROPER(dbls(nil)) → c48(DBLS(ok(nil)))
PROPER(dbls(01)) → c48(DBLS(ok(01)))
PROPER(cons(x0, dbl(z0))) → c50(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(cons(x0, s(z0))) → c50(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, dbls(z0))) → c50(CONS(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(cons(x0, cons(z0, z1))) → c50(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, sel(z0, z1))) → c50(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(cons(x0, indx(z0, z1))) → c50(CONS(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(cons(x0, from(z0))) → c50(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, dbl1(z0))) → c50(CONS(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(cons(x0, s1(z0))) → c50(CONS(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(cons(x0, sel1(z0, z1))) → c50(CONS(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(cons(x0, quote(z0))) → c50(CONS(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(cons(dbl(z0), x1)) → c50(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(cons(s(z0), x1)) → c50(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(dbls(z0), x1)) → c50(CONS(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c50(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(sel(z0, z1), x1)) → c50(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(cons(indx(z0, z1), x1)) → c50(CONS(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c50(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(dbl1(z0), x1)) → c50(CONS(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(cons(s1(z0), x1)) → c50(CONS(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(cons(sel1(z0, z1), x1)) → c50(CONS(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(cons(quote(z0), x1)) → c50(CONS(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c50(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c50(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, 01)) → c50(CONS(proper(x0), ok(01)), PROPER(x0))
PROPER(cons(0, x1)) → c50(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c50(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(01, x1)) → c50(CONS(ok(01), proper(x1)), PROPER(x1))
PROPER(sel(x0, dbl(z0))) → c51(SEL(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(sel(x0, s(z0))) → c51(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(sel(x0, dbls(z0))) → c51(SEL(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(sel(x0, cons(z0, z1))) → c51(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(sel(x0, sel(z0, z1))) → c51(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(sel(x0, indx(z0, z1))) → c51(SEL(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(sel(x0, from(z0))) → c51(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(sel(x0, dbl1(z0))) → c51(SEL(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(sel(x0, s1(z0))) → c51(SEL(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(sel(x0, sel1(z0, z1))) → c51(SEL(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(sel(x0, quote(z0))) → c51(SEL(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(sel(dbl(z0), x1)) → c51(SEL(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(sel(s(z0), x1)) → c51(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(sel(dbls(z0), x1)) → c51(SEL(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(sel(cons(z0, z1), x1)) → c51(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(sel(sel(z0, z1), x1)) → c51(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(sel(indx(z0, z1), x1)) → c51(SEL(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(sel(from(z0), x1)) → c51(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(sel(dbl1(z0), x1)) → c51(SEL(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(sel(s1(z0), x1)) → c51(SEL(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(sel(sel1(z0, z1), x1)) → c51(SEL(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(sel(quote(z0), x1)) → c51(SEL(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(sel(x0, 0)) → c51(SEL(proper(x0), ok(0)), PROPER(x0))
PROPER(sel(x0, nil)) → c51(SEL(proper(x0), ok(nil)), PROPER(x0))
PROPER(sel(x0, 01)) → c51(SEL(proper(x0), ok(01)), PROPER(x0))
PROPER(sel(0, x1)) → c51(SEL(ok(0), proper(x1)), PROPER(x1))
PROPER(sel(nil, x1)) → c51(SEL(ok(nil), proper(x1)), PROPER(x1))
PROPER(sel(01, x1)) → c51(SEL(ok(01), proper(x1)), PROPER(x1))
PROPER(indx(x0, dbl(z0))) → c52(INDX(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(indx(x0, s(z0))) → c52(INDX(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(indx(x0, dbls(z0))) → c52(INDX(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(indx(x0, cons(z0, z1))) → c52(INDX(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(indx(x0, sel(z0, z1))) → c52(INDX(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(indx(x0, indx(z0, z1))) → c52(INDX(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(indx(x0, from(z0))) → c52(INDX(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(indx(x0, dbl1(z0))) → c52(INDX(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(indx(x0, s1(z0))) → c52(INDX(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(indx(x0, sel1(z0, z1))) → c52(INDX(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(indx(x0, quote(z0))) → c52(INDX(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(indx(dbl(z0), x1)) → c52(INDX(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(indx(s(z0), x1)) → c52(INDX(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(indx(dbls(z0), x1)) → c52(INDX(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(indx(cons(z0, z1), x1)) → c52(INDX(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(indx(sel(z0, z1), x1)) → c52(INDX(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(indx(indx(z0, z1), x1)) → c52(INDX(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(indx(from(z0), x1)) → c52(INDX(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(indx(dbl1(z0), x1)) → c52(INDX(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(indx(s1(z0), x1)) → c52(INDX(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(indx(sel1(z0, z1), x1)) → c52(INDX(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(indx(quote(z0), x1)) → c52(INDX(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(indx(x0, 0)) → c52(INDX(proper(x0), ok(0)), PROPER(x0))
PROPER(indx(x0, nil)) → c52(INDX(proper(x0), ok(nil)), PROPER(x0))
PROPER(indx(x0, 01)) → c52(INDX(proper(x0), ok(01)), PROPER(x0))
PROPER(indx(0, x1)) → c52(INDX(ok(0), proper(x1)), PROPER(x1))
PROPER(indx(nil, x1)) → c52(INDX(ok(nil), proper(x1)), PROPER(x1))
PROPER(indx(01, x1)) → c52(INDX(ok(01), proper(x1)), PROPER(x1))
K tuples:none
Defined Rule Symbols:
active, s, dbl, cons, dbls, sel, indx, s1, dbl1, sel1, quote, proper, from
Defined Pair Symbols:
ACTIVE, DBL, DBLS, SEL, INDX, DBL1, S1, SEL1, QUOTE, PROPER, S, CONS, FROM, TOP
Compound Symbols:
c5, c12, c15, c16, c19, c20, c24, c25, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c53, c54, c56, c57, c58, c59, c60, c61, c62, c63, c8, c, c17, c17, c1, c18, c18, c2, c21, c21, c3, c22, c22, c4, c23, c23, c6, c26, c26, c7, c45, c45, c47, c47, c48, c48, c50, c50, c51, c51, c52, c52
(71) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
PROPER(
from(
z0)) →
c53(
FROM(
proper(
z0)),
PROPER(
z0)) by
PROPER(from(dbl(z0))) → c53(FROM(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(from(0)) → c53(FROM(ok(0)), PROPER(0))
PROPER(from(s(z0))) → c53(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(dbls(z0))) → c53(FROM(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(from(nil)) → c53(FROM(ok(nil)), PROPER(nil))
PROPER(from(cons(z0, z1))) → c53(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(sel(z0, z1))) → c53(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(from(indx(z0, z1))) → c53(FROM(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(from(from(z0))) → c53(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(dbl1(z0))) → c53(FROM(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(from(01)) → c53(FROM(ok(01)), PROPER(01))
PROPER(from(s1(z0))) → c53(FROM(s1(proper(z0))), PROPER(s1(z0)))
PROPER(from(sel1(z0, z1))) → c53(FROM(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(from(quote(z0))) → c53(FROM(quote(proper(z0))), PROPER(quote(z0)))
(72) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(dbl(0)) → mark(0)
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
active(dbls(nil)) → mark(nil)
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1)))
active(sel(0, cons(z0, z1))) → mark(z0)
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
active(indx(nil, z0)) → mark(nil)
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2)))
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(dbl1(0)) → mark(01)
active(dbl1(s(z0))) → mark(s1(s1(dbl1(z0))))
active(sel1(0, cons(z0, z1))) → mark(z0)
active(sel1(s(z0), cons(z1, z2))) → mark(sel1(z0, z2))
active(quote(0)) → mark(01)
active(quote(s(z0))) → mark(s1(quote(z0)))
active(quote(dbl(z0))) → mark(dbl1(z0))
active(quote(sel(z0, z1))) → mark(sel1(z0, z1))
active(dbl(z0)) → dbl(active(z0))
active(dbls(z0)) → dbls(active(z0))
active(sel(z0, z1)) → sel(active(z0), z1)
active(sel(z0, z1)) → sel(z0, active(z1))
active(indx(z0, z1)) → indx(active(z0), z1)
active(dbl1(z0)) → dbl1(active(z0))
active(s1(z0)) → s1(active(z0))
active(sel1(z0, z1)) → sel1(active(z0), z1)
active(sel1(z0, z1)) → sel1(z0, active(z1))
active(quote(z0)) → quote(active(z0))
s(ok(z0)) → ok(s(z0))
dbl(mark(z0)) → mark(dbl(z0))
dbl(ok(z0)) → ok(dbl(z0))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
dbls(mark(z0)) → mark(dbls(z0))
dbls(ok(z0)) → ok(dbls(z0))
sel(mark(z0), z1) → mark(sel(z0, z1))
sel(z0, mark(z1)) → mark(sel(z0, z1))
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
indx(mark(z0), z1) → mark(indx(z0, z1))
indx(ok(z0), ok(z1)) → ok(indx(z0, z1))
s1(mark(z0)) → mark(s1(z0))
s1(ok(z0)) → ok(s1(z0))
dbl1(mark(z0)) → mark(dbl1(z0))
dbl1(ok(z0)) → ok(dbl1(z0))
sel1(mark(z0), z1) → mark(sel1(z0, z1))
sel1(z0, mark(z1)) → mark(sel1(z0, z1))
sel1(ok(z0), ok(z1)) → ok(sel1(z0, z1))
quote(mark(z0)) → mark(quote(z0))
quote(ok(z0)) → ok(quote(z0))
proper(dbl(z0)) → dbl(proper(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(dbls(z0)) → dbls(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
proper(indx(z0, z1)) → indx(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(dbl1(z0)) → dbl1(proper(z0))
proper(01) → ok(01)
proper(s1(z0)) → s1(proper(z0))
proper(sel1(z0, z1)) → sel1(proper(z0), proper(z1))
proper(quote(z0)) → quote(proper(z0))
from(ok(z0)) → ok(from(z0))
Tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(dbl1(z0)) → c54(DBL1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c56(S1(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c57(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)))
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0))))))
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0))))))
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0)))
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(indx(sel1(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(indx(sel1(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel1(z0, z2)), x1), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(indx(quote(dbl(z0)), x1)) → c21(INDX(mark(dbl1(z0)), x1), ACTIVE(quote(dbl(z0))))
ACTIVE(indx(quote(sel(z0, z1)), x1)) → c21(INDX(mark(sel1(z0, z1)), x1), ACTIVE(quote(sel(z0, z1))))
ACTIVE(indx(dbl(z0), x1)) → c21(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
ACTIVE(indx(dbls(z0), x1)) → c21(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(indx(z0, z1), x1)) → c21(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1)))
ACTIVE(indx(dbl1(z0), x1)) → c21(INDX(dbl1(active(z0)), x1), ACTIVE(dbl1(z0)))
ACTIVE(indx(s1(z0), x1)) → c21(INDX(s1(active(z0)), x1), ACTIVE(s1(z0)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(active(z0), z1), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(z0, active(z1)), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(quote(z0), x1)) → c21(INDX(quote(active(z0)), x1), ACTIVE(quote(z0)))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)))
ACTIVE(indx(dbl(0), x1)) → c21(INDX(mark(0), x1))
ACTIVE(indx(dbls(nil), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(indx(indx(nil, z0), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0))))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1))
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0)))
ACTIVE(dbl1(sel(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl1(sel(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl1(sel1(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl1(sel1(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl1(quote(dbl(z0)))) → c22(DBL1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl1(quote(sel(z0, z1)))) → c22(DBL1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl1(dbl(z0))) → c22(DBL1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl1(dbls(z0))) → c22(DBL1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(indx(z0, z1))) → c22(DBL1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl1(dbl1(z0))) → c22(DBL1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl1(s1(z0))) → c22(DBL1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(quote(z0))) → c22(DBL1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(dbl1(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(dbl(0))) → c22(DBL1(mark(0)))
ACTIVE(dbl1(dbls(nil))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(indx(nil, z0))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(dbl1(0))) → c22(DBL1(mark(01)))
ACTIVE(dbl(dbl1(s(z0)))) → c4(DBL(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(DBLS(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(INDX(mark(s1(s1(dbl1(z0)))), x1))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(DBL1(mark(s(s(dbl(z0))))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(ACTIVE(dbl(s(z0))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(DBL1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(DBL1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl1(from(z0))) → c4(DBL1(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl1(from(z0))) → c4(ACTIVE(from(z0)))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(DBL1(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(s1(sel(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(s1(sel(s(z0), cons(z1, z2)))) → c23(S1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(s1(sel1(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(s1(sel1(s(z0), cons(z1, z2)))) → c23(S1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(s1(quote(dbl(z0)))) → c23(S1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(s1(quote(sel(z0, z1)))) → c23(S1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(s1(dbl(z0))) → c23(S1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(s1(dbls(z0))) → c23(S1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(s1(indx(z0, z1))) → c23(S1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(s1(dbl1(z0))) → c23(S1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(s1(s1(z0))) → c23(S1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(quote(z0))) → c23(S1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(s1(dbl(0))) → c23(S1(mark(0)))
ACTIVE(s1(dbls(nil))) → c23(S1(mark(nil)))
ACTIVE(s1(indx(nil, z0))) → c23(S1(mark(nil)))
ACTIVE(s1(dbl1(0))) → c23(S1(mark(01)))
ACTIVE(s1(dbl(s(z0)))) → c6(S1(mark(s(s(dbl(z0))))))
ACTIVE(s1(dbl(s(z0)))) → c6(ACTIVE(dbl(s(z0))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(S1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(S1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(s1(from(z0))) → c6(S1(mark(cons(z0, from(s(z0))))))
ACTIVE(s1(from(z0))) → c6(ACTIVE(from(z0)))
ACTIVE(s1(dbl1(s(z0)))) → c6(S1(mark(s1(s1(dbl1(z0))))))
ACTIVE(s1(dbl1(s(z0)))) → c6(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(sel(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(quote(sel(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(quote(sel1(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(quote(sel1(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(quote(quote(dbl(z0)))) → c26(QUOTE(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(quote(quote(sel(z0, z1)))) → c26(QUOTE(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(quote(dbl(z0))) → c26(QUOTE(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(quote(dbls(z0))) → c26(QUOTE(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(quote(indx(z0, z1))) → c26(QUOTE(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(quote(dbl1(z0))) → c26(QUOTE(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(quote(s1(z0))) → c26(QUOTE(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(quote(z0))) → c26(QUOTE(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(quote(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(quote(0))) → c22(DBL1(mark(01)))
ACTIVE(s1(quote(0))) → c23(S1(mark(01)))
ACTIVE(quote(dbl(0))) → c26(QUOTE(mark(0)))
ACTIVE(quote(dbls(nil))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(indx(nil, z0))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(dbl1(0))) → c26(QUOTE(mark(01)))
ACTIVE(quote(quote(0))) → c26(QUOTE(mark(01)))
ACTIVE(dbl(quote(s(z0)))) → c7(DBL(mark(s1(quote(z0)))))
ACTIVE(dbl(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(s(z0)))) → c7(DBLS(mark(s1(quote(z0)))))
ACTIVE(dbls(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(indx(quote(s(z0)), x1)) → c7(INDX(mark(s1(quote(z0))), x1))
ACTIVE(indx(quote(s(z0)), x1)) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbl1(quote(s(z0)))) → c7(DBL1(mark(s1(quote(z0)))))
ACTIVE(dbl1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(s1(quote(s(z0)))) → c7(S1(mark(s1(quote(z0)))))
ACTIVE(s1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(quote(dbl(s(z0)))) → c7(QUOTE(mark(s(s(dbl(z0))))))
ACTIVE(quote(dbl(s(z0)))) → c7(ACTIVE(dbl(s(z0))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(QUOTE(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(QUOTE(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(quote(from(z0))) → c7(QUOTE(mark(cons(z0, from(s(z0))))))
ACTIVE(quote(from(z0))) → c7(ACTIVE(from(z0)))
ACTIVE(quote(dbl1(s(z0)))) → c7(QUOTE(mark(s1(s1(dbl1(z0))))))
ACTIVE(quote(dbl1(s(z0)))) → c7(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(quote(s(z0)))) → c7(QUOTE(mark(s1(quote(z0)))))
ACTIVE(quote(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
PROPER(dbl(dbl(z0))) → c45(DBL(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbl(s(z0))) → c45(DBL(s(proper(z0))), PROPER(s(z0)))
PROPER(dbl(dbls(z0))) → c45(DBL(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbl(cons(z0, z1))) → c45(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbl(sel(z0, z1))) → c45(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbl(indx(z0, z1))) → c45(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbl(from(z0))) → c45(DBL(from(proper(z0))), PROPER(from(z0)))
PROPER(dbl(dbl1(z0))) → c45(DBL(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbl(s1(z0))) → c45(DBL(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbl(sel1(z0, z1))) → c45(DBL(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbl(quote(z0))) → c45(DBL(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbl(0)) → c45(DBL(ok(0)))
PROPER(dbl(nil)) → c45(DBL(ok(nil)))
PROPER(dbl(01)) → c45(DBL(ok(01)))
PROPER(s(dbl(z0))) → c47(S(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(s(s(z0))) → c47(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(dbls(z0))) → c47(S(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(s(cons(z0, z1))) → c47(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(sel(z0, z1))) → c47(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(s(indx(z0, z1))) → c47(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(s(from(z0))) → c47(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(dbl1(z0))) → c47(S(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(s(s1(z0))) → c47(S(s1(proper(z0))), PROPER(s1(z0)))
PROPER(s(sel1(z0, z1))) → c47(S(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(s(quote(z0))) → c47(S(quote(proper(z0))), PROPER(quote(z0)))
PROPER(s(0)) → c47(S(ok(0)))
PROPER(s(nil)) → c47(S(ok(nil)))
PROPER(s(01)) → c47(S(ok(01)))
PROPER(dbls(dbl(z0))) → c48(DBLS(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbls(s(z0))) → c48(DBLS(s(proper(z0))), PROPER(s(z0)))
PROPER(dbls(dbls(z0))) → c48(DBLS(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbls(cons(z0, z1))) → c48(DBLS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbls(sel(z0, z1))) → c48(DBLS(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbls(indx(z0, z1))) → c48(DBLS(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbls(from(z0))) → c48(DBLS(from(proper(z0))), PROPER(from(z0)))
PROPER(dbls(dbl1(z0))) → c48(DBLS(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbls(s1(z0))) → c48(DBLS(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbls(sel1(z0, z1))) → c48(DBLS(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbls(quote(z0))) → c48(DBLS(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbls(0)) → c48(DBLS(ok(0)))
PROPER(dbls(nil)) → c48(DBLS(ok(nil)))
PROPER(dbls(01)) → c48(DBLS(ok(01)))
PROPER(cons(x0, dbl(z0))) → c50(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(cons(x0, s(z0))) → c50(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, dbls(z0))) → c50(CONS(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(cons(x0, cons(z0, z1))) → c50(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, sel(z0, z1))) → c50(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(cons(x0, indx(z0, z1))) → c50(CONS(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(cons(x0, from(z0))) → c50(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, dbl1(z0))) → c50(CONS(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(cons(x0, s1(z0))) → c50(CONS(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(cons(x0, sel1(z0, z1))) → c50(CONS(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(cons(x0, quote(z0))) → c50(CONS(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(cons(dbl(z0), x1)) → c50(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(cons(s(z0), x1)) → c50(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(dbls(z0), x1)) → c50(CONS(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c50(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(sel(z0, z1), x1)) → c50(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(cons(indx(z0, z1), x1)) → c50(CONS(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c50(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(dbl1(z0), x1)) → c50(CONS(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(cons(s1(z0), x1)) → c50(CONS(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(cons(sel1(z0, z1), x1)) → c50(CONS(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(cons(quote(z0), x1)) → c50(CONS(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c50(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c50(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, 01)) → c50(CONS(proper(x0), ok(01)), PROPER(x0))
PROPER(cons(0, x1)) → c50(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c50(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(01, x1)) → c50(CONS(ok(01), proper(x1)), PROPER(x1))
PROPER(sel(x0, dbl(z0))) → c51(SEL(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(sel(x0, s(z0))) → c51(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(sel(x0, dbls(z0))) → c51(SEL(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(sel(x0, cons(z0, z1))) → c51(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(sel(x0, sel(z0, z1))) → c51(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(sel(x0, indx(z0, z1))) → c51(SEL(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(sel(x0, from(z0))) → c51(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(sel(x0, dbl1(z0))) → c51(SEL(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(sel(x0, s1(z0))) → c51(SEL(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(sel(x0, sel1(z0, z1))) → c51(SEL(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(sel(x0, quote(z0))) → c51(SEL(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(sel(dbl(z0), x1)) → c51(SEL(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(sel(s(z0), x1)) → c51(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(sel(dbls(z0), x1)) → c51(SEL(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(sel(cons(z0, z1), x1)) → c51(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(sel(sel(z0, z1), x1)) → c51(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(sel(indx(z0, z1), x1)) → c51(SEL(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(sel(from(z0), x1)) → c51(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(sel(dbl1(z0), x1)) → c51(SEL(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(sel(s1(z0), x1)) → c51(SEL(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(sel(sel1(z0, z1), x1)) → c51(SEL(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(sel(quote(z0), x1)) → c51(SEL(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(sel(x0, 0)) → c51(SEL(proper(x0), ok(0)), PROPER(x0))
PROPER(sel(x0, nil)) → c51(SEL(proper(x0), ok(nil)), PROPER(x0))
PROPER(sel(x0, 01)) → c51(SEL(proper(x0), ok(01)), PROPER(x0))
PROPER(sel(0, x1)) → c51(SEL(ok(0), proper(x1)), PROPER(x1))
PROPER(sel(nil, x1)) → c51(SEL(ok(nil), proper(x1)), PROPER(x1))
PROPER(sel(01, x1)) → c51(SEL(ok(01), proper(x1)), PROPER(x1))
PROPER(indx(x0, dbl(z0))) → c52(INDX(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(indx(x0, s(z0))) → c52(INDX(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(indx(x0, dbls(z0))) → c52(INDX(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(indx(x0, cons(z0, z1))) → c52(INDX(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(indx(x0, sel(z0, z1))) → c52(INDX(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(indx(x0, indx(z0, z1))) → c52(INDX(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(indx(x0, from(z0))) → c52(INDX(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(indx(x0, dbl1(z0))) → c52(INDX(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(indx(x0, s1(z0))) → c52(INDX(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(indx(x0, sel1(z0, z1))) → c52(INDX(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(indx(x0, quote(z0))) → c52(INDX(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(indx(dbl(z0), x1)) → c52(INDX(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(indx(s(z0), x1)) → c52(INDX(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(indx(dbls(z0), x1)) → c52(INDX(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(indx(cons(z0, z1), x1)) → c52(INDX(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(indx(sel(z0, z1), x1)) → c52(INDX(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(indx(indx(z0, z1), x1)) → c52(INDX(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(indx(from(z0), x1)) → c52(INDX(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(indx(dbl1(z0), x1)) → c52(INDX(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(indx(s1(z0), x1)) → c52(INDX(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(indx(sel1(z0, z1), x1)) → c52(INDX(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(indx(quote(z0), x1)) → c52(INDX(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(indx(x0, 0)) → c52(INDX(proper(x0), ok(0)), PROPER(x0))
PROPER(indx(x0, nil)) → c52(INDX(proper(x0), ok(nil)), PROPER(x0))
PROPER(indx(x0, 01)) → c52(INDX(proper(x0), ok(01)), PROPER(x0))
PROPER(indx(0, x1)) → c52(INDX(ok(0), proper(x1)), PROPER(x1))
PROPER(indx(nil, x1)) → c52(INDX(ok(nil), proper(x1)), PROPER(x1))
PROPER(indx(01, x1)) → c52(INDX(ok(01), proper(x1)), PROPER(x1))
PROPER(from(dbl(z0))) → c53(FROM(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(from(0)) → c53(FROM(ok(0)), PROPER(0))
PROPER(from(s(z0))) → c53(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(dbls(z0))) → c53(FROM(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(from(nil)) → c53(FROM(ok(nil)), PROPER(nil))
PROPER(from(cons(z0, z1))) → c53(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(sel(z0, z1))) → c53(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(from(indx(z0, z1))) → c53(FROM(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(from(from(z0))) → c53(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(dbl1(z0))) → c53(FROM(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(from(01)) → c53(FROM(ok(01)), PROPER(01))
PROPER(from(s1(z0))) → c53(FROM(s1(proper(z0))), PROPER(s1(z0)))
PROPER(from(sel1(z0, z1))) → c53(FROM(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(from(quote(z0))) → c53(FROM(quote(proper(z0))), PROPER(quote(z0)))
S tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(dbl1(z0)) → c54(DBL1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c56(S1(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c57(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)))
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0))))))
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0))))))
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0)))
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(indx(sel1(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(indx(sel1(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel1(z0, z2)), x1), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(indx(quote(dbl(z0)), x1)) → c21(INDX(mark(dbl1(z0)), x1), ACTIVE(quote(dbl(z0))))
ACTIVE(indx(quote(sel(z0, z1)), x1)) → c21(INDX(mark(sel1(z0, z1)), x1), ACTIVE(quote(sel(z0, z1))))
ACTIVE(indx(dbl(z0), x1)) → c21(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
ACTIVE(indx(dbls(z0), x1)) → c21(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(indx(z0, z1), x1)) → c21(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1)))
ACTIVE(indx(dbl1(z0), x1)) → c21(INDX(dbl1(active(z0)), x1), ACTIVE(dbl1(z0)))
ACTIVE(indx(s1(z0), x1)) → c21(INDX(s1(active(z0)), x1), ACTIVE(s1(z0)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(active(z0), z1), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(z0, active(z1)), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(quote(z0), x1)) → c21(INDX(quote(active(z0)), x1), ACTIVE(quote(z0)))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)))
ACTIVE(indx(dbl(0), x1)) → c21(INDX(mark(0), x1))
ACTIVE(indx(dbls(nil), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(indx(indx(nil, z0), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0))))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1))
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0)))
ACTIVE(dbl1(sel(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl1(sel(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl1(sel1(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl1(sel1(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl1(quote(dbl(z0)))) → c22(DBL1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl1(quote(sel(z0, z1)))) → c22(DBL1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl1(dbl(z0))) → c22(DBL1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl1(dbls(z0))) → c22(DBL1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(indx(z0, z1))) → c22(DBL1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl1(dbl1(z0))) → c22(DBL1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl1(s1(z0))) → c22(DBL1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(quote(z0))) → c22(DBL1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(dbl1(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(dbl(0))) → c22(DBL1(mark(0)))
ACTIVE(dbl1(dbls(nil))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(indx(nil, z0))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(dbl1(0))) → c22(DBL1(mark(01)))
ACTIVE(dbl(dbl1(s(z0)))) → c4(DBL(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(DBLS(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(INDX(mark(s1(s1(dbl1(z0)))), x1))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(DBL1(mark(s(s(dbl(z0))))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(ACTIVE(dbl(s(z0))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(DBL1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(DBL1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl1(from(z0))) → c4(DBL1(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl1(from(z0))) → c4(ACTIVE(from(z0)))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(DBL1(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(s1(sel(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(s1(sel(s(z0), cons(z1, z2)))) → c23(S1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(s1(sel1(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(s1(sel1(s(z0), cons(z1, z2)))) → c23(S1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(s1(quote(dbl(z0)))) → c23(S1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(s1(quote(sel(z0, z1)))) → c23(S1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(s1(dbl(z0))) → c23(S1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(s1(dbls(z0))) → c23(S1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(s1(indx(z0, z1))) → c23(S1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(s1(dbl1(z0))) → c23(S1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(s1(s1(z0))) → c23(S1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(quote(z0))) → c23(S1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(s1(dbl(0))) → c23(S1(mark(0)))
ACTIVE(s1(dbls(nil))) → c23(S1(mark(nil)))
ACTIVE(s1(indx(nil, z0))) → c23(S1(mark(nil)))
ACTIVE(s1(dbl1(0))) → c23(S1(mark(01)))
ACTIVE(s1(dbl(s(z0)))) → c6(S1(mark(s(s(dbl(z0))))))
ACTIVE(s1(dbl(s(z0)))) → c6(ACTIVE(dbl(s(z0))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(S1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(S1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(s1(from(z0))) → c6(S1(mark(cons(z0, from(s(z0))))))
ACTIVE(s1(from(z0))) → c6(ACTIVE(from(z0)))
ACTIVE(s1(dbl1(s(z0)))) → c6(S1(mark(s1(s1(dbl1(z0))))))
ACTIVE(s1(dbl1(s(z0)))) → c6(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(sel(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(quote(sel(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(quote(sel1(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(quote(sel1(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(quote(quote(dbl(z0)))) → c26(QUOTE(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(quote(quote(sel(z0, z1)))) → c26(QUOTE(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(quote(dbl(z0))) → c26(QUOTE(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(quote(dbls(z0))) → c26(QUOTE(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(quote(indx(z0, z1))) → c26(QUOTE(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(quote(dbl1(z0))) → c26(QUOTE(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(quote(s1(z0))) → c26(QUOTE(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(quote(z0))) → c26(QUOTE(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(quote(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(quote(0))) → c22(DBL1(mark(01)))
ACTIVE(s1(quote(0))) → c23(S1(mark(01)))
ACTIVE(quote(dbl(0))) → c26(QUOTE(mark(0)))
ACTIVE(quote(dbls(nil))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(indx(nil, z0))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(dbl1(0))) → c26(QUOTE(mark(01)))
ACTIVE(quote(quote(0))) → c26(QUOTE(mark(01)))
ACTIVE(dbl(quote(s(z0)))) → c7(DBL(mark(s1(quote(z0)))))
ACTIVE(dbl(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(s(z0)))) → c7(DBLS(mark(s1(quote(z0)))))
ACTIVE(dbls(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(indx(quote(s(z0)), x1)) → c7(INDX(mark(s1(quote(z0))), x1))
ACTIVE(indx(quote(s(z0)), x1)) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbl1(quote(s(z0)))) → c7(DBL1(mark(s1(quote(z0)))))
ACTIVE(dbl1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(s1(quote(s(z0)))) → c7(S1(mark(s1(quote(z0)))))
ACTIVE(s1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(quote(dbl(s(z0)))) → c7(QUOTE(mark(s(s(dbl(z0))))))
ACTIVE(quote(dbl(s(z0)))) → c7(ACTIVE(dbl(s(z0))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(QUOTE(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(QUOTE(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(quote(from(z0))) → c7(QUOTE(mark(cons(z0, from(s(z0))))))
ACTIVE(quote(from(z0))) → c7(ACTIVE(from(z0)))
ACTIVE(quote(dbl1(s(z0)))) → c7(QUOTE(mark(s1(s1(dbl1(z0))))))
ACTIVE(quote(dbl1(s(z0)))) → c7(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(quote(s(z0)))) → c7(QUOTE(mark(s1(quote(z0)))))
ACTIVE(quote(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
PROPER(dbl(dbl(z0))) → c45(DBL(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbl(s(z0))) → c45(DBL(s(proper(z0))), PROPER(s(z0)))
PROPER(dbl(dbls(z0))) → c45(DBL(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbl(cons(z0, z1))) → c45(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbl(sel(z0, z1))) → c45(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbl(indx(z0, z1))) → c45(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbl(from(z0))) → c45(DBL(from(proper(z0))), PROPER(from(z0)))
PROPER(dbl(dbl1(z0))) → c45(DBL(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbl(s1(z0))) → c45(DBL(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbl(sel1(z0, z1))) → c45(DBL(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbl(quote(z0))) → c45(DBL(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbl(0)) → c45(DBL(ok(0)))
PROPER(dbl(nil)) → c45(DBL(ok(nil)))
PROPER(dbl(01)) → c45(DBL(ok(01)))
PROPER(s(dbl(z0))) → c47(S(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(s(s(z0))) → c47(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(dbls(z0))) → c47(S(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(s(cons(z0, z1))) → c47(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(sel(z0, z1))) → c47(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(s(indx(z0, z1))) → c47(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(s(from(z0))) → c47(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(dbl1(z0))) → c47(S(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(s(s1(z0))) → c47(S(s1(proper(z0))), PROPER(s1(z0)))
PROPER(s(sel1(z0, z1))) → c47(S(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(s(quote(z0))) → c47(S(quote(proper(z0))), PROPER(quote(z0)))
PROPER(s(0)) → c47(S(ok(0)))
PROPER(s(nil)) → c47(S(ok(nil)))
PROPER(s(01)) → c47(S(ok(01)))
PROPER(dbls(dbl(z0))) → c48(DBLS(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbls(s(z0))) → c48(DBLS(s(proper(z0))), PROPER(s(z0)))
PROPER(dbls(dbls(z0))) → c48(DBLS(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbls(cons(z0, z1))) → c48(DBLS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbls(sel(z0, z1))) → c48(DBLS(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbls(indx(z0, z1))) → c48(DBLS(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbls(from(z0))) → c48(DBLS(from(proper(z0))), PROPER(from(z0)))
PROPER(dbls(dbl1(z0))) → c48(DBLS(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbls(s1(z0))) → c48(DBLS(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbls(sel1(z0, z1))) → c48(DBLS(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbls(quote(z0))) → c48(DBLS(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbls(0)) → c48(DBLS(ok(0)))
PROPER(dbls(nil)) → c48(DBLS(ok(nil)))
PROPER(dbls(01)) → c48(DBLS(ok(01)))
PROPER(cons(x0, dbl(z0))) → c50(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(cons(x0, s(z0))) → c50(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, dbls(z0))) → c50(CONS(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(cons(x0, cons(z0, z1))) → c50(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, sel(z0, z1))) → c50(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(cons(x0, indx(z0, z1))) → c50(CONS(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(cons(x0, from(z0))) → c50(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, dbl1(z0))) → c50(CONS(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(cons(x0, s1(z0))) → c50(CONS(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(cons(x0, sel1(z0, z1))) → c50(CONS(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(cons(x0, quote(z0))) → c50(CONS(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(cons(dbl(z0), x1)) → c50(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(cons(s(z0), x1)) → c50(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(dbls(z0), x1)) → c50(CONS(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c50(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(sel(z0, z1), x1)) → c50(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(cons(indx(z0, z1), x1)) → c50(CONS(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c50(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(dbl1(z0), x1)) → c50(CONS(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(cons(s1(z0), x1)) → c50(CONS(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(cons(sel1(z0, z1), x1)) → c50(CONS(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(cons(quote(z0), x1)) → c50(CONS(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c50(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c50(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, 01)) → c50(CONS(proper(x0), ok(01)), PROPER(x0))
PROPER(cons(0, x1)) → c50(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c50(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(01, x1)) → c50(CONS(ok(01), proper(x1)), PROPER(x1))
PROPER(sel(x0, dbl(z0))) → c51(SEL(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(sel(x0, s(z0))) → c51(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(sel(x0, dbls(z0))) → c51(SEL(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(sel(x0, cons(z0, z1))) → c51(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(sel(x0, sel(z0, z1))) → c51(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(sel(x0, indx(z0, z1))) → c51(SEL(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(sel(x0, from(z0))) → c51(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(sel(x0, dbl1(z0))) → c51(SEL(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(sel(x0, s1(z0))) → c51(SEL(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(sel(x0, sel1(z0, z1))) → c51(SEL(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(sel(x0, quote(z0))) → c51(SEL(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(sel(dbl(z0), x1)) → c51(SEL(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(sel(s(z0), x1)) → c51(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(sel(dbls(z0), x1)) → c51(SEL(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(sel(cons(z0, z1), x1)) → c51(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(sel(sel(z0, z1), x1)) → c51(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(sel(indx(z0, z1), x1)) → c51(SEL(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(sel(from(z0), x1)) → c51(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(sel(dbl1(z0), x1)) → c51(SEL(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(sel(s1(z0), x1)) → c51(SEL(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(sel(sel1(z0, z1), x1)) → c51(SEL(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(sel(quote(z0), x1)) → c51(SEL(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(sel(x0, 0)) → c51(SEL(proper(x0), ok(0)), PROPER(x0))
PROPER(sel(x0, nil)) → c51(SEL(proper(x0), ok(nil)), PROPER(x0))
PROPER(sel(x0, 01)) → c51(SEL(proper(x0), ok(01)), PROPER(x0))
PROPER(sel(0, x1)) → c51(SEL(ok(0), proper(x1)), PROPER(x1))
PROPER(sel(nil, x1)) → c51(SEL(ok(nil), proper(x1)), PROPER(x1))
PROPER(sel(01, x1)) → c51(SEL(ok(01), proper(x1)), PROPER(x1))
PROPER(indx(x0, dbl(z0))) → c52(INDX(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(indx(x0, s(z0))) → c52(INDX(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(indx(x0, dbls(z0))) → c52(INDX(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(indx(x0, cons(z0, z1))) → c52(INDX(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(indx(x0, sel(z0, z1))) → c52(INDX(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(indx(x0, indx(z0, z1))) → c52(INDX(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(indx(x0, from(z0))) → c52(INDX(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(indx(x0, dbl1(z0))) → c52(INDX(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(indx(x0, s1(z0))) → c52(INDX(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(indx(x0, sel1(z0, z1))) → c52(INDX(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(indx(x0, quote(z0))) → c52(INDX(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(indx(dbl(z0), x1)) → c52(INDX(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(indx(s(z0), x1)) → c52(INDX(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(indx(dbls(z0), x1)) → c52(INDX(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(indx(cons(z0, z1), x1)) → c52(INDX(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(indx(sel(z0, z1), x1)) → c52(INDX(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(indx(indx(z0, z1), x1)) → c52(INDX(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(indx(from(z0), x1)) → c52(INDX(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(indx(dbl1(z0), x1)) → c52(INDX(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(indx(s1(z0), x1)) → c52(INDX(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(indx(sel1(z0, z1), x1)) → c52(INDX(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(indx(quote(z0), x1)) → c52(INDX(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(indx(x0, 0)) → c52(INDX(proper(x0), ok(0)), PROPER(x0))
PROPER(indx(x0, nil)) → c52(INDX(proper(x0), ok(nil)), PROPER(x0))
PROPER(indx(x0, 01)) → c52(INDX(proper(x0), ok(01)), PROPER(x0))
PROPER(indx(0, x1)) → c52(INDX(ok(0), proper(x1)), PROPER(x1))
PROPER(indx(nil, x1)) → c52(INDX(ok(nil), proper(x1)), PROPER(x1))
PROPER(indx(01, x1)) → c52(INDX(ok(01), proper(x1)), PROPER(x1))
PROPER(from(dbl(z0))) → c53(FROM(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(from(0)) → c53(FROM(ok(0)), PROPER(0))
PROPER(from(s(z0))) → c53(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(dbls(z0))) → c53(FROM(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(from(nil)) → c53(FROM(ok(nil)), PROPER(nil))
PROPER(from(cons(z0, z1))) → c53(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(sel(z0, z1))) → c53(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(from(indx(z0, z1))) → c53(FROM(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(from(from(z0))) → c53(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(dbl1(z0))) → c53(FROM(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(from(01)) → c53(FROM(ok(01)), PROPER(01))
PROPER(from(s1(z0))) → c53(FROM(s1(proper(z0))), PROPER(s1(z0)))
PROPER(from(sel1(z0, z1))) → c53(FROM(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(from(quote(z0))) → c53(FROM(quote(proper(z0))), PROPER(quote(z0)))
K tuples:none
Defined Rule Symbols:
active, s, dbl, cons, dbls, sel, indx, s1, dbl1, sel1, quote, proper, from
Defined Pair Symbols:
ACTIVE, DBL, DBLS, SEL, INDX, DBL1, S1, SEL1, QUOTE, PROPER, S, CONS, FROM, TOP
Compound Symbols:
c5, c12, c15, c16, c19, c20, c24, c25, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c54, c56, c57, c58, c59, c60, c61, c62, c63, c8, c, c17, c17, c1, c18, c18, c2, c21, c21, c3, c22, c22, c4, c23, c23, c6, c26, c26, c7, c45, c45, c47, c47, c48, c48, c50, c50, c51, c51, c52, c52, c53
(73) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 3 trailing tuple parts
(74) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(dbl(0)) → mark(0)
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
active(dbls(nil)) → mark(nil)
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1)))
active(sel(0, cons(z0, z1))) → mark(z0)
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
active(indx(nil, z0)) → mark(nil)
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2)))
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(dbl1(0)) → mark(01)
active(dbl1(s(z0))) → mark(s1(s1(dbl1(z0))))
active(sel1(0, cons(z0, z1))) → mark(z0)
active(sel1(s(z0), cons(z1, z2))) → mark(sel1(z0, z2))
active(quote(0)) → mark(01)
active(quote(s(z0))) → mark(s1(quote(z0)))
active(quote(dbl(z0))) → mark(dbl1(z0))
active(quote(sel(z0, z1))) → mark(sel1(z0, z1))
active(dbl(z0)) → dbl(active(z0))
active(dbls(z0)) → dbls(active(z0))
active(sel(z0, z1)) → sel(active(z0), z1)
active(sel(z0, z1)) → sel(z0, active(z1))
active(indx(z0, z1)) → indx(active(z0), z1)
active(dbl1(z0)) → dbl1(active(z0))
active(s1(z0)) → s1(active(z0))
active(sel1(z0, z1)) → sel1(active(z0), z1)
active(sel1(z0, z1)) → sel1(z0, active(z1))
active(quote(z0)) → quote(active(z0))
s(ok(z0)) → ok(s(z0))
dbl(mark(z0)) → mark(dbl(z0))
dbl(ok(z0)) → ok(dbl(z0))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
dbls(mark(z0)) → mark(dbls(z0))
dbls(ok(z0)) → ok(dbls(z0))
sel(mark(z0), z1) → mark(sel(z0, z1))
sel(z0, mark(z1)) → mark(sel(z0, z1))
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
indx(mark(z0), z1) → mark(indx(z0, z1))
indx(ok(z0), ok(z1)) → ok(indx(z0, z1))
s1(mark(z0)) → mark(s1(z0))
s1(ok(z0)) → ok(s1(z0))
dbl1(mark(z0)) → mark(dbl1(z0))
dbl1(ok(z0)) → ok(dbl1(z0))
sel1(mark(z0), z1) → mark(sel1(z0, z1))
sel1(z0, mark(z1)) → mark(sel1(z0, z1))
sel1(ok(z0), ok(z1)) → ok(sel1(z0, z1))
quote(mark(z0)) → mark(quote(z0))
quote(ok(z0)) → ok(quote(z0))
proper(dbl(z0)) → dbl(proper(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(dbls(z0)) → dbls(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
proper(indx(z0, z1)) → indx(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(dbl1(z0)) → dbl1(proper(z0))
proper(01) → ok(01)
proper(s1(z0)) → s1(proper(z0))
proper(sel1(z0, z1)) → sel1(proper(z0), proper(z1))
proper(quote(z0)) → quote(proper(z0))
from(ok(z0)) → ok(from(z0))
Tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(dbl1(z0)) → c54(DBL1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c56(S1(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c57(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)))
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0))))))
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0))))))
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0)))
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(indx(sel1(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(indx(sel1(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel1(z0, z2)), x1), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(indx(quote(dbl(z0)), x1)) → c21(INDX(mark(dbl1(z0)), x1), ACTIVE(quote(dbl(z0))))
ACTIVE(indx(quote(sel(z0, z1)), x1)) → c21(INDX(mark(sel1(z0, z1)), x1), ACTIVE(quote(sel(z0, z1))))
ACTIVE(indx(dbl(z0), x1)) → c21(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
ACTIVE(indx(dbls(z0), x1)) → c21(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(indx(z0, z1), x1)) → c21(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1)))
ACTIVE(indx(dbl1(z0), x1)) → c21(INDX(dbl1(active(z0)), x1), ACTIVE(dbl1(z0)))
ACTIVE(indx(s1(z0), x1)) → c21(INDX(s1(active(z0)), x1), ACTIVE(s1(z0)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(active(z0), z1), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(z0, active(z1)), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(quote(z0), x1)) → c21(INDX(quote(active(z0)), x1), ACTIVE(quote(z0)))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)))
ACTIVE(indx(dbl(0), x1)) → c21(INDX(mark(0), x1))
ACTIVE(indx(dbls(nil), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(indx(indx(nil, z0), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0))))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1))
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0)))
ACTIVE(dbl1(sel(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl1(sel(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl1(sel1(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl1(sel1(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl1(quote(dbl(z0)))) → c22(DBL1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl1(quote(sel(z0, z1)))) → c22(DBL1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl1(dbl(z0))) → c22(DBL1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl1(dbls(z0))) → c22(DBL1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(indx(z0, z1))) → c22(DBL1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl1(dbl1(z0))) → c22(DBL1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl1(s1(z0))) → c22(DBL1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(quote(z0))) → c22(DBL1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(dbl1(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(dbl(0))) → c22(DBL1(mark(0)))
ACTIVE(dbl1(dbls(nil))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(indx(nil, z0))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(dbl1(0))) → c22(DBL1(mark(01)))
ACTIVE(dbl(dbl1(s(z0)))) → c4(DBL(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(DBLS(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(INDX(mark(s1(s1(dbl1(z0)))), x1))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(DBL1(mark(s(s(dbl(z0))))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(ACTIVE(dbl(s(z0))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(DBL1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(DBL1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl1(from(z0))) → c4(DBL1(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl1(from(z0))) → c4(ACTIVE(from(z0)))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(DBL1(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(s1(sel(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(s1(sel(s(z0), cons(z1, z2)))) → c23(S1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(s1(sel1(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(s1(sel1(s(z0), cons(z1, z2)))) → c23(S1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(s1(quote(dbl(z0)))) → c23(S1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(s1(quote(sel(z0, z1)))) → c23(S1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(s1(dbl(z0))) → c23(S1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(s1(dbls(z0))) → c23(S1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(s1(indx(z0, z1))) → c23(S1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(s1(dbl1(z0))) → c23(S1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(s1(s1(z0))) → c23(S1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(quote(z0))) → c23(S1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(s1(dbl(0))) → c23(S1(mark(0)))
ACTIVE(s1(dbls(nil))) → c23(S1(mark(nil)))
ACTIVE(s1(indx(nil, z0))) → c23(S1(mark(nil)))
ACTIVE(s1(dbl1(0))) → c23(S1(mark(01)))
ACTIVE(s1(dbl(s(z0)))) → c6(S1(mark(s(s(dbl(z0))))))
ACTIVE(s1(dbl(s(z0)))) → c6(ACTIVE(dbl(s(z0))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(S1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(S1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(s1(from(z0))) → c6(S1(mark(cons(z0, from(s(z0))))))
ACTIVE(s1(from(z0))) → c6(ACTIVE(from(z0)))
ACTIVE(s1(dbl1(s(z0)))) → c6(S1(mark(s1(s1(dbl1(z0))))))
ACTIVE(s1(dbl1(s(z0)))) → c6(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(sel(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(quote(sel(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(quote(sel1(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(quote(sel1(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(quote(quote(dbl(z0)))) → c26(QUOTE(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(quote(quote(sel(z0, z1)))) → c26(QUOTE(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(quote(dbl(z0))) → c26(QUOTE(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(quote(dbls(z0))) → c26(QUOTE(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(quote(indx(z0, z1))) → c26(QUOTE(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(quote(dbl1(z0))) → c26(QUOTE(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(quote(s1(z0))) → c26(QUOTE(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(quote(z0))) → c26(QUOTE(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(quote(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(quote(0))) → c22(DBL1(mark(01)))
ACTIVE(s1(quote(0))) → c23(S1(mark(01)))
ACTIVE(quote(dbl(0))) → c26(QUOTE(mark(0)))
ACTIVE(quote(dbls(nil))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(indx(nil, z0))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(dbl1(0))) → c26(QUOTE(mark(01)))
ACTIVE(quote(quote(0))) → c26(QUOTE(mark(01)))
ACTIVE(dbl(quote(s(z0)))) → c7(DBL(mark(s1(quote(z0)))))
ACTIVE(dbl(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(s(z0)))) → c7(DBLS(mark(s1(quote(z0)))))
ACTIVE(dbls(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(indx(quote(s(z0)), x1)) → c7(INDX(mark(s1(quote(z0))), x1))
ACTIVE(indx(quote(s(z0)), x1)) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbl1(quote(s(z0)))) → c7(DBL1(mark(s1(quote(z0)))))
ACTIVE(dbl1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(s1(quote(s(z0)))) → c7(S1(mark(s1(quote(z0)))))
ACTIVE(s1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(quote(dbl(s(z0)))) → c7(QUOTE(mark(s(s(dbl(z0))))))
ACTIVE(quote(dbl(s(z0)))) → c7(ACTIVE(dbl(s(z0))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(QUOTE(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(QUOTE(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(quote(from(z0))) → c7(QUOTE(mark(cons(z0, from(s(z0))))))
ACTIVE(quote(from(z0))) → c7(ACTIVE(from(z0)))
ACTIVE(quote(dbl1(s(z0)))) → c7(QUOTE(mark(s1(s1(dbl1(z0))))))
ACTIVE(quote(dbl1(s(z0)))) → c7(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(quote(s(z0)))) → c7(QUOTE(mark(s1(quote(z0)))))
ACTIVE(quote(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
PROPER(dbl(dbl(z0))) → c45(DBL(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbl(s(z0))) → c45(DBL(s(proper(z0))), PROPER(s(z0)))
PROPER(dbl(dbls(z0))) → c45(DBL(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbl(cons(z0, z1))) → c45(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbl(sel(z0, z1))) → c45(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbl(indx(z0, z1))) → c45(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbl(from(z0))) → c45(DBL(from(proper(z0))), PROPER(from(z0)))
PROPER(dbl(dbl1(z0))) → c45(DBL(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbl(s1(z0))) → c45(DBL(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbl(sel1(z0, z1))) → c45(DBL(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbl(quote(z0))) → c45(DBL(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbl(0)) → c45(DBL(ok(0)))
PROPER(dbl(nil)) → c45(DBL(ok(nil)))
PROPER(dbl(01)) → c45(DBL(ok(01)))
PROPER(s(dbl(z0))) → c47(S(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(s(s(z0))) → c47(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(dbls(z0))) → c47(S(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(s(cons(z0, z1))) → c47(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(sel(z0, z1))) → c47(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(s(indx(z0, z1))) → c47(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(s(from(z0))) → c47(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(dbl1(z0))) → c47(S(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(s(s1(z0))) → c47(S(s1(proper(z0))), PROPER(s1(z0)))
PROPER(s(sel1(z0, z1))) → c47(S(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(s(quote(z0))) → c47(S(quote(proper(z0))), PROPER(quote(z0)))
PROPER(s(0)) → c47(S(ok(0)))
PROPER(s(nil)) → c47(S(ok(nil)))
PROPER(s(01)) → c47(S(ok(01)))
PROPER(dbls(dbl(z0))) → c48(DBLS(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbls(s(z0))) → c48(DBLS(s(proper(z0))), PROPER(s(z0)))
PROPER(dbls(dbls(z0))) → c48(DBLS(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbls(cons(z0, z1))) → c48(DBLS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbls(sel(z0, z1))) → c48(DBLS(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbls(indx(z0, z1))) → c48(DBLS(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbls(from(z0))) → c48(DBLS(from(proper(z0))), PROPER(from(z0)))
PROPER(dbls(dbl1(z0))) → c48(DBLS(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbls(s1(z0))) → c48(DBLS(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbls(sel1(z0, z1))) → c48(DBLS(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbls(quote(z0))) → c48(DBLS(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbls(0)) → c48(DBLS(ok(0)))
PROPER(dbls(nil)) → c48(DBLS(ok(nil)))
PROPER(dbls(01)) → c48(DBLS(ok(01)))
PROPER(cons(x0, dbl(z0))) → c50(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(cons(x0, s(z0))) → c50(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, dbls(z0))) → c50(CONS(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(cons(x0, cons(z0, z1))) → c50(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, sel(z0, z1))) → c50(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(cons(x0, indx(z0, z1))) → c50(CONS(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(cons(x0, from(z0))) → c50(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, dbl1(z0))) → c50(CONS(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(cons(x0, s1(z0))) → c50(CONS(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(cons(x0, sel1(z0, z1))) → c50(CONS(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(cons(x0, quote(z0))) → c50(CONS(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(cons(dbl(z0), x1)) → c50(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(cons(s(z0), x1)) → c50(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(dbls(z0), x1)) → c50(CONS(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c50(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(sel(z0, z1), x1)) → c50(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(cons(indx(z0, z1), x1)) → c50(CONS(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c50(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(dbl1(z0), x1)) → c50(CONS(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(cons(s1(z0), x1)) → c50(CONS(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(cons(sel1(z0, z1), x1)) → c50(CONS(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(cons(quote(z0), x1)) → c50(CONS(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c50(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c50(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, 01)) → c50(CONS(proper(x0), ok(01)), PROPER(x0))
PROPER(cons(0, x1)) → c50(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c50(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(01, x1)) → c50(CONS(ok(01), proper(x1)), PROPER(x1))
PROPER(sel(x0, dbl(z0))) → c51(SEL(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(sel(x0, s(z0))) → c51(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(sel(x0, dbls(z0))) → c51(SEL(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(sel(x0, cons(z0, z1))) → c51(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(sel(x0, sel(z0, z1))) → c51(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(sel(x0, indx(z0, z1))) → c51(SEL(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(sel(x0, from(z0))) → c51(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(sel(x0, dbl1(z0))) → c51(SEL(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(sel(x0, s1(z0))) → c51(SEL(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(sel(x0, sel1(z0, z1))) → c51(SEL(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(sel(x0, quote(z0))) → c51(SEL(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(sel(dbl(z0), x1)) → c51(SEL(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(sel(s(z0), x1)) → c51(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(sel(dbls(z0), x1)) → c51(SEL(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(sel(cons(z0, z1), x1)) → c51(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(sel(sel(z0, z1), x1)) → c51(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(sel(indx(z0, z1), x1)) → c51(SEL(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(sel(from(z0), x1)) → c51(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(sel(dbl1(z0), x1)) → c51(SEL(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(sel(s1(z0), x1)) → c51(SEL(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(sel(sel1(z0, z1), x1)) → c51(SEL(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(sel(quote(z0), x1)) → c51(SEL(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(sel(x0, 0)) → c51(SEL(proper(x0), ok(0)), PROPER(x0))
PROPER(sel(x0, nil)) → c51(SEL(proper(x0), ok(nil)), PROPER(x0))
PROPER(sel(x0, 01)) → c51(SEL(proper(x0), ok(01)), PROPER(x0))
PROPER(sel(0, x1)) → c51(SEL(ok(0), proper(x1)), PROPER(x1))
PROPER(sel(nil, x1)) → c51(SEL(ok(nil), proper(x1)), PROPER(x1))
PROPER(sel(01, x1)) → c51(SEL(ok(01), proper(x1)), PROPER(x1))
PROPER(indx(x0, dbl(z0))) → c52(INDX(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(indx(x0, s(z0))) → c52(INDX(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(indx(x0, dbls(z0))) → c52(INDX(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(indx(x0, cons(z0, z1))) → c52(INDX(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(indx(x0, sel(z0, z1))) → c52(INDX(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(indx(x0, indx(z0, z1))) → c52(INDX(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(indx(x0, from(z0))) → c52(INDX(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(indx(x0, dbl1(z0))) → c52(INDX(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(indx(x0, s1(z0))) → c52(INDX(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(indx(x0, sel1(z0, z1))) → c52(INDX(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(indx(x0, quote(z0))) → c52(INDX(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(indx(dbl(z0), x1)) → c52(INDX(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(indx(s(z0), x1)) → c52(INDX(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(indx(dbls(z0), x1)) → c52(INDX(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(indx(cons(z0, z1), x1)) → c52(INDX(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(indx(sel(z0, z1), x1)) → c52(INDX(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(indx(indx(z0, z1), x1)) → c52(INDX(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(indx(from(z0), x1)) → c52(INDX(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(indx(dbl1(z0), x1)) → c52(INDX(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(indx(s1(z0), x1)) → c52(INDX(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(indx(sel1(z0, z1), x1)) → c52(INDX(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(indx(quote(z0), x1)) → c52(INDX(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(indx(x0, 0)) → c52(INDX(proper(x0), ok(0)), PROPER(x0))
PROPER(indx(x0, nil)) → c52(INDX(proper(x0), ok(nil)), PROPER(x0))
PROPER(indx(x0, 01)) → c52(INDX(proper(x0), ok(01)), PROPER(x0))
PROPER(indx(0, x1)) → c52(INDX(ok(0), proper(x1)), PROPER(x1))
PROPER(indx(nil, x1)) → c52(INDX(ok(nil), proper(x1)), PROPER(x1))
PROPER(indx(01, x1)) → c52(INDX(ok(01), proper(x1)), PROPER(x1))
PROPER(from(dbl(z0))) → c53(FROM(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(from(s(z0))) → c53(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(dbls(z0))) → c53(FROM(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(from(cons(z0, z1))) → c53(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(sel(z0, z1))) → c53(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(from(indx(z0, z1))) → c53(FROM(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(from(from(z0))) → c53(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(dbl1(z0))) → c53(FROM(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(from(s1(z0))) → c53(FROM(s1(proper(z0))), PROPER(s1(z0)))
PROPER(from(sel1(z0, z1))) → c53(FROM(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(from(quote(z0))) → c53(FROM(quote(proper(z0))), PROPER(quote(z0)))
PROPER(from(0)) → c53(FROM(ok(0)))
PROPER(from(nil)) → c53(FROM(ok(nil)))
PROPER(from(01)) → c53(FROM(ok(01)))
S tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(dbl1(z0)) → c54(DBL1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c56(S1(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c57(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)))
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0))))))
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0))))))
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0)))
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(indx(sel1(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(indx(sel1(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel1(z0, z2)), x1), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(indx(quote(dbl(z0)), x1)) → c21(INDX(mark(dbl1(z0)), x1), ACTIVE(quote(dbl(z0))))
ACTIVE(indx(quote(sel(z0, z1)), x1)) → c21(INDX(mark(sel1(z0, z1)), x1), ACTIVE(quote(sel(z0, z1))))
ACTIVE(indx(dbl(z0), x1)) → c21(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
ACTIVE(indx(dbls(z0), x1)) → c21(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(indx(z0, z1), x1)) → c21(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1)))
ACTIVE(indx(dbl1(z0), x1)) → c21(INDX(dbl1(active(z0)), x1), ACTIVE(dbl1(z0)))
ACTIVE(indx(s1(z0), x1)) → c21(INDX(s1(active(z0)), x1), ACTIVE(s1(z0)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(active(z0), z1), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(z0, active(z1)), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(quote(z0), x1)) → c21(INDX(quote(active(z0)), x1), ACTIVE(quote(z0)))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)))
ACTIVE(indx(dbl(0), x1)) → c21(INDX(mark(0), x1))
ACTIVE(indx(dbls(nil), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(indx(indx(nil, z0), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0))))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1))
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0)))
ACTIVE(dbl1(sel(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl1(sel(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl1(sel1(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl1(sel1(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl1(quote(dbl(z0)))) → c22(DBL1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl1(quote(sel(z0, z1)))) → c22(DBL1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl1(dbl(z0))) → c22(DBL1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl1(dbls(z0))) → c22(DBL1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(indx(z0, z1))) → c22(DBL1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl1(dbl1(z0))) → c22(DBL1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl1(s1(z0))) → c22(DBL1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(quote(z0))) → c22(DBL1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(dbl1(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(dbl(0))) → c22(DBL1(mark(0)))
ACTIVE(dbl1(dbls(nil))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(indx(nil, z0))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(dbl1(0))) → c22(DBL1(mark(01)))
ACTIVE(dbl(dbl1(s(z0)))) → c4(DBL(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(DBLS(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(INDX(mark(s1(s1(dbl1(z0)))), x1))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(DBL1(mark(s(s(dbl(z0))))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(ACTIVE(dbl(s(z0))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(DBL1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(DBL1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl1(from(z0))) → c4(DBL1(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl1(from(z0))) → c4(ACTIVE(from(z0)))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(DBL1(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(s1(sel(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(s1(sel(s(z0), cons(z1, z2)))) → c23(S1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(s1(sel1(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(s1(sel1(s(z0), cons(z1, z2)))) → c23(S1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(s1(quote(dbl(z0)))) → c23(S1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(s1(quote(sel(z0, z1)))) → c23(S1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(s1(dbl(z0))) → c23(S1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(s1(dbls(z0))) → c23(S1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(s1(indx(z0, z1))) → c23(S1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(s1(dbl1(z0))) → c23(S1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(s1(s1(z0))) → c23(S1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(quote(z0))) → c23(S1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(s1(dbl(0))) → c23(S1(mark(0)))
ACTIVE(s1(dbls(nil))) → c23(S1(mark(nil)))
ACTIVE(s1(indx(nil, z0))) → c23(S1(mark(nil)))
ACTIVE(s1(dbl1(0))) → c23(S1(mark(01)))
ACTIVE(s1(dbl(s(z0)))) → c6(S1(mark(s(s(dbl(z0))))))
ACTIVE(s1(dbl(s(z0)))) → c6(ACTIVE(dbl(s(z0))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(S1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(S1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(s1(from(z0))) → c6(S1(mark(cons(z0, from(s(z0))))))
ACTIVE(s1(from(z0))) → c6(ACTIVE(from(z0)))
ACTIVE(s1(dbl1(s(z0)))) → c6(S1(mark(s1(s1(dbl1(z0))))))
ACTIVE(s1(dbl1(s(z0)))) → c6(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(sel(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(quote(sel(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(quote(sel1(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(quote(sel1(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(quote(quote(dbl(z0)))) → c26(QUOTE(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(quote(quote(sel(z0, z1)))) → c26(QUOTE(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(quote(dbl(z0))) → c26(QUOTE(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(quote(dbls(z0))) → c26(QUOTE(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(quote(indx(z0, z1))) → c26(QUOTE(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(quote(dbl1(z0))) → c26(QUOTE(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(quote(s1(z0))) → c26(QUOTE(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(quote(z0))) → c26(QUOTE(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(quote(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(quote(0))) → c22(DBL1(mark(01)))
ACTIVE(s1(quote(0))) → c23(S1(mark(01)))
ACTIVE(quote(dbl(0))) → c26(QUOTE(mark(0)))
ACTIVE(quote(dbls(nil))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(indx(nil, z0))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(dbl1(0))) → c26(QUOTE(mark(01)))
ACTIVE(quote(quote(0))) → c26(QUOTE(mark(01)))
ACTIVE(dbl(quote(s(z0)))) → c7(DBL(mark(s1(quote(z0)))))
ACTIVE(dbl(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(s(z0)))) → c7(DBLS(mark(s1(quote(z0)))))
ACTIVE(dbls(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(indx(quote(s(z0)), x1)) → c7(INDX(mark(s1(quote(z0))), x1))
ACTIVE(indx(quote(s(z0)), x1)) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbl1(quote(s(z0)))) → c7(DBL1(mark(s1(quote(z0)))))
ACTIVE(dbl1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(s1(quote(s(z0)))) → c7(S1(mark(s1(quote(z0)))))
ACTIVE(s1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(quote(dbl(s(z0)))) → c7(QUOTE(mark(s(s(dbl(z0))))))
ACTIVE(quote(dbl(s(z0)))) → c7(ACTIVE(dbl(s(z0))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(QUOTE(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(QUOTE(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(quote(from(z0))) → c7(QUOTE(mark(cons(z0, from(s(z0))))))
ACTIVE(quote(from(z0))) → c7(ACTIVE(from(z0)))
ACTIVE(quote(dbl1(s(z0)))) → c7(QUOTE(mark(s1(s1(dbl1(z0))))))
ACTIVE(quote(dbl1(s(z0)))) → c7(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(quote(s(z0)))) → c7(QUOTE(mark(s1(quote(z0)))))
ACTIVE(quote(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
PROPER(dbl(dbl(z0))) → c45(DBL(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbl(s(z0))) → c45(DBL(s(proper(z0))), PROPER(s(z0)))
PROPER(dbl(dbls(z0))) → c45(DBL(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbl(cons(z0, z1))) → c45(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbl(sel(z0, z1))) → c45(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbl(indx(z0, z1))) → c45(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbl(from(z0))) → c45(DBL(from(proper(z0))), PROPER(from(z0)))
PROPER(dbl(dbl1(z0))) → c45(DBL(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbl(s1(z0))) → c45(DBL(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbl(sel1(z0, z1))) → c45(DBL(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbl(quote(z0))) → c45(DBL(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbl(0)) → c45(DBL(ok(0)))
PROPER(dbl(nil)) → c45(DBL(ok(nil)))
PROPER(dbl(01)) → c45(DBL(ok(01)))
PROPER(s(dbl(z0))) → c47(S(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(s(s(z0))) → c47(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(dbls(z0))) → c47(S(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(s(cons(z0, z1))) → c47(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(sel(z0, z1))) → c47(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(s(indx(z0, z1))) → c47(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(s(from(z0))) → c47(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(dbl1(z0))) → c47(S(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(s(s1(z0))) → c47(S(s1(proper(z0))), PROPER(s1(z0)))
PROPER(s(sel1(z0, z1))) → c47(S(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(s(quote(z0))) → c47(S(quote(proper(z0))), PROPER(quote(z0)))
PROPER(s(0)) → c47(S(ok(0)))
PROPER(s(nil)) → c47(S(ok(nil)))
PROPER(s(01)) → c47(S(ok(01)))
PROPER(dbls(dbl(z0))) → c48(DBLS(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbls(s(z0))) → c48(DBLS(s(proper(z0))), PROPER(s(z0)))
PROPER(dbls(dbls(z0))) → c48(DBLS(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbls(cons(z0, z1))) → c48(DBLS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbls(sel(z0, z1))) → c48(DBLS(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbls(indx(z0, z1))) → c48(DBLS(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbls(from(z0))) → c48(DBLS(from(proper(z0))), PROPER(from(z0)))
PROPER(dbls(dbl1(z0))) → c48(DBLS(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbls(s1(z0))) → c48(DBLS(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbls(sel1(z0, z1))) → c48(DBLS(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbls(quote(z0))) → c48(DBLS(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbls(0)) → c48(DBLS(ok(0)))
PROPER(dbls(nil)) → c48(DBLS(ok(nil)))
PROPER(dbls(01)) → c48(DBLS(ok(01)))
PROPER(cons(x0, dbl(z0))) → c50(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(cons(x0, s(z0))) → c50(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, dbls(z0))) → c50(CONS(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(cons(x0, cons(z0, z1))) → c50(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, sel(z0, z1))) → c50(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(cons(x0, indx(z0, z1))) → c50(CONS(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(cons(x0, from(z0))) → c50(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, dbl1(z0))) → c50(CONS(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(cons(x0, s1(z0))) → c50(CONS(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(cons(x0, sel1(z0, z1))) → c50(CONS(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(cons(x0, quote(z0))) → c50(CONS(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(cons(dbl(z0), x1)) → c50(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(cons(s(z0), x1)) → c50(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(dbls(z0), x1)) → c50(CONS(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c50(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(sel(z0, z1), x1)) → c50(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(cons(indx(z0, z1), x1)) → c50(CONS(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c50(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(dbl1(z0), x1)) → c50(CONS(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(cons(s1(z0), x1)) → c50(CONS(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(cons(sel1(z0, z1), x1)) → c50(CONS(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(cons(quote(z0), x1)) → c50(CONS(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c50(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c50(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, 01)) → c50(CONS(proper(x0), ok(01)), PROPER(x0))
PROPER(cons(0, x1)) → c50(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c50(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(01, x1)) → c50(CONS(ok(01), proper(x1)), PROPER(x1))
PROPER(sel(x0, dbl(z0))) → c51(SEL(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(sel(x0, s(z0))) → c51(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(sel(x0, dbls(z0))) → c51(SEL(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(sel(x0, cons(z0, z1))) → c51(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(sel(x0, sel(z0, z1))) → c51(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(sel(x0, indx(z0, z1))) → c51(SEL(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(sel(x0, from(z0))) → c51(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(sel(x0, dbl1(z0))) → c51(SEL(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(sel(x0, s1(z0))) → c51(SEL(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(sel(x0, sel1(z0, z1))) → c51(SEL(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(sel(x0, quote(z0))) → c51(SEL(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(sel(dbl(z0), x1)) → c51(SEL(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(sel(s(z0), x1)) → c51(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(sel(dbls(z0), x1)) → c51(SEL(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(sel(cons(z0, z1), x1)) → c51(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(sel(sel(z0, z1), x1)) → c51(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(sel(indx(z0, z1), x1)) → c51(SEL(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(sel(from(z0), x1)) → c51(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(sel(dbl1(z0), x1)) → c51(SEL(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(sel(s1(z0), x1)) → c51(SEL(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(sel(sel1(z0, z1), x1)) → c51(SEL(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(sel(quote(z0), x1)) → c51(SEL(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(sel(x0, 0)) → c51(SEL(proper(x0), ok(0)), PROPER(x0))
PROPER(sel(x0, nil)) → c51(SEL(proper(x0), ok(nil)), PROPER(x0))
PROPER(sel(x0, 01)) → c51(SEL(proper(x0), ok(01)), PROPER(x0))
PROPER(sel(0, x1)) → c51(SEL(ok(0), proper(x1)), PROPER(x1))
PROPER(sel(nil, x1)) → c51(SEL(ok(nil), proper(x1)), PROPER(x1))
PROPER(sel(01, x1)) → c51(SEL(ok(01), proper(x1)), PROPER(x1))
PROPER(indx(x0, dbl(z0))) → c52(INDX(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(indx(x0, s(z0))) → c52(INDX(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(indx(x0, dbls(z0))) → c52(INDX(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(indx(x0, cons(z0, z1))) → c52(INDX(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(indx(x0, sel(z0, z1))) → c52(INDX(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(indx(x0, indx(z0, z1))) → c52(INDX(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(indx(x0, from(z0))) → c52(INDX(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(indx(x0, dbl1(z0))) → c52(INDX(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(indx(x0, s1(z0))) → c52(INDX(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(indx(x0, sel1(z0, z1))) → c52(INDX(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(indx(x0, quote(z0))) → c52(INDX(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(indx(dbl(z0), x1)) → c52(INDX(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(indx(s(z0), x1)) → c52(INDX(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(indx(dbls(z0), x1)) → c52(INDX(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(indx(cons(z0, z1), x1)) → c52(INDX(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(indx(sel(z0, z1), x1)) → c52(INDX(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(indx(indx(z0, z1), x1)) → c52(INDX(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(indx(from(z0), x1)) → c52(INDX(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(indx(dbl1(z0), x1)) → c52(INDX(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(indx(s1(z0), x1)) → c52(INDX(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(indx(sel1(z0, z1), x1)) → c52(INDX(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(indx(quote(z0), x1)) → c52(INDX(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(indx(x0, 0)) → c52(INDX(proper(x0), ok(0)), PROPER(x0))
PROPER(indx(x0, nil)) → c52(INDX(proper(x0), ok(nil)), PROPER(x0))
PROPER(indx(x0, 01)) → c52(INDX(proper(x0), ok(01)), PROPER(x0))
PROPER(indx(0, x1)) → c52(INDX(ok(0), proper(x1)), PROPER(x1))
PROPER(indx(nil, x1)) → c52(INDX(ok(nil), proper(x1)), PROPER(x1))
PROPER(indx(01, x1)) → c52(INDX(ok(01), proper(x1)), PROPER(x1))
PROPER(from(dbl(z0))) → c53(FROM(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(from(s(z0))) → c53(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(dbls(z0))) → c53(FROM(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(from(cons(z0, z1))) → c53(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(sel(z0, z1))) → c53(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(from(indx(z0, z1))) → c53(FROM(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(from(from(z0))) → c53(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(dbl1(z0))) → c53(FROM(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(from(s1(z0))) → c53(FROM(s1(proper(z0))), PROPER(s1(z0)))
PROPER(from(sel1(z0, z1))) → c53(FROM(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(from(quote(z0))) → c53(FROM(quote(proper(z0))), PROPER(quote(z0)))
PROPER(from(0)) → c53(FROM(ok(0)))
PROPER(from(nil)) → c53(FROM(ok(nil)))
PROPER(from(01)) → c53(FROM(ok(01)))
K tuples:none
Defined Rule Symbols:
active, s, dbl, cons, dbls, sel, indx, s1, dbl1, sel1, quote, proper, from
Defined Pair Symbols:
ACTIVE, DBL, DBLS, SEL, INDX, DBL1, S1, SEL1, QUOTE, PROPER, S, CONS, FROM, TOP
Compound Symbols:
c5, c12, c15, c16, c19, c20, c24, c25, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c54, c56, c57, c58, c59, c60, c61, c62, c63, c8, c, c17, c17, c1, c18, c18, c2, c21, c21, c3, c22, c22, c4, c23, c23, c6, c26, c26, c7, c45, c45, c47, c47, c48, c48, c50, c50, c51, c51, c52, c52, c53, c53
(75) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
PROPER(
dbl1(
z0)) →
c54(
DBL1(
proper(
z0)),
PROPER(
z0)) by
PROPER(dbl1(dbl(z0))) → c54(DBL1(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbl1(0)) → c54(DBL1(ok(0)), PROPER(0))
PROPER(dbl1(s(z0))) → c54(DBL1(s(proper(z0))), PROPER(s(z0)))
PROPER(dbl1(dbls(z0))) → c54(DBL1(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbl1(nil)) → c54(DBL1(ok(nil)), PROPER(nil))
PROPER(dbl1(cons(z0, z1))) → c54(DBL1(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbl1(sel(z0, z1))) → c54(DBL1(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbl1(indx(z0, z1))) → c54(DBL1(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbl1(from(z0))) → c54(DBL1(from(proper(z0))), PROPER(from(z0)))
PROPER(dbl1(dbl1(z0))) → c54(DBL1(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbl1(01)) → c54(DBL1(ok(01)), PROPER(01))
PROPER(dbl1(s1(z0))) → c54(DBL1(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbl1(sel1(z0, z1))) → c54(DBL1(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbl1(quote(z0))) → c54(DBL1(quote(proper(z0))), PROPER(quote(z0)))
(76) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(dbl(0)) → mark(0)
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
active(dbls(nil)) → mark(nil)
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1)))
active(sel(0, cons(z0, z1))) → mark(z0)
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
active(indx(nil, z0)) → mark(nil)
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2)))
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(dbl1(0)) → mark(01)
active(dbl1(s(z0))) → mark(s1(s1(dbl1(z0))))
active(sel1(0, cons(z0, z1))) → mark(z0)
active(sel1(s(z0), cons(z1, z2))) → mark(sel1(z0, z2))
active(quote(0)) → mark(01)
active(quote(s(z0))) → mark(s1(quote(z0)))
active(quote(dbl(z0))) → mark(dbl1(z0))
active(quote(sel(z0, z1))) → mark(sel1(z0, z1))
active(dbl(z0)) → dbl(active(z0))
active(dbls(z0)) → dbls(active(z0))
active(sel(z0, z1)) → sel(active(z0), z1)
active(sel(z0, z1)) → sel(z0, active(z1))
active(indx(z0, z1)) → indx(active(z0), z1)
active(dbl1(z0)) → dbl1(active(z0))
active(s1(z0)) → s1(active(z0))
active(sel1(z0, z1)) → sel1(active(z0), z1)
active(sel1(z0, z1)) → sel1(z0, active(z1))
active(quote(z0)) → quote(active(z0))
s(ok(z0)) → ok(s(z0))
dbl(mark(z0)) → mark(dbl(z0))
dbl(ok(z0)) → ok(dbl(z0))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
dbls(mark(z0)) → mark(dbls(z0))
dbls(ok(z0)) → ok(dbls(z0))
sel(mark(z0), z1) → mark(sel(z0, z1))
sel(z0, mark(z1)) → mark(sel(z0, z1))
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
indx(mark(z0), z1) → mark(indx(z0, z1))
indx(ok(z0), ok(z1)) → ok(indx(z0, z1))
s1(mark(z0)) → mark(s1(z0))
s1(ok(z0)) → ok(s1(z0))
dbl1(mark(z0)) → mark(dbl1(z0))
dbl1(ok(z0)) → ok(dbl1(z0))
sel1(mark(z0), z1) → mark(sel1(z0, z1))
sel1(z0, mark(z1)) → mark(sel1(z0, z1))
sel1(ok(z0), ok(z1)) → ok(sel1(z0, z1))
quote(mark(z0)) → mark(quote(z0))
quote(ok(z0)) → ok(quote(z0))
proper(dbl(z0)) → dbl(proper(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(dbls(z0)) → dbls(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
proper(indx(z0, z1)) → indx(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(dbl1(z0)) → dbl1(proper(z0))
proper(01) → ok(01)
proper(s1(z0)) → s1(proper(z0))
proper(sel1(z0, z1)) → sel1(proper(z0), proper(z1))
proper(quote(z0)) → quote(proper(z0))
from(ok(z0)) → ok(from(z0))
Tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(s1(z0)) → c56(S1(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c57(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)))
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0))))))
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0))))))
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0)))
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(indx(sel1(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(indx(sel1(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel1(z0, z2)), x1), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(indx(quote(dbl(z0)), x1)) → c21(INDX(mark(dbl1(z0)), x1), ACTIVE(quote(dbl(z0))))
ACTIVE(indx(quote(sel(z0, z1)), x1)) → c21(INDX(mark(sel1(z0, z1)), x1), ACTIVE(quote(sel(z0, z1))))
ACTIVE(indx(dbl(z0), x1)) → c21(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
ACTIVE(indx(dbls(z0), x1)) → c21(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(indx(z0, z1), x1)) → c21(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1)))
ACTIVE(indx(dbl1(z0), x1)) → c21(INDX(dbl1(active(z0)), x1), ACTIVE(dbl1(z0)))
ACTIVE(indx(s1(z0), x1)) → c21(INDX(s1(active(z0)), x1), ACTIVE(s1(z0)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(active(z0), z1), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(z0, active(z1)), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(quote(z0), x1)) → c21(INDX(quote(active(z0)), x1), ACTIVE(quote(z0)))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)))
ACTIVE(indx(dbl(0), x1)) → c21(INDX(mark(0), x1))
ACTIVE(indx(dbls(nil), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(indx(indx(nil, z0), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0))))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1))
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0)))
ACTIVE(dbl1(sel(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl1(sel(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl1(sel1(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl1(sel1(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl1(quote(dbl(z0)))) → c22(DBL1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl1(quote(sel(z0, z1)))) → c22(DBL1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl1(dbl(z0))) → c22(DBL1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl1(dbls(z0))) → c22(DBL1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(indx(z0, z1))) → c22(DBL1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl1(dbl1(z0))) → c22(DBL1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl1(s1(z0))) → c22(DBL1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(quote(z0))) → c22(DBL1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(dbl1(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(dbl(0))) → c22(DBL1(mark(0)))
ACTIVE(dbl1(dbls(nil))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(indx(nil, z0))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(dbl1(0))) → c22(DBL1(mark(01)))
ACTIVE(dbl(dbl1(s(z0)))) → c4(DBL(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(DBLS(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(INDX(mark(s1(s1(dbl1(z0)))), x1))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(DBL1(mark(s(s(dbl(z0))))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(ACTIVE(dbl(s(z0))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(DBL1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(DBL1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl1(from(z0))) → c4(DBL1(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl1(from(z0))) → c4(ACTIVE(from(z0)))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(DBL1(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(s1(sel(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(s1(sel(s(z0), cons(z1, z2)))) → c23(S1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(s1(sel1(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(s1(sel1(s(z0), cons(z1, z2)))) → c23(S1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(s1(quote(dbl(z0)))) → c23(S1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(s1(quote(sel(z0, z1)))) → c23(S1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(s1(dbl(z0))) → c23(S1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(s1(dbls(z0))) → c23(S1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(s1(indx(z0, z1))) → c23(S1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(s1(dbl1(z0))) → c23(S1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(s1(s1(z0))) → c23(S1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(quote(z0))) → c23(S1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(s1(dbl(0))) → c23(S1(mark(0)))
ACTIVE(s1(dbls(nil))) → c23(S1(mark(nil)))
ACTIVE(s1(indx(nil, z0))) → c23(S1(mark(nil)))
ACTIVE(s1(dbl1(0))) → c23(S1(mark(01)))
ACTIVE(s1(dbl(s(z0)))) → c6(S1(mark(s(s(dbl(z0))))))
ACTIVE(s1(dbl(s(z0)))) → c6(ACTIVE(dbl(s(z0))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(S1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(S1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(s1(from(z0))) → c6(S1(mark(cons(z0, from(s(z0))))))
ACTIVE(s1(from(z0))) → c6(ACTIVE(from(z0)))
ACTIVE(s1(dbl1(s(z0)))) → c6(S1(mark(s1(s1(dbl1(z0))))))
ACTIVE(s1(dbl1(s(z0)))) → c6(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(sel(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(quote(sel(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(quote(sel1(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(quote(sel1(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(quote(quote(dbl(z0)))) → c26(QUOTE(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(quote(quote(sel(z0, z1)))) → c26(QUOTE(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(quote(dbl(z0))) → c26(QUOTE(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(quote(dbls(z0))) → c26(QUOTE(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(quote(indx(z0, z1))) → c26(QUOTE(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(quote(dbl1(z0))) → c26(QUOTE(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(quote(s1(z0))) → c26(QUOTE(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(quote(z0))) → c26(QUOTE(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(quote(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(quote(0))) → c22(DBL1(mark(01)))
ACTIVE(s1(quote(0))) → c23(S1(mark(01)))
ACTIVE(quote(dbl(0))) → c26(QUOTE(mark(0)))
ACTIVE(quote(dbls(nil))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(indx(nil, z0))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(dbl1(0))) → c26(QUOTE(mark(01)))
ACTIVE(quote(quote(0))) → c26(QUOTE(mark(01)))
ACTIVE(dbl(quote(s(z0)))) → c7(DBL(mark(s1(quote(z0)))))
ACTIVE(dbl(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(s(z0)))) → c7(DBLS(mark(s1(quote(z0)))))
ACTIVE(dbls(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(indx(quote(s(z0)), x1)) → c7(INDX(mark(s1(quote(z0))), x1))
ACTIVE(indx(quote(s(z0)), x1)) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbl1(quote(s(z0)))) → c7(DBL1(mark(s1(quote(z0)))))
ACTIVE(dbl1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(s1(quote(s(z0)))) → c7(S1(mark(s1(quote(z0)))))
ACTIVE(s1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(quote(dbl(s(z0)))) → c7(QUOTE(mark(s(s(dbl(z0))))))
ACTIVE(quote(dbl(s(z0)))) → c7(ACTIVE(dbl(s(z0))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(QUOTE(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(QUOTE(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(quote(from(z0))) → c7(QUOTE(mark(cons(z0, from(s(z0))))))
ACTIVE(quote(from(z0))) → c7(ACTIVE(from(z0)))
ACTIVE(quote(dbl1(s(z0)))) → c7(QUOTE(mark(s1(s1(dbl1(z0))))))
ACTIVE(quote(dbl1(s(z0)))) → c7(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(quote(s(z0)))) → c7(QUOTE(mark(s1(quote(z0)))))
ACTIVE(quote(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
PROPER(dbl(dbl(z0))) → c45(DBL(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbl(s(z0))) → c45(DBL(s(proper(z0))), PROPER(s(z0)))
PROPER(dbl(dbls(z0))) → c45(DBL(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbl(cons(z0, z1))) → c45(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbl(sel(z0, z1))) → c45(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbl(indx(z0, z1))) → c45(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbl(from(z0))) → c45(DBL(from(proper(z0))), PROPER(from(z0)))
PROPER(dbl(dbl1(z0))) → c45(DBL(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbl(s1(z0))) → c45(DBL(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbl(sel1(z0, z1))) → c45(DBL(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbl(quote(z0))) → c45(DBL(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbl(0)) → c45(DBL(ok(0)))
PROPER(dbl(nil)) → c45(DBL(ok(nil)))
PROPER(dbl(01)) → c45(DBL(ok(01)))
PROPER(s(dbl(z0))) → c47(S(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(s(s(z0))) → c47(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(dbls(z0))) → c47(S(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(s(cons(z0, z1))) → c47(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(sel(z0, z1))) → c47(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(s(indx(z0, z1))) → c47(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(s(from(z0))) → c47(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(dbl1(z0))) → c47(S(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(s(s1(z0))) → c47(S(s1(proper(z0))), PROPER(s1(z0)))
PROPER(s(sel1(z0, z1))) → c47(S(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(s(quote(z0))) → c47(S(quote(proper(z0))), PROPER(quote(z0)))
PROPER(s(0)) → c47(S(ok(0)))
PROPER(s(nil)) → c47(S(ok(nil)))
PROPER(s(01)) → c47(S(ok(01)))
PROPER(dbls(dbl(z0))) → c48(DBLS(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbls(s(z0))) → c48(DBLS(s(proper(z0))), PROPER(s(z0)))
PROPER(dbls(dbls(z0))) → c48(DBLS(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbls(cons(z0, z1))) → c48(DBLS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbls(sel(z0, z1))) → c48(DBLS(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbls(indx(z0, z1))) → c48(DBLS(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbls(from(z0))) → c48(DBLS(from(proper(z0))), PROPER(from(z0)))
PROPER(dbls(dbl1(z0))) → c48(DBLS(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbls(s1(z0))) → c48(DBLS(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbls(sel1(z0, z1))) → c48(DBLS(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbls(quote(z0))) → c48(DBLS(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbls(0)) → c48(DBLS(ok(0)))
PROPER(dbls(nil)) → c48(DBLS(ok(nil)))
PROPER(dbls(01)) → c48(DBLS(ok(01)))
PROPER(cons(x0, dbl(z0))) → c50(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(cons(x0, s(z0))) → c50(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, dbls(z0))) → c50(CONS(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(cons(x0, cons(z0, z1))) → c50(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, sel(z0, z1))) → c50(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(cons(x0, indx(z0, z1))) → c50(CONS(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(cons(x0, from(z0))) → c50(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, dbl1(z0))) → c50(CONS(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(cons(x0, s1(z0))) → c50(CONS(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(cons(x0, sel1(z0, z1))) → c50(CONS(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(cons(x0, quote(z0))) → c50(CONS(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(cons(dbl(z0), x1)) → c50(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(cons(s(z0), x1)) → c50(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(dbls(z0), x1)) → c50(CONS(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c50(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(sel(z0, z1), x1)) → c50(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(cons(indx(z0, z1), x1)) → c50(CONS(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c50(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(dbl1(z0), x1)) → c50(CONS(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(cons(s1(z0), x1)) → c50(CONS(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(cons(sel1(z0, z1), x1)) → c50(CONS(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(cons(quote(z0), x1)) → c50(CONS(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c50(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c50(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, 01)) → c50(CONS(proper(x0), ok(01)), PROPER(x0))
PROPER(cons(0, x1)) → c50(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c50(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(01, x1)) → c50(CONS(ok(01), proper(x1)), PROPER(x1))
PROPER(sel(x0, dbl(z0))) → c51(SEL(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(sel(x0, s(z0))) → c51(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(sel(x0, dbls(z0))) → c51(SEL(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(sel(x0, cons(z0, z1))) → c51(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(sel(x0, sel(z0, z1))) → c51(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(sel(x0, indx(z0, z1))) → c51(SEL(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(sel(x0, from(z0))) → c51(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(sel(x0, dbl1(z0))) → c51(SEL(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(sel(x0, s1(z0))) → c51(SEL(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(sel(x0, sel1(z0, z1))) → c51(SEL(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(sel(x0, quote(z0))) → c51(SEL(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(sel(dbl(z0), x1)) → c51(SEL(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(sel(s(z0), x1)) → c51(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(sel(dbls(z0), x1)) → c51(SEL(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(sel(cons(z0, z1), x1)) → c51(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(sel(sel(z0, z1), x1)) → c51(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(sel(indx(z0, z1), x1)) → c51(SEL(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(sel(from(z0), x1)) → c51(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(sel(dbl1(z0), x1)) → c51(SEL(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(sel(s1(z0), x1)) → c51(SEL(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(sel(sel1(z0, z1), x1)) → c51(SEL(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(sel(quote(z0), x1)) → c51(SEL(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(sel(x0, 0)) → c51(SEL(proper(x0), ok(0)), PROPER(x0))
PROPER(sel(x0, nil)) → c51(SEL(proper(x0), ok(nil)), PROPER(x0))
PROPER(sel(x0, 01)) → c51(SEL(proper(x0), ok(01)), PROPER(x0))
PROPER(sel(0, x1)) → c51(SEL(ok(0), proper(x1)), PROPER(x1))
PROPER(sel(nil, x1)) → c51(SEL(ok(nil), proper(x1)), PROPER(x1))
PROPER(sel(01, x1)) → c51(SEL(ok(01), proper(x1)), PROPER(x1))
PROPER(indx(x0, dbl(z0))) → c52(INDX(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(indx(x0, s(z0))) → c52(INDX(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(indx(x0, dbls(z0))) → c52(INDX(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(indx(x0, cons(z0, z1))) → c52(INDX(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(indx(x0, sel(z0, z1))) → c52(INDX(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(indx(x0, indx(z0, z1))) → c52(INDX(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(indx(x0, from(z0))) → c52(INDX(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(indx(x0, dbl1(z0))) → c52(INDX(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(indx(x0, s1(z0))) → c52(INDX(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(indx(x0, sel1(z0, z1))) → c52(INDX(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(indx(x0, quote(z0))) → c52(INDX(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(indx(dbl(z0), x1)) → c52(INDX(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(indx(s(z0), x1)) → c52(INDX(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(indx(dbls(z0), x1)) → c52(INDX(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(indx(cons(z0, z1), x1)) → c52(INDX(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(indx(sel(z0, z1), x1)) → c52(INDX(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(indx(indx(z0, z1), x1)) → c52(INDX(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(indx(from(z0), x1)) → c52(INDX(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(indx(dbl1(z0), x1)) → c52(INDX(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(indx(s1(z0), x1)) → c52(INDX(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(indx(sel1(z0, z1), x1)) → c52(INDX(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(indx(quote(z0), x1)) → c52(INDX(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(indx(x0, 0)) → c52(INDX(proper(x0), ok(0)), PROPER(x0))
PROPER(indx(x0, nil)) → c52(INDX(proper(x0), ok(nil)), PROPER(x0))
PROPER(indx(x0, 01)) → c52(INDX(proper(x0), ok(01)), PROPER(x0))
PROPER(indx(0, x1)) → c52(INDX(ok(0), proper(x1)), PROPER(x1))
PROPER(indx(nil, x1)) → c52(INDX(ok(nil), proper(x1)), PROPER(x1))
PROPER(indx(01, x1)) → c52(INDX(ok(01), proper(x1)), PROPER(x1))
PROPER(from(dbl(z0))) → c53(FROM(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(from(s(z0))) → c53(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(dbls(z0))) → c53(FROM(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(from(cons(z0, z1))) → c53(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(sel(z0, z1))) → c53(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(from(indx(z0, z1))) → c53(FROM(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(from(from(z0))) → c53(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(dbl1(z0))) → c53(FROM(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(from(s1(z0))) → c53(FROM(s1(proper(z0))), PROPER(s1(z0)))
PROPER(from(sel1(z0, z1))) → c53(FROM(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(from(quote(z0))) → c53(FROM(quote(proper(z0))), PROPER(quote(z0)))
PROPER(from(0)) → c53(FROM(ok(0)))
PROPER(from(nil)) → c53(FROM(ok(nil)))
PROPER(from(01)) → c53(FROM(ok(01)))
PROPER(dbl1(dbl(z0))) → c54(DBL1(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbl1(0)) → c54(DBL1(ok(0)), PROPER(0))
PROPER(dbl1(s(z0))) → c54(DBL1(s(proper(z0))), PROPER(s(z0)))
PROPER(dbl1(dbls(z0))) → c54(DBL1(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbl1(nil)) → c54(DBL1(ok(nil)), PROPER(nil))
PROPER(dbl1(cons(z0, z1))) → c54(DBL1(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbl1(sel(z0, z1))) → c54(DBL1(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbl1(indx(z0, z1))) → c54(DBL1(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbl1(from(z0))) → c54(DBL1(from(proper(z0))), PROPER(from(z0)))
PROPER(dbl1(dbl1(z0))) → c54(DBL1(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbl1(01)) → c54(DBL1(ok(01)), PROPER(01))
PROPER(dbl1(s1(z0))) → c54(DBL1(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbl1(sel1(z0, z1))) → c54(DBL1(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbl1(quote(z0))) → c54(DBL1(quote(proper(z0))), PROPER(quote(z0)))
S tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(s1(z0)) → c56(S1(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c57(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)))
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0))))))
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0))))))
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0)))
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(indx(sel1(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(indx(sel1(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel1(z0, z2)), x1), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(indx(quote(dbl(z0)), x1)) → c21(INDX(mark(dbl1(z0)), x1), ACTIVE(quote(dbl(z0))))
ACTIVE(indx(quote(sel(z0, z1)), x1)) → c21(INDX(mark(sel1(z0, z1)), x1), ACTIVE(quote(sel(z0, z1))))
ACTIVE(indx(dbl(z0), x1)) → c21(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
ACTIVE(indx(dbls(z0), x1)) → c21(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(indx(z0, z1), x1)) → c21(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1)))
ACTIVE(indx(dbl1(z0), x1)) → c21(INDX(dbl1(active(z0)), x1), ACTIVE(dbl1(z0)))
ACTIVE(indx(s1(z0), x1)) → c21(INDX(s1(active(z0)), x1), ACTIVE(s1(z0)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(active(z0), z1), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(z0, active(z1)), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(quote(z0), x1)) → c21(INDX(quote(active(z0)), x1), ACTIVE(quote(z0)))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)))
ACTIVE(indx(dbl(0), x1)) → c21(INDX(mark(0), x1))
ACTIVE(indx(dbls(nil), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(indx(indx(nil, z0), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0))))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1))
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0)))
ACTIVE(dbl1(sel(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl1(sel(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl1(sel1(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl1(sel1(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl1(quote(dbl(z0)))) → c22(DBL1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl1(quote(sel(z0, z1)))) → c22(DBL1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl1(dbl(z0))) → c22(DBL1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl1(dbls(z0))) → c22(DBL1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(indx(z0, z1))) → c22(DBL1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl1(dbl1(z0))) → c22(DBL1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl1(s1(z0))) → c22(DBL1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(quote(z0))) → c22(DBL1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(dbl1(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(dbl(0))) → c22(DBL1(mark(0)))
ACTIVE(dbl1(dbls(nil))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(indx(nil, z0))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(dbl1(0))) → c22(DBL1(mark(01)))
ACTIVE(dbl(dbl1(s(z0)))) → c4(DBL(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(DBLS(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(INDX(mark(s1(s1(dbl1(z0)))), x1))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(DBL1(mark(s(s(dbl(z0))))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(ACTIVE(dbl(s(z0))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(DBL1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(DBL1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl1(from(z0))) → c4(DBL1(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl1(from(z0))) → c4(ACTIVE(from(z0)))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(DBL1(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(s1(sel(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(s1(sel(s(z0), cons(z1, z2)))) → c23(S1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(s1(sel1(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(s1(sel1(s(z0), cons(z1, z2)))) → c23(S1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(s1(quote(dbl(z0)))) → c23(S1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(s1(quote(sel(z0, z1)))) → c23(S1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(s1(dbl(z0))) → c23(S1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(s1(dbls(z0))) → c23(S1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(s1(indx(z0, z1))) → c23(S1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(s1(dbl1(z0))) → c23(S1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(s1(s1(z0))) → c23(S1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(quote(z0))) → c23(S1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(s1(dbl(0))) → c23(S1(mark(0)))
ACTIVE(s1(dbls(nil))) → c23(S1(mark(nil)))
ACTIVE(s1(indx(nil, z0))) → c23(S1(mark(nil)))
ACTIVE(s1(dbl1(0))) → c23(S1(mark(01)))
ACTIVE(s1(dbl(s(z0)))) → c6(S1(mark(s(s(dbl(z0))))))
ACTIVE(s1(dbl(s(z0)))) → c6(ACTIVE(dbl(s(z0))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(S1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(S1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(s1(from(z0))) → c6(S1(mark(cons(z0, from(s(z0))))))
ACTIVE(s1(from(z0))) → c6(ACTIVE(from(z0)))
ACTIVE(s1(dbl1(s(z0)))) → c6(S1(mark(s1(s1(dbl1(z0))))))
ACTIVE(s1(dbl1(s(z0)))) → c6(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(sel(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(quote(sel(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(quote(sel1(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(quote(sel1(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(quote(quote(dbl(z0)))) → c26(QUOTE(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(quote(quote(sel(z0, z1)))) → c26(QUOTE(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(quote(dbl(z0))) → c26(QUOTE(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(quote(dbls(z0))) → c26(QUOTE(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(quote(indx(z0, z1))) → c26(QUOTE(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(quote(dbl1(z0))) → c26(QUOTE(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(quote(s1(z0))) → c26(QUOTE(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(quote(z0))) → c26(QUOTE(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(quote(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(quote(0))) → c22(DBL1(mark(01)))
ACTIVE(s1(quote(0))) → c23(S1(mark(01)))
ACTIVE(quote(dbl(0))) → c26(QUOTE(mark(0)))
ACTIVE(quote(dbls(nil))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(indx(nil, z0))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(dbl1(0))) → c26(QUOTE(mark(01)))
ACTIVE(quote(quote(0))) → c26(QUOTE(mark(01)))
ACTIVE(dbl(quote(s(z0)))) → c7(DBL(mark(s1(quote(z0)))))
ACTIVE(dbl(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(s(z0)))) → c7(DBLS(mark(s1(quote(z0)))))
ACTIVE(dbls(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(indx(quote(s(z0)), x1)) → c7(INDX(mark(s1(quote(z0))), x1))
ACTIVE(indx(quote(s(z0)), x1)) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbl1(quote(s(z0)))) → c7(DBL1(mark(s1(quote(z0)))))
ACTIVE(dbl1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(s1(quote(s(z0)))) → c7(S1(mark(s1(quote(z0)))))
ACTIVE(s1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(quote(dbl(s(z0)))) → c7(QUOTE(mark(s(s(dbl(z0))))))
ACTIVE(quote(dbl(s(z0)))) → c7(ACTIVE(dbl(s(z0))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(QUOTE(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(QUOTE(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(quote(from(z0))) → c7(QUOTE(mark(cons(z0, from(s(z0))))))
ACTIVE(quote(from(z0))) → c7(ACTIVE(from(z0)))
ACTIVE(quote(dbl1(s(z0)))) → c7(QUOTE(mark(s1(s1(dbl1(z0))))))
ACTIVE(quote(dbl1(s(z0)))) → c7(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(quote(s(z0)))) → c7(QUOTE(mark(s1(quote(z0)))))
ACTIVE(quote(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
PROPER(dbl(dbl(z0))) → c45(DBL(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbl(s(z0))) → c45(DBL(s(proper(z0))), PROPER(s(z0)))
PROPER(dbl(dbls(z0))) → c45(DBL(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbl(cons(z0, z1))) → c45(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbl(sel(z0, z1))) → c45(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbl(indx(z0, z1))) → c45(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbl(from(z0))) → c45(DBL(from(proper(z0))), PROPER(from(z0)))
PROPER(dbl(dbl1(z0))) → c45(DBL(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbl(s1(z0))) → c45(DBL(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbl(sel1(z0, z1))) → c45(DBL(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbl(quote(z0))) → c45(DBL(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbl(0)) → c45(DBL(ok(0)))
PROPER(dbl(nil)) → c45(DBL(ok(nil)))
PROPER(dbl(01)) → c45(DBL(ok(01)))
PROPER(s(dbl(z0))) → c47(S(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(s(s(z0))) → c47(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(dbls(z0))) → c47(S(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(s(cons(z0, z1))) → c47(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(sel(z0, z1))) → c47(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(s(indx(z0, z1))) → c47(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(s(from(z0))) → c47(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(dbl1(z0))) → c47(S(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(s(s1(z0))) → c47(S(s1(proper(z0))), PROPER(s1(z0)))
PROPER(s(sel1(z0, z1))) → c47(S(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(s(quote(z0))) → c47(S(quote(proper(z0))), PROPER(quote(z0)))
PROPER(s(0)) → c47(S(ok(0)))
PROPER(s(nil)) → c47(S(ok(nil)))
PROPER(s(01)) → c47(S(ok(01)))
PROPER(dbls(dbl(z0))) → c48(DBLS(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbls(s(z0))) → c48(DBLS(s(proper(z0))), PROPER(s(z0)))
PROPER(dbls(dbls(z0))) → c48(DBLS(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbls(cons(z0, z1))) → c48(DBLS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbls(sel(z0, z1))) → c48(DBLS(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbls(indx(z0, z1))) → c48(DBLS(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbls(from(z0))) → c48(DBLS(from(proper(z0))), PROPER(from(z0)))
PROPER(dbls(dbl1(z0))) → c48(DBLS(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbls(s1(z0))) → c48(DBLS(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbls(sel1(z0, z1))) → c48(DBLS(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbls(quote(z0))) → c48(DBLS(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbls(0)) → c48(DBLS(ok(0)))
PROPER(dbls(nil)) → c48(DBLS(ok(nil)))
PROPER(dbls(01)) → c48(DBLS(ok(01)))
PROPER(cons(x0, dbl(z0))) → c50(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(cons(x0, s(z0))) → c50(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, dbls(z0))) → c50(CONS(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(cons(x0, cons(z0, z1))) → c50(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, sel(z0, z1))) → c50(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(cons(x0, indx(z0, z1))) → c50(CONS(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(cons(x0, from(z0))) → c50(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, dbl1(z0))) → c50(CONS(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(cons(x0, s1(z0))) → c50(CONS(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(cons(x0, sel1(z0, z1))) → c50(CONS(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(cons(x0, quote(z0))) → c50(CONS(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(cons(dbl(z0), x1)) → c50(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(cons(s(z0), x1)) → c50(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(dbls(z0), x1)) → c50(CONS(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c50(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(sel(z0, z1), x1)) → c50(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(cons(indx(z0, z1), x1)) → c50(CONS(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c50(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(dbl1(z0), x1)) → c50(CONS(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(cons(s1(z0), x1)) → c50(CONS(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(cons(sel1(z0, z1), x1)) → c50(CONS(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(cons(quote(z0), x1)) → c50(CONS(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c50(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c50(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, 01)) → c50(CONS(proper(x0), ok(01)), PROPER(x0))
PROPER(cons(0, x1)) → c50(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c50(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(01, x1)) → c50(CONS(ok(01), proper(x1)), PROPER(x1))
PROPER(sel(x0, dbl(z0))) → c51(SEL(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(sel(x0, s(z0))) → c51(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(sel(x0, dbls(z0))) → c51(SEL(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(sel(x0, cons(z0, z1))) → c51(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(sel(x0, sel(z0, z1))) → c51(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(sel(x0, indx(z0, z1))) → c51(SEL(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(sel(x0, from(z0))) → c51(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(sel(x0, dbl1(z0))) → c51(SEL(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(sel(x0, s1(z0))) → c51(SEL(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(sel(x0, sel1(z0, z1))) → c51(SEL(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(sel(x0, quote(z0))) → c51(SEL(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(sel(dbl(z0), x1)) → c51(SEL(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(sel(s(z0), x1)) → c51(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(sel(dbls(z0), x1)) → c51(SEL(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(sel(cons(z0, z1), x1)) → c51(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(sel(sel(z0, z1), x1)) → c51(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(sel(indx(z0, z1), x1)) → c51(SEL(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(sel(from(z0), x1)) → c51(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(sel(dbl1(z0), x1)) → c51(SEL(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(sel(s1(z0), x1)) → c51(SEL(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(sel(sel1(z0, z1), x1)) → c51(SEL(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(sel(quote(z0), x1)) → c51(SEL(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(sel(x0, 0)) → c51(SEL(proper(x0), ok(0)), PROPER(x0))
PROPER(sel(x0, nil)) → c51(SEL(proper(x0), ok(nil)), PROPER(x0))
PROPER(sel(x0, 01)) → c51(SEL(proper(x0), ok(01)), PROPER(x0))
PROPER(sel(0, x1)) → c51(SEL(ok(0), proper(x1)), PROPER(x1))
PROPER(sel(nil, x1)) → c51(SEL(ok(nil), proper(x1)), PROPER(x1))
PROPER(sel(01, x1)) → c51(SEL(ok(01), proper(x1)), PROPER(x1))
PROPER(indx(x0, dbl(z0))) → c52(INDX(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(indx(x0, s(z0))) → c52(INDX(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(indx(x0, dbls(z0))) → c52(INDX(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(indx(x0, cons(z0, z1))) → c52(INDX(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(indx(x0, sel(z0, z1))) → c52(INDX(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(indx(x0, indx(z0, z1))) → c52(INDX(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(indx(x0, from(z0))) → c52(INDX(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(indx(x0, dbl1(z0))) → c52(INDX(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(indx(x0, s1(z0))) → c52(INDX(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(indx(x0, sel1(z0, z1))) → c52(INDX(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(indx(x0, quote(z0))) → c52(INDX(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(indx(dbl(z0), x1)) → c52(INDX(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(indx(s(z0), x1)) → c52(INDX(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(indx(dbls(z0), x1)) → c52(INDX(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(indx(cons(z0, z1), x1)) → c52(INDX(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(indx(sel(z0, z1), x1)) → c52(INDX(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(indx(indx(z0, z1), x1)) → c52(INDX(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(indx(from(z0), x1)) → c52(INDX(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(indx(dbl1(z0), x1)) → c52(INDX(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(indx(s1(z0), x1)) → c52(INDX(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(indx(sel1(z0, z1), x1)) → c52(INDX(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(indx(quote(z0), x1)) → c52(INDX(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(indx(x0, 0)) → c52(INDX(proper(x0), ok(0)), PROPER(x0))
PROPER(indx(x0, nil)) → c52(INDX(proper(x0), ok(nil)), PROPER(x0))
PROPER(indx(x0, 01)) → c52(INDX(proper(x0), ok(01)), PROPER(x0))
PROPER(indx(0, x1)) → c52(INDX(ok(0), proper(x1)), PROPER(x1))
PROPER(indx(nil, x1)) → c52(INDX(ok(nil), proper(x1)), PROPER(x1))
PROPER(indx(01, x1)) → c52(INDX(ok(01), proper(x1)), PROPER(x1))
PROPER(from(dbl(z0))) → c53(FROM(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(from(s(z0))) → c53(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(dbls(z0))) → c53(FROM(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(from(cons(z0, z1))) → c53(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(sel(z0, z1))) → c53(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(from(indx(z0, z1))) → c53(FROM(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(from(from(z0))) → c53(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(dbl1(z0))) → c53(FROM(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(from(s1(z0))) → c53(FROM(s1(proper(z0))), PROPER(s1(z0)))
PROPER(from(sel1(z0, z1))) → c53(FROM(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(from(quote(z0))) → c53(FROM(quote(proper(z0))), PROPER(quote(z0)))
PROPER(from(0)) → c53(FROM(ok(0)))
PROPER(from(nil)) → c53(FROM(ok(nil)))
PROPER(from(01)) → c53(FROM(ok(01)))
PROPER(dbl1(dbl(z0))) → c54(DBL1(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbl1(0)) → c54(DBL1(ok(0)), PROPER(0))
PROPER(dbl1(s(z0))) → c54(DBL1(s(proper(z0))), PROPER(s(z0)))
PROPER(dbl1(dbls(z0))) → c54(DBL1(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbl1(nil)) → c54(DBL1(ok(nil)), PROPER(nil))
PROPER(dbl1(cons(z0, z1))) → c54(DBL1(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbl1(sel(z0, z1))) → c54(DBL1(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbl1(indx(z0, z1))) → c54(DBL1(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbl1(from(z0))) → c54(DBL1(from(proper(z0))), PROPER(from(z0)))
PROPER(dbl1(dbl1(z0))) → c54(DBL1(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbl1(01)) → c54(DBL1(ok(01)), PROPER(01))
PROPER(dbl1(s1(z0))) → c54(DBL1(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbl1(sel1(z0, z1))) → c54(DBL1(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbl1(quote(z0))) → c54(DBL1(quote(proper(z0))), PROPER(quote(z0)))
K tuples:none
Defined Rule Symbols:
active, s, dbl, cons, dbls, sel, indx, s1, dbl1, sel1, quote, proper, from
Defined Pair Symbols:
ACTIVE, DBL, DBLS, SEL, INDX, DBL1, S1, SEL1, QUOTE, PROPER, S, CONS, FROM, TOP
Compound Symbols:
c5, c12, c15, c16, c19, c20, c24, c25, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c56, c57, c58, c59, c60, c61, c62, c63, c8, c, c17, c17, c1, c18, c18, c2, c21, c21, c3, c22, c22, c4, c23, c23, c6, c26, c26, c7, c45, c45, c47, c47, c48, c48, c50, c50, c51, c51, c52, c52, c53, c53, c54
(77) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 3 trailing tuple parts
(78) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(dbl(0)) → mark(0)
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
active(dbls(nil)) → mark(nil)
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1)))
active(sel(0, cons(z0, z1))) → mark(z0)
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
active(indx(nil, z0)) → mark(nil)
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2)))
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(dbl1(0)) → mark(01)
active(dbl1(s(z0))) → mark(s1(s1(dbl1(z0))))
active(sel1(0, cons(z0, z1))) → mark(z0)
active(sel1(s(z0), cons(z1, z2))) → mark(sel1(z0, z2))
active(quote(0)) → mark(01)
active(quote(s(z0))) → mark(s1(quote(z0)))
active(quote(dbl(z0))) → mark(dbl1(z0))
active(quote(sel(z0, z1))) → mark(sel1(z0, z1))
active(dbl(z0)) → dbl(active(z0))
active(dbls(z0)) → dbls(active(z0))
active(sel(z0, z1)) → sel(active(z0), z1)
active(sel(z0, z1)) → sel(z0, active(z1))
active(indx(z0, z1)) → indx(active(z0), z1)
active(dbl1(z0)) → dbl1(active(z0))
active(s1(z0)) → s1(active(z0))
active(sel1(z0, z1)) → sel1(active(z0), z1)
active(sel1(z0, z1)) → sel1(z0, active(z1))
active(quote(z0)) → quote(active(z0))
s(ok(z0)) → ok(s(z0))
dbl(mark(z0)) → mark(dbl(z0))
dbl(ok(z0)) → ok(dbl(z0))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
dbls(mark(z0)) → mark(dbls(z0))
dbls(ok(z0)) → ok(dbls(z0))
sel(mark(z0), z1) → mark(sel(z0, z1))
sel(z0, mark(z1)) → mark(sel(z0, z1))
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
indx(mark(z0), z1) → mark(indx(z0, z1))
indx(ok(z0), ok(z1)) → ok(indx(z0, z1))
s1(mark(z0)) → mark(s1(z0))
s1(ok(z0)) → ok(s1(z0))
dbl1(mark(z0)) → mark(dbl1(z0))
dbl1(ok(z0)) → ok(dbl1(z0))
sel1(mark(z0), z1) → mark(sel1(z0, z1))
sel1(z0, mark(z1)) → mark(sel1(z0, z1))
sel1(ok(z0), ok(z1)) → ok(sel1(z0, z1))
quote(mark(z0)) → mark(quote(z0))
quote(ok(z0)) → ok(quote(z0))
proper(dbl(z0)) → dbl(proper(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(dbls(z0)) → dbls(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
proper(indx(z0, z1)) → indx(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(dbl1(z0)) → dbl1(proper(z0))
proper(01) → ok(01)
proper(s1(z0)) → s1(proper(z0))
proper(sel1(z0, z1)) → sel1(proper(z0), proper(z1))
proper(quote(z0)) → quote(proper(z0))
from(ok(z0)) → ok(from(z0))
Tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(s1(z0)) → c56(S1(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c57(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)))
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0))))))
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0))))))
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0)))
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(indx(sel1(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(indx(sel1(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel1(z0, z2)), x1), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(indx(quote(dbl(z0)), x1)) → c21(INDX(mark(dbl1(z0)), x1), ACTIVE(quote(dbl(z0))))
ACTIVE(indx(quote(sel(z0, z1)), x1)) → c21(INDX(mark(sel1(z0, z1)), x1), ACTIVE(quote(sel(z0, z1))))
ACTIVE(indx(dbl(z0), x1)) → c21(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
ACTIVE(indx(dbls(z0), x1)) → c21(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(indx(z0, z1), x1)) → c21(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1)))
ACTIVE(indx(dbl1(z0), x1)) → c21(INDX(dbl1(active(z0)), x1), ACTIVE(dbl1(z0)))
ACTIVE(indx(s1(z0), x1)) → c21(INDX(s1(active(z0)), x1), ACTIVE(s1(z0)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(active(z0), z1), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(z0, active(z1)), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(quote(z0), x1)) → c21(INDX(quote(active(z0)), x1), ACTIVE(quote(z0)))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)))
ACTIVE(indx(dbl(0), x1)) → c21(INDX(mark(0), x1))
ACTIVE(indx(dbls(nil), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(indx(indx(nil, z0), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0))))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1))
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0)))
ACTIVE(dbl1(sel(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl1(sel(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl1(sel1(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl1(sel1(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl1(quote(dbl(z0)))) → c22(DBL1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl1(quote(sel(z0, z1)))) → c22(DBL1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl1(dbl(z0))) → c22(DBL1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl1(dbls(z0))) → c22(DBL1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(indx(z0, z1))) → c22(DBL1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl1(dbl1(z0))) → c22(DBL1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl1(s1(z0))) → c22(DBL1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(quote(z0))) → c22(DBL1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(dbl1(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(dbl(0))) → c22(DBL1(mark(0)))
ACTIVE(dbl1(dbls(nil))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(indx(nil, z0))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(dbl1(0))) → c22(DBL1(mark(01)))
ACTIVE(dbl(dbl1(s(z0)))) → c4(DBL(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(DBLS(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(INDX(mark(s1(s1(dbl1(z0)))), x1))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(DBL1(mark(s(s(dbl(z0))))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(ACTIVE(dbl(s(z0))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(DBL1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(DBL1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl1(from(z0))) → c4(DBL1(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl1(from(z0))) → c4(ACTIVE(from(z0)))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(DBL1(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(s1(sel(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(s1(sel(s(z0), cons(z1, z2)))) → c23(S1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(s1(sel1(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(s1(sel1(s(z0), cons(z1, z2)))) → c23(S1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(s1(quote(dbl(z0)))) → c23(S1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(s1(quote(sel(z0, z1)))) → c23(S1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(s1(dbl(z0))) → c23(S1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(s1(dbls(z0))) → c23(S1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(s1(indx(z0, z1))) → c23(S1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(s1(dbl1(z0))) → c23(S1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(s1(s1(z0))) → c23(S1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(quote(z0))) → c23(S1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(s1(dbl(0))) → c23(S1(mark(0)))
ACTIVE(s1(dbls(nil))) → c23(S1(mark(nil)))
ACTIVE(s1(indx(nil, z0))) → c23(S1(mark(nil)))
ACTIVE(s1(dbl1(0))) → c23(S1(mark(01)))
ACTIVE(s1(dbl(s(z0)))) → c6(S1(mark(s(s(dbl(z0))))))
ACTIVE(s1(dbl(s(z0)))) → c6(ACTIVE(dbl(s(z0))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(S1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(S1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(s1(from(z0))) → c6(S1(mark(cons(z0, from(s(z0))))))
ACTIVE(s1(from(z0))) → c6(ACTIVE(from(z0)))
ACTIVE(s1(dbl1(s(z0)))) → c6(S1(mark(s1(s1(dbl1(z0))))))
ACTIVE(s1(dbl1(s(z0)))) → c6(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(sel(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(quote(sel(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(quote(sel1(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(quote(sel1(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(quote(quote(dbl(z0)))) → c26(QUOTE(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(quote(quote(sel(z0, z1)))) → c26(QUOTE(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(quote(dbl(z0))) → c26(QUOTE(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(quote(dbls(z0))) → c26(QUOTE(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(quote(indx(z0, z1))) → c26(QUOTE(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(quote(dbl1(z0))) → c26(QUOTE(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(quote(s1(z0))) → c26(QUOTE(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(quote(z0))) → c26(QUOTE(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(quote(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(quote(0))) → c22(DBL1(mark(01)))
ACTIVE(s1(quote(0))) → c23(S1(mark(01)))
ACTIVE(quote(dbl(0))) → c26(QUOTE(mark(0)))
ACTIVE(quote(dbls(nil))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(indx(nil, z0))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(dbl1(0))) → c26(QUOTE(mark(01)))
ACTIVE(quote(quote(0))) → c26(QUOTE(mark(01)))
ACTIVE(dbl(quote(s(z0)))) → c7(DBL(mark(s1(quote(z0)))))
ACTIVE(dbl(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(s(z0)))) → c7(DBLS(mark(s1(quote(z0)))))
ACTIVE(dbls(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(indx(quote(s(z0)), x1)) → c7(INDX(mark(s1(quote(z0))), x1))
ACTIVE(indx(quote(s(z0)), x1)) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbl1(quote(s(z0)))) → c7(DBL1(mark(s1(quote(z0)))))
ACTIVE(dbl1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(s1(quote(s(z0)))) → c7(S1(mark(s1(quote(z0)))))
ACTIVE(s1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(quote(dbl(s(z0)))) → c7(QUOTE(mark(s(s(dbl(z0))))))
ACTIVE(quote(dbl(s(z0)))) → c7(ACTIVE(dbl(s(z0))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(QUOTE(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(QUOTE(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(quote(from(z0))) → c7(QUOTE(mark(cons(z0, from(s(z0))))))
ACTIVE(quote(from(z0))) → c7(ACTIVE(from(z0)))
ACTIVE(quote(dbl1(s(z0)))) → c7(QUOTE(mark(s1(s1(dbl1(z0))))))
ACTIVE(quote(dbl1(s(z0)))) → c7(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(quote(s(z0)))) → c7(QUOTE(mark(s1(quote(z0)))))
ACTIVE(quote(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
PROPER(dbl(dbl(z0))) → c45(DBL(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbl(s(z0))) → c45(DBL(s(proper(z0))), PROPER(s(z0)))
PROPER(dbl(dbls(z0))) → c45(DBL(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbl(cons(z0, z1))) → c45(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbl(sel(z0, z1))) → c45(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbl(indx(z0, z1))) → c45(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbl(from(z0))) → c45(DBL(from(proper(z0))), PROPER(from(z0)))
PROPER(dbl(dbl1(z0))) → c45(DBL(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbl(s1(z0))) → c45(DBL(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbl(sel1(z0, z1))) → c45(DBL(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbl(quote(z0))) → c45(DBL(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbl(0)) → c45(DBL(ok(0)))
PROPER(dbl(nil)) → c45(DBL(ok(nil)))
PROPER(dbl(01)) → c45(DBL(ok(01)))
PROPER(s(dbl(z0))) → c47(S(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(s(s(z0))) → c47(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(dbls(z0))) → c47(S(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(s(cons(z0, z1))) → c47(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(sel(z0, z1))) → c47(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(s(indx(z0, z1))) → c47(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(s(from(z0))) → c47(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(dbl1(z0))) → c47(S(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(s(s1(z0))) → c47(S(s1(proper(z0))), PROPER(s1(z0)))
PROPER(s(sel1(z0, z1))) → c47(S(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(s(quote(z0))) → c47(S(quote(proper(z0))), PROPER(quote(z0)))
PROPER(s(0)) → c47(S(ok(0)))
PROPER(s(nil)) → c47(S(ok(nil)))
PROPER(s(01)) → c47(S(ok(01)))
PROPER(dbls(dbl(z0))) → c48(DBLS(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbls(s(z0))) → c48(DBLS(s(proper(z0))), PROPER(s(z0)))
PROPER(dbls(dbls(z0))) → c48(DBLS(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbls(cons(z0, z1))) → c48(DBLS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbls(sel(z0, z1))) → c48(DBLS(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbls(indx(z0, z1))) → c48(DBLS(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbls(from(z0))) → c48(DBLS(from(proper(z0))), PROPER(from(z0)))
PROPER(dbls(dbl1(z0))) → c48(DBLS(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbls(s1(z0))) → c48(DBLS(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbls(sel1(z0, z1))) → c48(DBLS(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbls(quote(z0))) → c48(DBLS(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbls(0)) → c48(DBLS(ok(0)))
PROPER(dbls(nil)) → c48(DBLS(ok(nil)))
PROPER(dbls(01)) → c48(DBLS(ok(01)))
PROPER(cons(x0, dbl(z0))) → c50(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(cons(x0, s(z0))) → c50(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, dbls(z0))) → c50(CONS(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(cons(x0, cons(z0, z1))) → c50(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, sel(z0, z1))) → c50(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(cons(x0, indx(z0, z1))) → c50(CONS(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(cons(x0, from(z0))) → c50(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, dbl1(z0))) → c50(CONS(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(cons(x0, s1(z0))) → c50(CONS(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(cons(x0, sel1(z0, z1))) → c50(CONS(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(cons(x0, quote(z0))) → c50(CONS(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(cons(dbl(z0), x1)) → c50(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(cons(s(z0), x1)) → c50(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(dbls(z0), x1)) → c50(CONS(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c50(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(sel(z0, z1), x1)) → c50(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(cons(indx(z0, z1), x1)) → c50(CONS(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c50(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(dbl1(z0), x1)) → c50(CONS(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(cons(s1(z0), x1)) → c50(CONS(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(cons(sel1(z0, z1), x1)) → c50(CONS(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(cons(quote(z0), x1)) → c50(CONS(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c50(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c50(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, 01)) → c50(CONS(proper(x0), ok(01)), PROPER(x0))
PROPER(cons(0, x1)) → c50(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c50(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(01, x1)) → c50(CONS(ok(01), proper(x1)), PROPER(x1))
PROPER(sel(x0, dbl(z0))) → c51(SEL(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(sel(x0, s(z0))) → c51(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(sel(x0, dbls(z0))) → c51(SEL(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(sel(x0, cons(z0, z1))) → c51(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(sel(x0, sel(z0, z1))) → c51(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(sel(x0, indx(z0, z1))) → c51(SEL(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(sel(x0, from(z0))) → c51(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(sel(x0, dbl1(z0))) → c51(SEL(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(sel(x0, s1(z0))) → c51(SEL(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(sel(x0, sel1(z0, z1))) → c51(SEL(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(sel(x0, quote(z0))) → c51(SEL(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(sel(dbl(z0), x1)) → c51(SEL(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(sel(s(z0), x1)) → c51(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(sel(dbls(z0), x1)) → c51(SEL(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(sel(cons(z0, z1), x1)) → c51(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(sel(sel(z0, z1), x1)) → c51(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(sel(indx(z0, z1), x1)) → c51(SEL(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(sel(from(z0), x1)) → c51(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(sel(dbl1(z0), x1)) → c51(SEL(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(sel(s1(z0), x1)) → c51(SEL(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(sel(sel1(z0, z1), x1)) → c51(SEL(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(sel(quote(z0), x1)) → c51(SEL(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(sel(x0, 0)) → c51(SEL(proper(x0), ok(0)), PROPER(x0))
PROPER(sel(x0, nil)) → c51(SEL(proper(x0), ok(nil)), PROPER(x0))
PROPER(sel(x0, 01)) → c51(SEL(proper(x0), ok(01)), PROPER(x0))
PROPER(sel(0, x1)) → c51(SEL(ok(0), proper(x1)), PROPER(x1))
PROPER(sel(nil, x1)) → c51(SEL(ok(nil), proper(x1)), PROPER(x1))
PROPER(sel(01, x1)) → c51(SEL(ok(01), proper(x1)), PROPER(x1))
PROPER(indx(x0, dbl(z0))) → c52(INDX(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(indx(x0, s(z0))) → c52(INDX(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(indx(x0, dbls(z0))) → c52(INDX(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(indx(x0, cons(z0, z1))) → c52(INDX(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(indx(x0, sel(z0, z1))) → c52(INDX(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(indx(x0, indx(z0, z1))) → c52(INDX(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(indx(x0, from(z0))) → c52(INDX(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(indx(x0, dbl1(z0))) → c52(INDX(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(indx(x0, s1(z0))) → c52(INDX(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(indx(x0, sel1(z0, z1))) → c52(INDX(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(indx(x0, quote(z0))) → c52(INDX(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(indx(dbl(z0), x1)) → c52(INDX(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(indx(s(z0), x1)) → c52(INDX(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(indx(dbls(z0), x1)) → c52(INDX(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(indx(cons(z0, z1), x1)) → c52(INDX(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(indx(sel(z0, z1), x1)) → c52(INDX(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(indx(indx(z0, z1), x1)) → c52(INDX(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(indx(from(z0), x1)) → c52(INDX(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(indx(dbl1(z0), x1)) → c52(INDX(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(indx(s1(z0), x1)) → c52(INDX(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(indx(sel1(z0, z1), x1)) → c52(INDX(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(indx(quote(z0), x1)) → c52(INDX(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(indx(x0, 0)) → c52(INDX(proper(x0), ok(0)), PROPER(x0))
PROPER(indx(x0, nil)) → c52(INDX(proper(x0), ok(nil)), PROPER(x0))
PROPER(indx(x0, 01)) → c52(INDX(proper(x0), ok(01)), PROPER(x0))
PROPER(indx(0, x1)) → c52(INDX(ok(0), proper(x1)), PROPER(x1))
PROPER(indx(nil, x1)) → c52(INDX(ok(nil), proper(x1)), PROPER(x1))
PROPER(indx(01, x1)) → c52(INDX(ok(01), proper(x1)), PROPER(x1))
PROPER(from(dbl(z0))) → c53(FROM(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(from(s(z0))) → c53(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(dbls(z0))) → c53(FROM(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(from(cons(z0, z1))) → c53(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(sel(z0, z1))) → c53(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(from(indx(z0, z1))) → c53(FROM(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(from(from(z0))) → c53(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(dbl1(z0))) → c53(FROM(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(from(s1(z0))) → c53(FROM(s1(proper(z0))), PROPER(s1(z0)))
PROPER(from(sel1(z0, z1))) → c53(FROM(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(from(quote(z0))) → c53(FROM(quote(proper(z0))), PROPER(quote(z0)))
PROPER(from(0)) → c53(FROM(ok(0)))
PROPER(from(nil)) → c53(FROM(ok(nil)))
PROPER(from(01)) → c53(FROM(ok(01)))
PROPER(dbl1(dbl(z0))) → c54(DBL1(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbl1(s(z0))) → c54(DBL1(s(proper(z0))), PROPER(s(z0)))
PROPER(dbl1(dbls(z0))) → c54(DBL1(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbl1(cons(z0, z1))) → c54(DBL1(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbl1(sel(z0, z1))) → c54(DBL1(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbl1(indx(z0, z1))) → c54(DBL1(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbl1(from(z0))) → c54(DBL1(from(proper(z0))), PROPER(from(z0)))
PROPER(dbl1(dbl1(z0))) → c54(DBL1(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbl1(s1(z0))) → c54(DBL1(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbl1(sel1(z0, z1))) → c54(DBL1(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbl1(quote(z0))) → c54(DBL1(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbl1(0)) → c54(DBL1(ok(0)))
PROPER(dbl1(nil)) → c54(DBL1(ok(nil)))
PROPER(dbl1(01)) → c54(DBL1(ok(01)))
S tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(s1(z0)) → c56(S1(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c57(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)))
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0))))))
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0))))))
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0)))
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(indx(sel1(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(indx(sel1(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel1(z0, z2)), x1), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(indx(quote(dbl(z0)), x1)) → c21(INDX(mark(dbl1(z0)), x1), ACTIVE(quote(dbl(z0))))
ACTIVE(indx(quote(sel(z0, z1)), x1)) → c21(INDX(mark(sel1(z0, z1)), x1), ACTIVE(quote(sel(z0, z1))))
ACTIVE(indx(dbl(z0), x1)) → c21(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
ACTIVE(indx(dbls(z0), x1)) → c21(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(indx(z0, z1), x1)) → c21(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1)))
ACTIVE(indx(dbl1(z0), x1)) → c21(INDX(dbl1(active(z0)), x1), ACTIVE(dbl1(z0)))
ACTIVE(indx(s1(z0), x1)) → c21(INDX(s1(active(z0)), x1), ACTIVE(s1(z0)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(active(z0), z1), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(z0, active(z1)), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(quote(z0), x1)) → c21(INDX(quote(active(z0)), x1), ACTIVE(quote(z0)))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)))
ACTIVE(indx(dbl(0), x1)) → c21(INDX(mark(0), x1))
ACTIVE(indx(dbls(nil), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(indx(indx(nil, z0), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0))))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1))
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0)))
ACTIVE(dbl1(sel(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl1(sel(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl1(sel1(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl1(sel1(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl1(quote(dbl(z0)))) → c22(DBL1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl1(quote(sel(z0, z1)))) → c22(DBL1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl1(dbl(z0))) → c22(DBL1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl1(dbls(z0))) → c22(DBL1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(indx(z0, z1))) → c22(DBL1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl1(dbl1(z0))) → c22(DBL1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl1(s1(z0))) → c22(DBL1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(quote(z0))) → c22(DBL1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(dbl1(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(dbl(0))) → c22(DBL1(mark(0)))
ACTIVE(dbl1(dbls(nil))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(indx(nil, z0))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(dbl1(0))) → c22(DBL1(mark(01)))
ACTIVE(dbl(dbl1(s(z0)))) → c4(DBL(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(DBLS(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(INDX(mark(s1(s1(dbl1(z0)))), x1))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(DBL1(mark(s(s(dbl(z0))))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(ACTIVE(dbl(s(z0))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(DBL1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(DBL1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl1(from(z0))) → c4(DBL1(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl1(from(z0))) → c4(ACTIVE(from(z0)))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(DBL1(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(s1(sel(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(s1(sel(s(z0), cons(z1, z2)))) → c23(S1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(s1(sel1(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(s1(sel1(s(z0), cons(z1, z2)))) → c23(S1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(s1(quote(dbl(z0)))) → c23(S1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(s1(quote(sel(z0, z1)))) → c23(S1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(s1(dbl(z0))) → c23(S1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(s1(dbls(z0))) → c23(S1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(s1(indx(z0, z1))) → c23(S1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(s1(dbl1(z0))) → c23(S1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(s1(s1(z0))) → c23(S1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(quote(z0))) → c23(S1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(s1(dbl(0))) → c23(S1(mark(0)))
ACTIVE(s1(dbls(nil))) → c23(S1(mark(nil)))
ACTIVE(s1(indx(nil, z0))) → c23(S1(mark(nil)))
ACTIVE(s1(dbl1(0))) → c23(S1(mark(01)))
ACTIVE(s1(dbl(s(z0)))) → c6(S1(mark(s(s(dbl(z0))))))
ACTIVE(s1(dbl(s(z0)))) → c6(ACTIVE(dbl(s(z0))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(S1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(S1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(s1(from(z0))) → c6(S1(mark(cons(z0, from(s(z0))))))
ACTIVE(s1(from(z0))) → c6(ACTIVE(from(z0)))
ACTIVE(s1(dbl1(s(z0)))) → c6(S1(mark(s1(s1(dbl1(z0))))))
ACTIVE(s1(dbl1(s(z0)))) → c6(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(sel(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(quote(sel(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(quote(sel1(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(quote(sel1(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(quote(quote(dbl(z0)))) → c26(QUOTE(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(quote(quote(sel(z0, z1)))) → c26(QUOTE(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(quote(dbl(z0))) → c26(QUOTE(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(quote(dbls(z0))) → c26(QUOTE(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(quote(indx(z0, z1))) → c26(QUOTE(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(quote(dbl1(z0))) → c26(QUOTE(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(quote(s1(z0))) → c26(QUOTE(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(quote(z0))) → c26(QUOTE(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(quote(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(quote(0))) → c22(DBL1(mark(01)))
ACTIVE(s1(quote(0))) → c23(S1(mark(01)))
ACTIVE(quote(dbl(0))) → c26(QUOTE(mark(0)))
ACTIVE(quote(dbls(nil))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(indx(nil, z0))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(dbl1(0))) → c26(QUOTE(mark(01)))
ACTIVE(quote(quote(0))) → c26(QUOTE(mark(01)))
ACTIVE(dbl(quote(s(z0)))) → c7(DBL(mark(s1(quote(z0)))))
ACTIVE(dbl(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(s(z0)))) → c7(DBLS(mark(s1(quote(z0)))))
ACTIVE(dbls(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(indx(quote(s(z0)), x1)) → c7(INDX(mark(s1(quote(z0))), x1))
ACTIVE(indx(quote(s(z0)), x1)) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbl1(quote(s(z0)))) → c7(DBL1(mark(s1(quote(z0)))))
ACTIVE(dbl1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(s1(quote(s(z0)))) → c7(S1(mark(s1(quote(z0)))))
ACTIVE(s1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(quote(dbl(s(z0)))) → c7(QUOTE(mark(s(s(dbl(z0))))))
ACTIVE(quote(dbl(s(z0)))) → c7(ACTIVE(dbl(s(z0))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(QUOTE(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(QUOTE(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(quote(from(z0))) → c7(QUOTE(mark(cons(z0, from(s(z0))))))
ACTIVE(quote(from(z0))) → c7(ACTIVE(from(z0)))
ACTIVE(quote(dbl1(s(z0)))) → c7(QUOTE(mark(s1(s1(dbl1(z0))))))
ACTIVE(quote(dbl1(s(z0)))) → c7(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(quote(s(z0)))) → c7(QUOTE(mark(s1(quote(z0)))))
ACTIVE(quote(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
PROPER(dbl(dbl(z0))) → c45(DBL(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbl(s(z0))) → c45(DBL(s(proper(z0))), PROPER(s(z0)))
PROPER(dbl(dbls(z0))) → c45(DBL(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbl(cons(z0, z1))) → c45(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbl(sel(z0, z1))) → c45(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbl(indx(z0, z1))) → c45(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbl(from(z0))) → c45(DBL(from(proper(z0))), PROPER(from(z0)))
PROPER(dbl(dbl1(z0))) → c45(DBL(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbl(s1(z0))) → c45(DBL(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbl(sel1(z0, z1))) → c45(DBL(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbl(quote(z0))) → c45(DBL(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbl(0)) → c45(DBL(ok(0)))
PROPER(dbl(nil)) → c45(DBL(ok(nil)))
PROPER(dbl(01)) → c45(DBL(ok(01)))
PROPER(s(dbl(z0))) → c47(S(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(s(s(z0))) → c47(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(dbls(z0))) → c47(S(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(s(cons(z0, z1))) → c47(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(sel(z0, z1))) → c47(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(s(indx(z0, z1))) → c47(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(s(from(z0))) → c47(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(dbl1(z0))) → c47(S(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(s(s1(z0))) → c47(S(s1(proper(z0))), PROPER(s1(z0)))
PROPER(s(sel1(z0, z1))) → c47(S(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(s(quote(z0))) → c47(S(quote(proper(z0))), PROPER(quote(z0)))
PROPER(s(0)) → c47(S(ok(0)))
PROPER(s(nil)) → c47(S(ok(nil)))
PROPER(s(01)) → c47(S(ok(01)))
PROPER(dbls(dbl(z0))) → c48(DBLS(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbls(s(z0))) → c48(DBLS(s(proper(z0))), PROPER(s(z0)))
PROPER(dbls(dbls(z0))) → c48(DBLS(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbls(cons(z0, z1))) → c48(DBLS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbls(sel(z0, z1))) → c48(DBLS(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbls(indx(z0, z1))) → c48(DBLS(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbls(from(z0))) → c48(DBLS(from(proper(z0))), PROPER(from(z0)))
PROPER(dbls(dbl1(z0))) → c48(DBLS(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbls(s1(z0))) → c48(DBLS(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbls(sel1(z0, z1))) → c48(DBLS(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbls(quote(z0))) → c48(DBLS(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbls(0)) → c48(DBLS(ok(0)))
PROPER(dbls(nil)) → c48(DBLS(ok(nil)))
PROPER(dbls(01)) → c48(DBLS(ok(01)))
PROPER(cons(x0, dbl(z0))) → c50(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(cons(x0, s(z0))) → c50(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, dbls(z0))) → c50(CONS(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(cons(x0, cons(z0, z1))) → c50(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, sel(z0, z1))) → c50(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(cons(x0, indx(z0, z1))) → c50(CONS(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(cons(x0, from(z0))) → c50(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, dbl1(z0))) → c50(CONS(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(cons(x0, s1(z0))) → c50(CONS(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(cons(x0, sel1(z0, z1))) → c50(CONS(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(cons(x0, quote(z0))) → c50(CONS(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(cons(dbl(z0), x1)) → c50(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(cons(s(z0), x1)) → c50(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(dbls(z0), x1)) → c50(CONS(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c50(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(sel(z0, z1), x1)) → c50(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(cons(indx(z0, z1), x1)) → c50(CONS(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c50(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(dbl1(z0), x1)) → c50(CONS(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(cons(s1(z0), x1)) → c50(CONS(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(cons(sel1(z0, z1), x1)) → c50(CONS(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(cons(quote(z0), x1)) → c50(CONS(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c50(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c50(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, 01)) → c50(CONS(proper(x0), ok(01)), PROPER(x0))
PROPER(cons(0, x1)) → c50(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c50(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(01, x1)) → c50(CONS(ok(01), proper(x1)), PROPER(x1))
PROPER(sel(x0, dbl(z0))) → c51(SEL(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(sel(x0, s(z0))) → c51(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(sel(x0, dbls(z0))) → c51(SEL(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(sel(x0, cons(z0, z1))) → c51(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(sel(x0, sel(z0, z1))) → c51(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(sel(x0, indx(z0, z1))) → c51(SEL(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(sel(x0, from(z0))) → c51(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(sel(x0, dbl1(z0))) → c51(SEL(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(sel(x0, s1(z0))) → c51(SEL(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(sel(x0, sel1(z0, z1))) → c51(SEL(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(sel(x0, quote(z0))) → c51(SEL(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(sel(dbl(z0), x1)) → c51(SEL(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(sel(s(z0), x1)) → c51(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(sel(dbls(z0), x1)) → c51(SEL(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(sel(cons(z0, z1), x1)) → c51(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(sel(sel(z0, z1), x1)) → c51(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(sel(indx(z0, z1), x1)) → c51(SEL(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(sel(from(z0), x1)) → c51(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(sel(dbl1(z0), x1)) → c51(SEL(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(sel(s1(z0), x1)) → c51(SEL(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(sel(sel1(z0, z1), x1)) → c51(SEL(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(sel(quote(z0), x1)) → c51(SEL(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(sel(x0, 0)) → c51(SEL(proper(x0), ok(0)), PROPER(x0))
PROPER(sel(x0, nil)) → c51(SEL(proper(x0), ok(nil)), PROPER(x0))
PROPER(sel(x0, 01)) → c51(SEL(proper(x0), ok(01)), PROPER(x0))
PROPER(sel(0, x1)) → c51(SEL(ok(0), proper(x1)), PROPER(x1))
PROPER(sel(nil, x1)) → c51(SEL(ok(nil), proper(x1)), PROPER(x1))
PROPER(sel(01, x1)) → c51(SEL(ok(01), proper(x1)), PROPER(x1))
PROPER(indx(x0, dbl(z0))) → c52(INDX(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(indx(x0, s(z0))) → c52(INDX(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(indx(x0, dbls(z0))) → c52(INDX(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(indx(x0, cons(z0, z1))) → c52(INDX(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(indx(x0, sel(z0, z1))) → c52(INDX(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(indx(x0, indx(z0, z1))) → c52(INDX(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(indx(x0, from(z0))) → c52(INDX(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(indx(x0, dbl1(z0))) → c52(INDX(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(indx(x0, s1(z0))) → c52(INDX(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(indx(x0, sel1(z0, z1))) → c52(INDX(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(indx(x0, quote(z0))) → c52(INDX(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(indx(dbl(z0), x1)) → c52(INDX(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(indx(s(z0), x1)) → c52(INDX(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(indx(dbls(z0), x1)) → c52(INDX(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(indx(cons(z0, z1), x1)) → c52(INDX(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(indx(sel(z0, z1), x1)) → c52(INDX(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(indx(indx(z0, z1), x1)) → c52(INDX(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(indx(from(z0), x1)) → c52(INDX(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(indx(dbl1(z0), x1)) → c52(INDX(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(indx(s1(z0), x1)) → c52(INDX(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(indx(sel1(z0, z1), x1)) → c52(INDX(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(indx(quote(z0), x1)) → c52(INDX(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(indx(x0, 0)) → c52(INDX(proper(x0), ok(0)), PROPER(x0))
PROPER(indx(x0, nil)) → c52(INDX(proper(x0), ok(nil)), PROPER(x0))
PROPER(indx(x0, 01)) → c52(INDX(proper(x0), ok(01)), PROPER(x0))
PROPER(indx(0, x1)) → c52(INDX(ok(0), proper(x1)), PROPER(x1))
PROPER(indx(nil, x1)) → c52(INDX(ok(nil), proper(x1)), PROPER(x1))
PROPER(indx(01, x1)) → c52(INDX(ok(01), proper(x1)), PROPER(x1))
PROPER(from(dbl(z0))) → c53(FROM(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(from(s(z0))) → c53(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(dbls(z0))) → c53(FROM(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(from(cons(z0, z1))) → c53(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(sel(z0, z1))) → c53(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(from(indx(z0, z1))) → c53(FROM(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(from(from(z0))) → c53(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(dbl1(z0))) → c53(FROM(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(from(s1(z0))) → c53(FROM(s1(proper(z0))), PROPER(s1(z0)))
PROPER(from(sel1(z0, z1))) → c53(FROM(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(from(quote(z0))) → c53(FROM(quote(proper(z0))), PROPER(quote(z0)))
PROPER(from(0)) → c53(FROM(ok(0)))
PROPER(from(nil)) → c53(FROM(ok(nil)))
PROPER(from(01)) → c53(FROM(ok(01)))
PROPER(dbl1(dbl(z0))) → c54(DBL1(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbl1(s(z0))) → c54(DBL1(s(proper(z0))), PROPER(s(z0)))
PROPER(dbl1(dbls(z0))) → c54(DBL1(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbl1(cons(z0, z1))) → c54(DBL1(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbl1(sel(z0, z1))) → c54(DBL1(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbl1(indx(z0, z1))) → c54(DBL1(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbl1(from(z0))) → c54(DBL1(from(proper(z0))), PROPER(from(z0)))
PROPER(dbl1(dbl1(z0))) → c54(DBL1(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbl1(s1(z0))) → c54(DBL1(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbl1(sel1(z0, z1))) → c54(DBL1(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbl1(quote(z0))) → c54(DBL1(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbl1(0)) → c54(DBL1(ok(0)))
PROPER(dbl1(nil)) → c54(DBL1(ok(nil)))
PROPER(dbl1(01)) → c54(DBL1(ok(01)))
K tuples:none
Defined Rule Symbols:
active, s, dbl, cons, dbls, sel, indx, s1, dbl1, sel1, quote, proper, from
Defined Pair Symbols:
ACTIVE, DBL, DBLS, SEL, INDX, DBL1, S1, SEL1, QUOTE, PROPER, S, CONS, FROM, TOP
Compound Symbols:
c5, c12, c15, c16, c19, c20, c24, c25, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c56, c57, c58, c59, c60, c61, c62, c63, c8, c, c17, c17, c1, c18, c18, c2, c21, c21, c3, c22, c22, c4, c23, c23, c6, c26, c26, c7, c45, c45, c47, c47, c48, c48, c50, c50, c51, c51, c52, c52, c53, c53, c54, c54
(79) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
PROPER(
s1(
z0)) →
c56(
S1(
proper(
z0)),
PROPER(
z0)) by
PROPER(s1(dbl(z0))) → c56(S1(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(s1(0)) → c56(S1(ok(0)), PROPER(0))
PROPER(s1(s(z0))) → c56(S1(s(proper(z0))), PROPER(s(z0)))
PROPER(s1(dbls(z0))) → c56(S1(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(s1(nil)) → c56(S1(ok(nil)), PROPER(nil))
PROPER(s1(cons(z0, z1))) → c56(S1(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s1(sel(z0, z1))) → c56(S1(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(s1(indx(z0, z1))) → c56(S1(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(s1(from(z0))) → c56(S1(from(proper(z0))), PROPER(from(z0)))
PROPER(s1(dbl1(z0))) → c56(S1(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(s1(01)) → c56(S1(ok(01)), PROPER(01))
PROPER(s1(s1(z0))) → c56(S1(s1(proper(z0))), PROPER(s1(z0)))
PROPER(s1(sel1(z0, z1))) → c56(S1(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(s1(quote(z0))) → c56(S1(quote(proper(z0))), PROPER(quote(z0)))
(80) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(dbl(0)) → mark(0)
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
active(dbls(nil)) → mark(nil)
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1)))
active(sel(0, cons(z0, z1))) → mark(z0)
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
active(indx(nil, z0)) → mark(nil)
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2)))
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(dbl1(0)) → mark(01)
active(dbl1(s(z0))) → mark(s1(s1(dbl1(z0))))
active(sel1(0, cons(z0, z1))) → mark(z0)
active(sel1(s(z0), cons(z1, z2))) → mark(sel1(z0, z2))
active(quote(0)) → mark(01)
active(quote(s(z0))) → mark(s1(quote(z0)))
active(quote(dbl(z0))) → mark(dbl1(z0))
active(quote(sel(z0, z1))) → mark(sel1(z0, z1))
active(dbl(z0)) → dbl(active(z0))
active(dbls(z0)) → dbls(active(z0))
active(sel(z0, z1)) → sel(active(z0), z1)
active(sel(z0, z1)) → sel(z0, active(z1))
active(indx(z0, z1)) → indx(active(z0), z1)
active(dbl1(z0)) → dbl1(active(z0))
active(s1(z0)) → s1(active(z0))
active(sel1(z0, z1)) → sel1(active(z0), z1)
active(sel1(z0, z1)) → sel1(z0, active(z1))
active(quote(z0)) → quote(active(z0))
s(ok(z0)) → ok(s(z0))
dbl(mark(z0)) → mark(dbl(z0))
dbl(ok(z0)) → ok(dbl(z0))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
dbls(mark(z0)) → mark(dbls(z0))
dbls(ok(z0)) → ok(dbls(z0))
sel(mark(z0), z1) → mark(sel(z0, z1))
sel(z0, mark(z1)) → mark(sel(z0, z1))
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
indx(mark(z0), z1) → mark(indx(z0, z1))
indx(ok(z0), ok(z1)) → ok(indx(z0, z1))
s1(mark(z0)) → mark(s1(z0))
s1(ok(z0)) → ok(s1(z0))
dbl1(mark(z0)) → mark(dbl1(z0))
dbl1(ok(z0)) → ok(dbl1(z0))
sel1(mark(z0), z1) → mark(sel1(z0, z1))
sel1(z0, mark(z1)) → mark(sel1(z0, z1))
sel1(ok(z0), ok(z1)) → ok(sel1(z0, z1))
quote(mark(z0)) → mark(quote(z0))
quote(ok(z0)) → ok(quote(z0))
proper(dbl(z0)) → dbl(proper(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(dbls(z0)) → dbls(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
proper(indx(z0, z1)) → indx(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(dbl1(z0)) → dbl1(proper(z0))
proper(01) → ok(01)
proper(s1(z0)) → s1(proper(z0))
proper(sel1(z0, z1)) → sel1(proper(z0), proper(z1))
proper(quote(z0)) → quote(proper(z0))
from(ok(z0)) → ok(from(z0))
Tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(sel1(z0, z1)) → c57(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)))
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0))))))
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0))))))
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0)))
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(indx(sel1(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(indx(sel1(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel1(z0, z2)), x1), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(indx(quote(dbl(z0)), x1)) → c21(INDX(mark(dbl1(z0)), x1), ACTIVE(quote(dbl(z0))))
ACTIVE(indx(quote(sel(z0, z1)), x1)) → c21(INDX(mark(sel1(z0, z1)), x1), ACTIVE(quote(sel(z0, z1))))
ACTIVE(indx(dbl(z0), x1)) → c21(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
ACTIVE(indx(dbls(z0), x1)) → c21(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(indx(z0, z1), x1)) → c21(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1)))
ACTIVE(indx(dbl1(z0), x1)) → c21(INDX(dbl1(active(z0)), x1), ACTIVE(dbl1(z0)))
ACTIVE(indx(s1(z0), x1)) → c21(INDX(s1(active(z0)), x1), ACTIVE(s1(z0)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(active(z0), z1), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(z0, active(z1)), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(quote(z0), x1)) → c21(INDX(quote(active(z0)), x1), ACTIVE(quote(z0)))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)))
ACTIVE(indx(dbl(0), x1)) → c21(INDX(mark(0), x1))
ACTIVE(indx(dbls(nil), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(indx(indx(nil, z0), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0))))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1))
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0)))
ACTIVE(dbl1(sel(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl1(sel(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl1(sel1(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl1(sel1(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl1(quote(dbl(z0)))) → c22(DBL1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl1(quote(sel(z0, z1)))) → c22(DBL1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl1(dbl(z0))) → c22(DBL1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl1(dbls(z0))) → c22(DBL1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(indx(z0, z1))) → c22(DBL1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl1(dbl1(z0))) → c22(DBL1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl1(s1(z0))) → c22(DBL1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(quote(z0))) → c22(DBL1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(dbl1(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(dbl(0))) → c22(DBL1(mark(0)))
ACTIVE(dbl1(dbls(nil))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(indx(nil, z0))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(dbl1(0))) → c22(DBL1(mark(01)))
ACTIVE(dbl(dbl1(s(z0)))) → c4(DBL(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(DBLS(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(INDX(mark(s1(s1(dbl1(z0)))), x1))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(DBL1(mark(s(s(dbl(z0))))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(ACTIVE(dbl(s(z0))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(DBL1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(DBL1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl1(from(z0))) → c4(DBL1(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl1(from(z0))) → c4(ACTIVE(from(z0)))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(DBL1(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(s1(sel(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(s1(sel(s(z0), cons(z1, z2)))) → c23(S1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(s1(sel1(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(s1(sel1(s(z0), cons(z1, z2)))) → c23(S1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(s1(quote(dbl(z0)))) → c23(S1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(s1(quote(sel(z0, z1)))) → c23(S1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(s1(dbl(z0))) → c23(S1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(s1(dbls(z0))) → c23(S1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(s1(indx(z0, z1))) → c23(S1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(s1(dbl1(z0))) → c23(S1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(s1(s1(z0))) → c23(S1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(quote(z0))) → c23(S1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(s1(dbl(0))) → c23(S1(mark(0)))
ACTIVE(s1(dbls(nil))) → c23(S1(mark(nil)))
ACTIVE(s1(indx(nil, z0))) → c23(S1(mark(nil)))
ACTIVE(s1(dbl1(0))) → c23(S1(mark(01)))
ACTIVE(s1(dbl(s(z0)))) → c6(S1(mark(s(s(dbl(z0))))))
ACTIVE(s1(dbl(s(z0)))) → c6(ACTIVE(dbl(s(z0))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(S1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(S1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(s1(from(z0))) → c6(S1(mark(cons(z0, from(s(z0))))))
ACTIVE(s1(from(z0))) → c6(ACTIVE(from(z0)))
ACTIVE(s1(dbl1(s(z0)))) → c6(S1(mark(s1(s1(dbl1(z0))))))
ACTIVE(s1(dbl1(s(z0)))) → c6(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(sel(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(quote(sel(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(quote(sel1(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(quote(sel1(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(quote(quote(dbl(z0)))) → c26(QUOTE(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(quote(quote(sel(z0, z1)))) → c26(QUOTE(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(quote(dbl(z0))) → c26(QUOTE(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(quote(dbls(z0))) → c26(QUOTE(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(quote(indx(z0, z1))) → c26(QUOTE(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(quote(dbl1(z0))) → c26(QUOTE(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(quote(s1(z0))) → c26(QUOTE(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(quote(z0))) → c26(QUOTE(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(quote(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(quote(0))) → c22(DBL1(mark(01)))
ACTIVE(s1(quote(0))) → c23(S1(mark(01)))
ACTIVE(quote(dbl(0))) → c26(QUOTE(mark(0)))
ACTIVE(quote(dbls(nil))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(indx(nil, z0))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(dbl1(0))) → c26(QUOTE(mark(01)))
ACTIVE(quote(quote(0))) → c26(QUOTE(mark(01)))
ACTIVE(dbl(quote(s(z0)))) → c7(DBL(mark(s1(quote(z0)))))
ACTIVE(dbl(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(s(z0)))) → c7(DBLS(mark(s1(quote(z0)))))
ACTIVE(dbls(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(indx(quote(s(z0)), x1)) → c7(INDX(mark(s1(quote(z0))), x1))
ACTIVE(indx(quote(s(z0)), x1)) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbl1(quote(s(z0)))) → c7(DBL1(mark(s1(quote(z0)))))
ACTIVE(dbl1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(s1(quote(s(z0)))) → c7(S1(mark(s1(quote(z0)))))
ACTIVE(s1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(quote(dbl(s(z0)))) → c7(QUOTE(mark(s(s(dbl(z0))))))
ACTIVE(quote(dbl(s(z0)))) → c7(ACTIVE(dbl(s(z0))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(QUOTE(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(QUOTE(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(quote(from(z0))) → c7(QUOTE(mark(cons(z0, from(s(z0))))))
ACTIVE(quote(from(z0))) → c7(ACTIVE(from(z0)))
ACTIVE(quote(dbl1(s(z0)))) → c7(QUOTE(mark(s1(s1(dbl1(z0))))))
ACTIVE(quote(dbl1(s(z0)))) → c7(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(quote(s(z0)))) → c7(QUOTE(mark(s1(quote(z0)))))
ACTIVE(quote(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
PROPER(dbl(dbl(z0))) → c45(DBL(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbl(s(z0))) → c45(DBL(s(proper(z0))), PROPER(s(z0)))
PROPER(dbl(dbls(z0))) → c45(DBL(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbl(cons(z0, z1))) → c45(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbl(sel(z0, z1))) → c45(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbl(indx(z0, z1))) → c45(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbl(from(z0))) → c45(DBL(from(proper(z0))), PROPER(from(z0)))
PROPER(dbl(dbl1(z0))) → c45(DBL(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbl(s1(z0))) → c45(DBL(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbl(sel1(z0, z1))) → c45(DBL(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbl(quote(z0))) → c45(DBL(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbl(0)) → c45(DBL(ok(0)))
PROPER(dbl(nil)) → c45(DBL(ok(nil)))
PROPER(dbl(01)) → c45(DBL(ok(01)))
PROPER(s(dbl(z0))) → c47(S(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(s(s(z0))) → c47(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(dbls(z0))) → c47(S(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(s(cons(z0, z1))) → c47(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(sel(z0, z1))) → c47(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(s(indx(z0, z1))) → c47(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(s(from(z0))) → c47(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(dbl1(z0))) → c47(S(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(s(s1(z0))) → c47(S(s1(proper(z0))), PROPER(s1(z0)))
PROPER(s(sel1(z0, z1))) → c47(S(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(s(quote(z0))) → c47(S(quote(proper(z0))), PROPER(quote(z0)))
PROPER(s(0)) → c47(S(ok(0)))
PROPER(s(nil)) → c47(S(ok(nil)))
PROPER(s(01)) → c47(S(ok(01)))
PROPER(dbls(dbl(z0))) → c48(DBLS(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbls(s(z0))) → c48(DBLS(s(proper(z0))), PROPER(s(z0)))
PROPER(dbls(dbls(z0))) → c48(DBLS(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbls(cons(z0, z1))) → c48(DBLS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbls(sel(z0, z1))) → c48(DBLS(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbls(indx(z0, z1))) → c48(DBLS(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbls(from(z0))) → c48(DBLS(from(proper(z0))), PROPER(from(z0)))
PROPER(dbls(dbl1(z0))) → c48(DBLS(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbls(s1(z0))) → c48(DBLS(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbls(sel1(z0, z1))) → c48(DBLS(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbls(quote(z0))) → c48(DBLS(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbls(0)) → c48(DBLS(ok(0)))
PROPER(dbls(nil)) → c48(DBLS(ok(nil)))
PROPER(dbls(01)) → c48(DBLS(ok(01)))
PROPER(cons(x0, dbl(z0))) → c50(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(cons(x0, s(z0))) → c50(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, dbls(z0))) → c50(CONS(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(cons(x0, cons(z0, z1))) → c50(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, sel(z0, z1))) → c50(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(cons(x0, indx(z0, z1))) → c50(CONS(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(cons(x0, from(z0))) → c50(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, dbl1(z0))) → c50(CONS(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(cons(x0, s1(z0))) → c50(CONS(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(cons(x0, sel1(z0, z1))) → c50(CONS(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(cons(x0, quote(z0))) → c50(CONS(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(cons(dbl(z0), x1)) → c50(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(cons(s(z0), x1)) → c50(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(dbls(z0), x1)) → c50(CONS(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c50(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(sel(z0, z1), x1)) → c50(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(cons(indx(z0, z1), x1)) → c50(CONS(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c50(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(dbl1(z0), x1)) → c50(CONS(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(cons(s1(z0), x1)) → c50(CONS(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(cons(sel1(z0, z1), x1)) → c50(CONS(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(cons(quote(z0), x1)) → c50(CONS(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c50(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c50(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, 01)) → c50(CONS(proper(x0), ok(01)), PROPER(x0))
PROPER(cons(0, x1)) → c50(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c50(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(01, x1)) → c50(CONS(ok(01), proper(x1)), PROPER(x1))
PROPER(sel(x0, dbl(z0))) → c51(SEL(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(sel(x0, s(z0))) → c51(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(sel(x0, dbls(z0))) → c51(SEL(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(sel(x0, cons(z0, z1))) → c51(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(sel(x0, sel(z0, z1))) → c51(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(sel(x0, indx(z0, z1))) → c51(SEL(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(sel(x0, from(z0))) → c51(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(sel(x0, dbl1(z0))) → c51(SEL(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(sel(x0, s1(z0))) → c51(SEL(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(sel(x0, sel1(z0, z1))) → c51(SEL(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(sel(x0, quote(z0))) → c51(SEL(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(sel(dbl(z0), x1)) → c51(SEL(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(sel(s(z0), x1)) → c51(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(sel(dbls(z0), x1)) → c51(SEL(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(sel(cons(z0, z1), x1)) → c51(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(sel(sel(z0, z1), x1)) → c51(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(sel(indx(z0, z1), x1)) → c51(SEL(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(sel(from(z0), x1)) → c51(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(sel(dbl1(z0), x1)) → c51(SEL(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(sel(s1(z0), x1)) → c51(SEL(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(sel(sel1(z0, z1), x1)) → c51(SEL(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(sel(quote(z0), x1)) → c51(SEL(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(sel(x0, 0)) → c51(SEL(proper(x0), ok(0)), PROPER(x0))
PROPER(sel(x0, nil)) → c51(SEL(proper(x0), ok(nil)), PROPER(x0))
PROPER(sel(x0, 01)) → c51(SEL(proper(x0), ok(01)), PROPER(x0))
PROPER(sel(0, x1)) → c51(SEL(ok(0), proper(x1)), PROPER(x1))
PROPER(sel(nil, x1)) → c51(SEL(ok(nil), proper(x1)), PROPER(x1))
PROPER(sel(01, x1)) → c51(SEL(ok(01), proper(x1)), PROPER(x1))
PROPER(indx(x0, dbl(z0))) → c52(INDX(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(indx(x0, s(z0))) → c52(INDX(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(indx(x0, dbls(z0))) → c52(INDX(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(indx(x0, cons(z0, z1))) → c52(INDX(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(indx(x0, sel(z0, z1))) → c52(INDX(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(indx(x0, indx(z0, z1))) → c52(INDX(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(indx(x0, from(z0))) → c52(INDX(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(indx(x0, dbl1(z0))) → c52(INDX(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(indx(x0, s1(z0))) → c52(INDX(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(indx(x0, sel1(z0, z1))) → c52(INDX(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(indx(x0, quote(z0))) → c52(INDX(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(indx(dbl(z0), x1)) → c52(INDX(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(indx(s(z0), x1)) → c52(INDX(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(indx(dbls(z0), x1)) → c52(INDX(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(indx(cons(z0, z1), x1)) → c52(INDX(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(indx(sel(z0, z1), x1)) → c52(INDX(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(indx(indx(z0, z1), x1)) → c52(INDX(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(indx(from(z0), x1)) → c52(INDX(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(indx(dbl1(z0), x1)) → c52(INDX(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(indx(s1(z0), x1)) → c52(INDX(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(indx(sel1(z0, z1), x1)) → c52(INDX(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(indx(quote(z0), x1)) → c52(INDX(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(indx(x0, 0)) → c52(INDX(proper(x0), ok(0)), PROPER(x0))
PROPER(indx(x0, nil)) → c52(INDX(proper(x0), ok(nil)), PROPER(x0))
PROPER(indx(x0, 01)) → c52(INDX(proper(x0), ok(01)), PROPER(x0))
PROPER(indx(0, x1)) → c52(INDX(ok(0), proper(x1)), PROPER(x1))
PROPER(indx(nil, x1)) → c52(INDX(ok(nil), proper(x1)), PROPER(x1))
PROPER(indx(01, x1)) → c52(INDX(ok(01), proper(x1)), PROPER(x1))
PROPER(from(dbl(z0))) → c53(FROM(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(from(s(z0))) → c53(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(dbls(z0))) → c53(FROM(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(from(cons(z0, z1))) → c53(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(sel(z0, z1))) → c53(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(from(indx(z0, z1))) → c53(FROM(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(from(from(z0))) → c53(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(dbl1(z0))) → c53(FROM(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(from(s1(z0))) → c53(FROM(s1(proper(z0))), PROPER(s1(z0)))
PROPER(from(sel1(z0, z1))) → c53(FROM(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(from(quote(z0))) → c53(FROM(quote(proper(z0))), PROPER(quote(z0)))
PROPER(from(0)) → c53(FROM(ok(0)))
PROPER(from(nil)) → c53(FROM(ok(nil)))
PROPER(from(01)) → c53(FROM(ok(01)))
PROPER(dbl1(dbl(z0))) → c54(DBL1(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbl1(s(z0))) → c54(DBL1(s(proper(z0))), PROPER(s(z0)))
PROPER(dbl1(dbls(z0))) → c54(DBL1(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbl1(cons(z0, z1))) → c54(DBL1(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbl1(sel(z0, z1))) → c54(DBL1(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbl1(indx(z0, z1))) → c54(DBL1(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbl1(from(z0))) → c54(DBL1(from(proper(z0))), PROPER(from(z0)))
PROPER(dbl1(dbl1(z0))) → c54(DBL1(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbl1(s1(z0))) → c54(DBL1(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbl1(sel1(z0, z1))) → c54(DBL1(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbl1(quote(z0))) → c54(DBL1(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbl1(0)) → c54(DBL1(ok(0)))
PROPER(dbl1(nil)) → c54(DBL1(ok(nil)))
PROPER(dbl1(01)) → c54(DBL1(ok(01)))
PROPER(s1(dbl(z0))) → c56(S1(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(s1(0)) → c56(S1(ok(0)), PROPER(0))
PROPER(s1(s(z0))) → c56(S1(s(proper(z0))), PROPER(s(z0)))
PROPER(s1(dbls(z0))) → c56(S1(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(s1(nil)) → c56(S1(ok(nil)), PROPER(nil))
PROPER(s1(cons(z0, z1))) → c56(S1(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s1(sel(z0, z1))) → c56(S1(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(s1(indx(z0, z1))) → c56(S1(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(s1(from(z0))) → c56(S1(from(proper(z0))), PROPER(from(z0)))
PROPER(s1(dbl1(z0))) → c56(S1(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(s1(01)) → c56(S1(ok(01)), PROPER(01))
PROPER(s1(s1(z0))) → c56(S1(s1(proper(z0))), PROPER(s1(z0)))
PROPER(s1(sel1(z0, z1))) → c56(S1(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(s1(quote(z0))) → c56(S1(quote(proper(z0))), PROPER(quote(z0)))
S tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(sel1(z0, z1)) → c57(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)))
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0))))))
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0))))))
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0)))
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(indx(sel1(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(indx(sel1(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel1(z0, z2)), x1), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(indx(quote(dbl(z0)), x1)) → c21(INDX(mark(dbl1(z0)), x1), ACTIVE(quote(dbl(z0))))
ACTIVE(indx(quote(sel(z0, z1)), x1)) → c21(INDX(mark(sel1(z0, z1)), x1), ACTIVE(quote(sel(z0, z1))))
ACTIVE(indx(dbl(z0), x1)) → c21(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
ACTIVE(indx(dbls(z0), x1)) → c21(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(indx(z0, z1), x1)) → c21(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1)))
ACTIVE(indx(dbl1(z0), x1)) → c21(INDX(dbl1(active(z0)), x1), ACTIVE(dbl1(z0)))
ACTIVE(indx(s1(z0), x1)) → c21(INDX(s1(active(z0)), x1), ACTIVE(s1(z0)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(active(z0), z1), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(z0, active(z1)), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(quote(z0), x1)) → c21(INDX(quote(active(z0)), x1), ACTIVE(quote(z0)))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)))
ACTIVE(indx(dbl(0), x1)) → c21(INDX(mark(0), x1))
ACTIVE(indx(dbls(nil), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(indx(indx(nil, z0), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0))))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1))
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0)))
ACTIVE(dbl1(sel(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl1(sel(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl1(sel1(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl1(sel1(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl1(quote(dbl(z0)))) → c22(DBL1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl1(quote(sel(z0, z1)))) → c22(DBL1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl1(dbl(z0))) → c22(DBL1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl1(dbls(z0))) → c22(DBL1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(indx(z0, z1))) → c22(DBL1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl1(dbl1(z0))) → c22(DBL1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl1(s1(z0))) → c22(DBL1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(quote(z0))) → c22(DBL1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(dbl1(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(dbl(0))) → c22(DBL1(mark(0)))
ACTIVE(dbl1(dbls(nil))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(indx(nil, z0))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(dbl1(0))) → c22(DBL1(mark(01)))
ACTIVE(dbl(dbl1(s(z0)))) → c4(DBL(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(DBLS(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(INDX(mark(s1(s1(dbl1(z0)))), x1))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(DBL1(mark(s(s(dbl(z0))))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(ACTIVE(dbl(s(z0))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(DBL1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(DBL1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl1(from(z0))) → c4(DBL1(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl1(from(z0))) → c4(ACTIVE(from(z0)))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(DBL1(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(s1(sel(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(s1(sel(s(z0), cons(z1, z2)))) → c23(S1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(s1(sel1(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(s1(sel1(s(z0), cons(z1, z2)))) → c23(S1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(s1(quote(dbl(z0)))) → c23(S1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(s1(quote(sel(z0, z1)))) → c23(S1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(s1(dbl(z0))) → c23(S1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(s1(dbls(z0))) → c23(S1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(s1(indx(z0, z1))) → c23(S1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(s1(dbl1(z0))) → c23(S1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(s1(s1(z0))) → c23(S1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(quote(z0))) → c23(S1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(s1(dbl(0))) → c23(S1(mark(0)))
ACTIVE(s1(dbls(nil))) → c23(S1(mark(nil)))
ACTIVE(s1(indx(nil, z0))) → c23(S1(mark(nil)))
ACTIVE(s1(dbl1(0))) → c23(S1(mark(01)))
ACTIVE(s1(dbl(s(z0)))) → c6(S1(mark(s(s(dbl(z0))))))
ACTIVE(s1(dbl(s(z0)))) → c6(ACTIVE(dbl(s(z0))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(S1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(S1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(s1(from(z0))) → c6(S1(mark(cons(z0, from(s(z0))))))
ACTIVE(s1(from(z0))) → c6(ACTIVE(from(z0)))
ACTIVE(s1(dbl1(s(z0)))) → c6(S1(mark(s1(s1(dbl1(z0))))))
ACTIVE(s1(dbl1(s(z0)))) → c6(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(sel(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(quote(sel(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(quote(sel1(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(quote(sel1(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(quote(quote(dbl(z0)))) → c26(QUOTE(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(quote(quote(sel(z0, z1)))) → c26(QUOTE(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(quote(dbl(z0))) → c26(QUOTE(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(quote(dbls(z0))) → c26(QUOTE(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(quote(indx(z0, z1))) → c26(QUOTE(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(quote(dbl1(z0))) → c26(QUOTE(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(quote(s1(z0))) → c26(QUOTE(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(quote(z0))) → c26(QUOTE(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(quote(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(quote(0))) → c22(DBL1(mark(01)))
ACTIVE(s1(quote(0))) → c23(S1(mark(01)))
ACTIVE(quote(dbl(0))) → c26(QUOTE(mark(0)))
ACTIVE(quote(dbls(nil))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(indx(nil, z0))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(dbl1(0))) → c26(QUOTE(mark(01)))
ACTIVE(quote(quote(0))) → c26(QUOTE(mark(01)))
ACTIVE(dbl(quote(s(z0)))) → c7(DBL(mark(s1(quote(z0)))))
ACTIVE(dbl(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(s(z0)))) → c7(DBLS(mark(s1(quote(z0)))))
ACTIVE(dbls(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(indx(quote(s(z0)), x1)) → c7(INDX(mark(s1(quote(z0))), x1))
ACTIVE(indx(quote(s(z0)), x1)) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbl1(quote(s(z0)))) → c7(DBL1(mark(s1(quote(z0)))))
ACTIVE(dbl1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(s1(quote(s(z0)))) → c7(S1(mark(s1(quote(z0)))))
ACTIVE(s1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(quote(dbl(s(z0)))) → c7(QUOTE(mark(s(s(dbl(z0))))))
ACTIVE(quote(dbl(s(z0)))) → c7(ACTIVE(dbl(s(z0))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(QUOTE(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(QUOTE(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(quote(from(z0))) → c7(QUOTE(mark(cons(z0, from(s(z0))))))
ACTIVE(quote(from(z0))) → c7(ACTIVE(from(z0)))
ACTIVE(quote(dbl1(s(z0)))) → c7(QUOTE(mark(s1(s1(dbl1(z0))))))
ACTIVE(quote(dbl1(s(z0)))) → c7(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(quote(s(z0)))) → c7(QUOTE(mark(s1(quote(z0)))))
ACTIVE(quote(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
PROPER(dbl(dbl(z0))) → c45(DBL(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbl(s(z0))) → c45(DBL(s(proper(z0))), PROPER(s(z0)))
PROPER(dbl(dbls(z0))) → c45(DBL(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbl(cons(z0, z1))) → c45(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbl(sel(z0, z1))) → c45(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbl(indx(z0, z1))) → c45(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbl(from(z0))) → c45(DBL(from(proper(z0))), PROPER(from(z0)))
PROPER(dbl(dbl1(z0))) → c45(DBL(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbl(s1(z0))) → c45(DBL(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbl(sel1(z0, z1))) → c45(DBL(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbl(quote(z0))) → c45(DBL(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbl(0)) → c45(DBL(ok(0)))
PROPER(dbl(nil)) → c45(DBL(ok(nil)))
PROPER(dbl(01)) → c45(DBL(ok(01)))
PROPER(s(dbl(z0))) → c47(S(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(s(s(z0))) → c47(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(dbls(z0))) → c47(S(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(s(cons(z0, z1))) → c47(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(sel(z0, z1))) → c47(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(s(indx(z0, z1))) → c47(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(s(from(z0))) → c47(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(dbl1(z0))) → c47(S(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(s(s1(z0))) → c47(S(s1(proper(z0))), PROPER(s1(z0)))
PROPER(s(sel1(z0, z1))) → c47(S(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(s(quote(z0))) → c47(S(quote(proper(z0))), PROPER(quote(z0)))
PROPER(s(0)) → c47(S(ok(0)))
PROPER(s(nil)) → c47(S(ok(nil)))
PROPER(s(01)) → c47(S(ok(01)))
PROPER(dbls(dbl(z0))) → c48(DBLS(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbls(s(z0))) → c48(DBLS(s(proper(z0))), PROPER(s(z0)))
PROPER(dbls(dbls(z0))) → c48(DBLS(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbls(cons(z0, z1))) → c48(DBLS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbls(sel(z0, z1))) → c48(DBLS(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbls(indx(z0, z1))) → c48(DBLS(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbls(from(z0))) → c48(DBLS(from(proper(z0))), PROPER(from(z0)))
PROPER(dbls(dbl1(z0))) → c48(DBLS(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbls(s1(z0))) → c48(DBLS(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbls(sel1(z0, z1))) → c48(DBLS(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbls(quote(z0))) → c48(DBLS(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbls(0)) → c48(DBLS(ok(0)))
PROPER(dbls(nil)) → c48(DBLS(ok(nil)))
PROPER(dbls(01)) → c48(DBLS(ok(01)))
PROPER(cons(x0, dbl(z0))) → c50(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(cons(x0, s(z0))) → c50(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, dbls(z0))) → c50(CONS(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(cons(x0, cons(z0, z1))) → c50(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, sel(z0, z1))) → c50(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(cons(x0, indx(z0, z1))) → c50(CONS(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(cons(x0, from(z0))) → c50(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, dbl1(z0))) → c50(CONS(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(cons(x0, s1(z0))) → c50(CONS(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(cons(x0, sel1(z0, z1))) → c50(CONS(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(cons(x0, quote(z0))) → c50(CONS(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(cons(dbl(z0), x1)) → c50(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(cons(s(z0), x1)) → c50(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(dbls(z0), x1)) → c50(CONS(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c50(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(sel(z0, z1), x1)) → c50(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(cons(indx(z0, z1), x1)) → c50(CONS(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c50(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(dbl1(z0), x1)) → c50(CONS(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(cons(s1(z0), x1)) → c50(CONS(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(cons(sel1(z0, z1), x1)) → c50(CONS(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(cons(quote(z0), x1)) → c50(CONS(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c50(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c50(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, 01)) → c50(CONS(proper(x0), ok(01)), PROPER(x0))
PROPER(cons(0, x1)) → c50(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c50(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(01, x1)) → c50(CONS(ok(01), proper(x1)), PROPER(x1))
PROPER(sel(x0, dbl(z0))) → c51(SEL(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(sel(x0, s(z0))) → c51(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(sel(x0, dbls(z0))) → c51(SEL(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(sel(x0, cons(z0, z1))) → c51(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(sel(x0, sel(z0, z1))) → c51(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(sel(x0, indx(z0, z1))) → c51(SEL(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(sel(x0, from(z0))) → c51(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(sel(x0, dbl1(z0))) → c51(SEL(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(sel(x0, s1(z0))) → c51(SEL(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(sel(x0, sel1(z0, z1))) → c51(SEL(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(sel(x0, quote(z0))) → c51(SEL(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(sel(dbl(z0), x1)) → c51(SEL(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(sel(s(z0), x1)) → c51(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(sel(dbls(z0), x1)) → c51(SEL(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(sel(cons(z0, z1), x1)) → c51(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(sel(sel(z0, z1), x1)) → c51(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(sel(indx(z0, z1), x1)) → c51(SEL(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(sel(from(z0), x1)) → c51(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(sel(dbl1(z0), x1)) → c51(SEL(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(sel(s1(z0), x1)) → c51(SEL(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(sel(sel1(z0, z1), x1)) → c51(SEL(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(sel(quote(z0), x1)) → c51(SEL(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(sel(x0, 0)) → c51(SEL(proper(x0), ok(0)), PROPER(x0))
PROPER(sel(x0, nil)) → c51(SEL(proper(x0), ok(nil)), PROPER(x0))
PROPER(sel(x0, 01)) → c51(SEL(proper(x0), ok(01)), PROPER(x0))
PROPER(sel(0, x1)) → c51(SEL(ok(0), proper(x1)), PROPER(x1))
PROPER(sel(nil, x1)) → c51(SEL(ok(nil), proper(x1)), PROPER(x1))
PROPER(sel(01, x1)) → c51(SEL(ok(01), proper(x1)), PROPER(x1))
PROPER(indx(x0, dbl(z0))) → c52(INDX(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(indx(x0, s(z0))) → c52(INDX(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(indx(x0, dbls(z0))) → c52(INDX(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(indx(x0, cons(z0, z1))) → c52(INDX(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(indx(x0, sel(z0, z1))) → c52(INDX(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(indx(x0, indx(z0, z1))) → c52(INDX(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(indx(x0, from(z0))) → c52(INDX(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(indx(x0, dbl1(z0))) → c52(INDX(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(indx(x0, s1(z0))) → c52(INDX(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(indx(x0, sel1(z0, z1))) → c52(INDX(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(indx(x0, quote(z0))) → c52(INDX(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(indx(dbl(z0), x1)) → c52(INDX(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(indx(s(z0), x1)) → c52(INDX(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(indx(dbls(z0), x1)) → c52(INDX(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(indx(cons(z0, z1), x1)) → c52(INDX(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(indx(sel(z0, z1), x1)) → c52(INDX(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(indx(indx(z0, z1), x1)) → c52(INDX(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(indx(from(z0), x1)) → c52(INDX(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(indx(dbl1(z0), x1)) → c52(INDX(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(indx(s1(z0), x1)) → c52(INDX(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(indx(sel1(z0, z1), x1)) → c52(INDX(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(indx(quote(z0), x1)) → c52(INDX(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(indx(x0, 0)) → c52(INDX(proper(x0), ok(0)), PROPER(x0))
PROPER(indx(x0, nil)) → c52(INDX(proper(x0), ok(nil)), PROPER(x0))
PROPER(indx(x0, 01)) → c52(INDX(proper(x0), ok(01)), PROPER(x0))
PROPER(indx(0, x1)) → c52(INDX(ok(0), proper(x1)), PROPER(x1))
PROPER(indx(nil, x1)) → c52(INDX(ok(nil), proper(x1)), PROPER(x1))
PROPER(indx(01, x1)) → c52(INDX(ok(01), proper(x1)), PROPER(x1))
PROPER(from(dbl(z0))) → c53(FROM(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(from(s(z0))) → c53(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(dbls(z0))) → c53(FROM(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(from(cons(z0, z1))) → c53(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(sel(z0, z1))) → c53(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(from(indx(z0, z1))) → c53(FROM(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(from(from(z0))) → c53(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(dbl1(z0))) → c53(FROM(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(from(s1(z0))) → c53(FROM(s1(proper(z0))), PROPER(s1(z0)))
PROPER(from(sel1(z0, z1))) → c53(FROM(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(from(quote(z0))) → c53(FROM(quote(proper(z0))), PROPER(quote(z0)))
PROPER(from(0)) → c53(FROM(ok(0)))
PROPER(from(nil)) → c53(FROM(ok(nil)))
PROPER(from(01)) → c53(FROM(ok(01)))
PROPER(dbl1(dbl(z0))) → c54(DBL1(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbl1(s(z0))) → c54(DBL1(s(proper(z0))), PROPER(s(z0)))
PROPER(dbl1(dbls(z0))) → c54(DBL1(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbl1(cons(z0, z1))) → c54(DBL1(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbl1(sel(z0, z1))) → c54(DBL1(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbl1(indx(z0, z1))) → c54(DBL1(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbl1(from(z0))) → c54(DBL1(from(proper(z0))), PROPER(from(z0)))
PROPER(dbl1(dbl1(z0))) → c54(DBL1(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbl1(s1(z0))) → c54(DBL1(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbl1(sel1(z0, z1))) → c54(DBL1(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbl1(quote(z0))) → c54(DBL1(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbl1(0)) → c54(DBL1(ok(0)))
PROPER(dbl1(nil)) → c54(DBL1(ok(nil)))
PROPER(dbl1(01)) → c54(DBL1(ok(01)))
PROPER(s1(dbl(z0))) → c56(S1(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(s1(0)) → c56(S1(ok(0)), PROPER(0))
PROPER(s1(s(z0))) → c56(S1(s(proper(z0))), PROPER(s(z0)))
PROPER(s1(dbls(z0))) → c56(S1(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(s1(nil)) → c56(S1(ok(nil)), PROPER(nil))
PROPER(s1(cons(z0, z1))) → c56(S1(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s1(sel(z0, z1))) → c56(S1(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(s1(indx(z0, z1))) → c56(S1(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(s1(from(z0))) → c56(S1(from(proper(z0))), PROPER(from(z0)))
PROPER(s1(dbl1(z0))) → c56(S1(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(s1(01)) → c56(S1(ok(01)), PROPER(01))
PROPER(s1(s1(z0))) → c56(S1(s1(proper(z0))), PROPER(s1(z0)))
PROPER(s1(sel1(z0, z1))) → c56(S1(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(s1(quote(z0))) → c56(S1(quote(proper(z0))), PROPER(quote(z0)))
K tuples:none
Defined Rule Symbols:
active, s, dbl, cons, dbls, sel, indx, s1, dbl1, sel1, quote, proper, from
Defined Pair Symbols:
ACTIVE, DBL, DBLS, SEL, INDX, DBL1, S1, SEL1, QUOTE, PROPER, S, CONS, FROM, TOP
Compound Symbols:
c5, c12, c15, c16, c19, c20, c24, c25, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c57, c58, c59, c60, c61, c62, c63, c8, c, c17, c17, c1, c18, c18, c2, c21, c21, c3, c22, c22, c4, c23, c23, c6, c26, c26, c7, c45, c45, c47, c47, c48, c48, c50, c50, c51, c51, c52, c52, c53, c53, c54, c54, c56
(81) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 3 trailing tuple parts
(82) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(dbl(0)) → mark(0)
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
active(dbls(nil)) → mark(nil)
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1)))
active(sel(0, cons(z0, z1))) → mark(z0)
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
active(indx(nil, z0)) → mark(nil)
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2)))
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(dbl1(0)) → mark(01)
active(dbl1(s(z0))) → mark(s1(s1(dbl1(z0))))
active(sel1(0, cons(z0, z1))) → mark(z0)
active(sel1(s(z0), cons(z1, z2))) → mark(sel1(z0, z2))
active(quote(0)) → mark(01)
active(quote(s(z0))) → mark(s1(quote(z0)))
active(quote(dbl(z0))) → mark(dbl1(z0))
active(quote(sel(z0, z1))) → mark(sel1(z0, z1))
active(dbl(z0)) → dbl(active(z0))
active(dbls(z0)) → dbls(active(z0))
active(sel(z0, z1)) → sel(active(z0), z1)
active(sel(z0, z1)) → sel(z0, active(z1))
active(indx(z0, z1)) → indx(active(z0), z1)
active(dbl1(z0)) → dbl1(active(z0))
active(s1(z0)) → s1(active(z0))
active(sel1(z0, z1)) → sel1(active(z0), z1)
active(sel1(z0, z1)) → sel1(z0, active(z1))
active(quote(z0)) → quote(active(z0))
s(ok(z0)) → ok(s(z0))
dbl(mark(z0)) → mark(dbl(z0))
dbl(ok(z0)) → ok(dbl(z0))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
dbls(mark(z0)) → mark(dbls(z0))
dbls(ok(z0)) → ok(dbls(z0))
sel(mark(z0), z1) → mark(sel(z0, z1))
sel(z0, mark(z1)) → mark(sel(z0, z1))
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
indx(mark(z0), z1) → mark(indx(z0, z1))
indx(ok(z0), ok(z1)) → ok(indx(z0, z1))
s1(mark(z0)) → mark(s1(z0))
s1(ok(z0)) → ok(s1(z0))
dbl1(mark(z0)) → mark(dbl1(z0))
dbl1(ok(z0)) → ok(dbl1(z0))
sel1(mark(z0), z1) → mark(sel1(z0, z1))
sel1(z0, mark(z1)) → mark(sel1(z0, z1))
sel1(ok(z0), ok(z1)) → ok(sel1(z0, z1))
quote(mark(z0)) → mark(quote(z0))
quote(ok(z0)) → ok(quote(z0))
proper(dbl(z0)) → dbl(proper(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(dbls(z0)) → dbls(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
proper(indx(z0, z1)) → indx(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(dbl1(z0)) → dbl1(proper(z0))
proper(01) → ok(01)
proper(s1(z0)) → s1(proper(z0))
proper(sel1(z0, z1)) → sel1(proper(z0), proper(z1))
proper(quote(z0)) → quote(proper(z0))
from(ok(z0)) → ok(from(z0))
Tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(sel1(z0, z1)) → c57(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)))
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0))))))
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0))))))
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0)))
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(indx(sel1(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(indx(sel1(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel1(z0, z2)), x1), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(indx(quote(dbl(z0)), x1)) → c21(INDX(mark(dbl1(z0)), x1), ACTIVE(quote(dbl(z0))))
ACTIVE(indx(quote(sel(z0, z1)), x1)) → c21(INDX(mark(sel1(z0, z1)), x1), ACTIVE(quote(sel(z0, z1))))
ACTIVE(indx(dbl(z0), x1)) → c21(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
ACTIVE(indx(dbls(z0), x1)) → c21(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(indx(z0, z1), x1)) → c21(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1)))
ACTIVE(indx(dbl1(z0), x1)) → c21(INDX(dbl1(active(z0)), x1), ACTIVE(dbl1(z0)))
ACTIVE(indx(s1(z0), x1)) → c21(INDX(s1(active(z0)), x1), ACTIVE(s1(z0)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(active(z0), z1), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(z0, active(z1)), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(quote(z0), x1)) → c21(INDX(quote(active(z0)), x1), ACTIVE(quote(z0)))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)))
ACTIVE(indx(dbl(0), x1)) → c21(INDX(mark(0), x1))
ACTIVE(indx(dbls(nil), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(indx(indx(nil, z0), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0))))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1))
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0)))
ACTIVE(dbl1(sel(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl1(sel(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl1(sel1(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl1(sel1(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl1(quote(dbl(z0)))) → c22(DBL1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl1(quote(sel(z0, z1)))) → c22(DBL1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl1(dbl(z0))) → c22(DBL1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl1(dbls(z0))) → c22(DBL1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(indx(z0, z1))) → c22(DBL1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl1(dbl1(z0))) → c22(DBL1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl1(s1(z0))) → c22(DBL1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(quote(z0))) → c22(DBL1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(dbl1(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(dbl(0))) → c22(DBL1(mark(0)))
ACTIVE(dbl1(dbls(nil))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(indx(nil, z0))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(dbl1(0))) → c22(DBL1(mark(01)))
ACTIVE(dbl(dbl1(s(z0)))) → c4(DBL(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(DBLS(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(INDX(mark(s1(s1(dbl1(z0)))), x1))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(DBL1(mark(s(s(dbl(z0))))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(ACTIVE(dbl(s(z0))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(DBL1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(DBL1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl1(from(z0))) → c4(DBL1(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl1(from(z0))) → c4(ACTIVE(from(z0)))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(DBL1(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(s1(sel(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(s1(sel(s(z0), cons(z1, z2)))) → c23(S1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(s1(sel1(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(s1(sel1(s(z0), cons(z1, z2)))) → c23(S1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(s1(quote(dbl(z0)))) → c23(S1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(s1(quote(sel(z0, z1)))) → c23(S1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(s1(dbl(z0))) → c23(S1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(s1(dbls(z0))) → c23(S1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(s1(indx(z0, z1))) → c23(S1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(s1(dbl1(z0))) → c23(S1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(s1(s1(z0))) → c23(S1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(quote(z0))) → c23(S1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(s1(dbl(0))) → c23(S1(mark(0)))
ACTIVE(s1(dbls(nil))) → c23(S1(mark(nil)))
ACTIVE(s1(indx(nil, z0))) → c23(S1(mark(nil)))
ACTIVE(s1(dbl1(0))) → c23(S1(mark(01)))
ACTIVE(s1(dbl(s(z0)))) → c6(S1(mark(s(s(dbl(z0))))))
ACTIVE(s1(dbl(s(z0)))) → c6(ACTIVE(dbl(s(z0))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(S1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(S1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(s1(from(z0))) → c6(S1(mark(cons(z0, from(s(z0))))))
ACTIVE(s1(from(z0))) → c6(ACTIVE(from(z0)))
ACTIVE(s1(dbl1(s(z0)))) → c6(S1(mark(s1(s1(dbl1(z0))))))
ACTIVE(s1(dbl1(s(z0)))) → c6(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(sel(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(quote(sel(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(quote(sel1(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(quote(sel1(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(quote(quote(dbl(z0)))) → c26(QUOTE(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(quote(quote(sel(z0, z1)))) → c26(QUOTE(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(quote(dbl(z0))) → c26(QUOTE(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(quote(dbls(z0))) → c26(QUOTE(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(quote(indx(z0, z1))) → c26(QUOTE(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(quote(dbl1(z0))) → c26(QUOTE(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(quote(s1(z0))) → c26(QUOTE(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(quote(z0))) → c26(QUOTE(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(quote(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(quote(0))) → c22(DBL1(mark(01)))
ACTIVE(s1(quote(0))) → c23(S1(mark(01)))
ACTIVE(quote(dbl(0))) → c26(QUOTE(mark(0)))
ACTIVE(quote(dbls(nil))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(indx(nil, z0))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(dbl1(0))) → c26(QUOTE(mark(01)))
ACTIVE(quote(quote(0))) → c26(QUOTE(mark(01)))
ACTIVE(dbl(quote(s(z0)))) → c7(DBL(mark(s1(quote(z0)))))
ACTIVE(dbl(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(s(z0)))) → c7(DBLS(mark(s1(quote(z0)))))
ACTIVE(dbls(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(indx(quote(s(z0)), x1)) → c7(INDX(mark(s1(quote(z0))), x1))
ACTIVE(indx(quote(s(z0)), x1)) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbl1(quote(s(z0)))) → c7(DBL1(mark(s1(quote(z0)))))
ACTIVE(dbl1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(s1(quote(s(z0)))) → c7(S1(mark(s1(quote(z0)))))
ACTIVE(s1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(quote(dbl(s(z0)))) → c7(QUOTE(mark(s(s(dbl(z0))))))
ACTIVE(quote(dbl(s(z0)))) → c7(ACTIVE(dbl(s(z0))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(QUOTE(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(QUOTE(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(quote(from(z0))) → c7(QUOTE(mark(cons(z0, from(s(z0))))))
ACTIVE(quote(from(z0))) → c7(ACTIVE(from(z0)))
ACTIVE(quote(dbl1(s(z0)))) → c7(QUOTE(mark(s1(s1(dbl1(z0))))))
ACTIVE(quote(dbl1(s(z0)))) → c7(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(quote(s(z0)))) → c7(QUOTE(mark(s1(quote(z0)))))
ACTIVE(quote(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
PROPER(dbl(dbl(z0))) → c45(DBL(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbl(s(z0))) → c45(DBL(s(proper(z0))), PROPER(s(z0)))
PROPER(dbl(dbls(z0))) → c45(DBL(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbl(cons(z0, z1))) → c45(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbl(sel(z0, z1))) → c45(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbl(indx(z0, z1))) → c45(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbl(from(z0))) → c45(DBL(from(proper(z0))), PROPER(from(z0)))
PROPER(dbl(dbl1(z0))) → c45(DBL(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbl(s1(z0))) → c45(DBL(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbl(sel1(z0, z1))) → c45(DBL(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbl(quote(z0))) → c45(DBL(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbl(0)) → c45(DBL(ok(0)))
PROPER(dbl(nil)) → c45(DBL(ok(nil)))
PROPER(dbl(01)) → c45(DBL(ok(01)))
PROPER(s(dbl(z0))) → c47(S(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(s(s(z0))) → c47(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(dbls(z0))) → c47(S(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(s(cons(z0, z1))) → c47(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(sel(z0, z1))) → c47(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(s(indx(z0, z1))) → c47(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(s(from(z0))) → c47(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(dbl1(z0))) → c47(S(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(s(s1(z0))) → c47(S(s1(proper(z0))), PROPER(s1(z0)))
PROPER(s(sel1(z0, z1))) → c47(S(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(s(quote(z0))) → c47(S(quote(proper(z0))), PROPER(quote(z0)))
PROPER(s(0)) → c47(S(ok(0)))
PROPER(s(nil)) → c47(S(ok(nil)))
PROPER(s(01)) → c47(S(ok(01)))
PROPER(dbls(dbl(z0))) → c48(DBLS(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbls(s(z0))) → c48(DBLS(s(proper(z0))), PROPER(s(z0)))
PROPER(dbls(dbls(z0))) → c48(DBLS(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbls(cons(z0, z1))) → c48(DBLS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbls(sel(z0, z1))) → c48(DBLS(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbls(indx(z0, z1))) → c48(DBLS(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbls(from(z0))) → c48(DBLS(from(proper(z0))), PROPER(from(z0)))
PROPER(dbls(dbl1(z0))) → c48(DBLS(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbls(s1(z0))) → c48(DBLS(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbls(sel1(z0, z1))) → c48(DBLS(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbls(quote(z0))) → c48(DBLS(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbls(0)) → c48(DBLS(ok(0)))
PROPER(dbls(nil)) → c48(DBLS(ok(nil)))
PROPER(dbls(01)) → c48(DBLS(ok(01)))
PROPER(cons(x0, dbl(z0))) → c50(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(cons(x0, s(z0))) → c50(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, dbls(z0))) → c50(CONS(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(cons(x0, cons(z0, z1))) → c50(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, sel(z0, z1))) → c50(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(cons(x0, indx(z0, z1))) → c50(CONS(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(cons(x0, from(z0))) → c50(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, dbl1(z0))) → c50(CONS(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(cons(x0, s1(z0))) → c50(CONS(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(cons(x0, sel1(z0, z1))) → c50(CONS(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(cons(x0, quote(z0))) → c50(CONS(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(cons(dbl(z0), x1)) → c50(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(cons(s(z0), x1)) → c50(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(dbls(z0), x1)) → c50(CONS(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c50(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(sel(z0, z1), x1)) → c50(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(cons(indx(z0, z1), x1)) → c50(CONS(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c50(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(dbl1(z0), x1)) → c50(CONS(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(cons(s1(z0), x1)) → c50(CONS(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(cons(sel1(z0, z1), x1)) → c50(CONS(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(cons(quote(z0), x1)) → c50(CONS(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c50(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c50(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, 01)) → c50(CONS(proper(x0), ok(01)), PROPER(x0))
PROPER(cons(0, x1)) → c50(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c50(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(01, x1)) → c50(CONS(ok(01), proper(x1)), PROPER(x1))
PROPER(sel(x0, dbl(z0))) → c51(SEL(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(sel(x0, s(z0))) → c51(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(sel(x0, dbls(z0))) → c51(SEL(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(sel(x0, cons(z0, z1))) → c51(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(sel(x0, sel(z0, z1))) → c51(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(sel(x0, indx(z0, z1))) → c51(SEL(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(sel(x0, from(z0))) → c51(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(sel(x0, dbl1(z0))) → c51(SEL(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(sel(x0, s1(z0))) → c51(SEL(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(sel(x0, sel1(z0, z1))) → c51(SEL(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(sel(x0, quote(z0))) → c51(SEL(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(sel(dbl(z0), x1)) → c51(SEL(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(sel(s(z0), x1)) → c51(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(sel(dbls(z0), x1)) → c51(SEL(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(sel(cons(z0, z1), x1)) → c51(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(sel(sel(z0, z1), x1)) → c51(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(sel(indx(z0, z1), x1)) → c51(SEL(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(sel(from(z0), x1)) → c51(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(sel(dbl1(z0), x1)) → c51(SEL(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(sel(s1(z0), x1)) → c51(SEL(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(sel(sel1(z0, z1), x1)) → c51(SEL(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(sel(quote(z0), x1)) → c51(SEL(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(sel(x0, 0)) → c51(SEL(proper(x0), ok(0)), PROPER(x0))
PROPER(sel(x0, nil)) → c51(SEL(proper(x0), ok(nil)), PROPER(x0))
PROPER(sel(x0, 01)) → c51(SEL(proper(x0), ok(01)), PROPER(x0))
PROPER(sel(0, x1)) → c51(SEL(ok(0), proper(x1)), PROPER(x1))
PROPER(sel(nil, x1)) → c51(SEL(ok(nil), proper(x1)), PROPER(x1))
PROPER(sel(01, x1)) → c51(SEL(ok(01), proper(x1)), PROPER(x1))
PROPER(indx(x0, dbl(z0))) → c52(INDX(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(indx(x0, s(z0))) → c52(INDX(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(indx(x0, dbls(z0))) → c52(INDX(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(indx(x0, cons(z0, z1))) → c52(INDX(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(indx(x0, sel(z0, z1))) → c52(INDX(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(indx(x0, indx(z0, z1))) → c52(INDX(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(indx(x0, from(z0))) → c52(INDX(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(indx(x0, dbl1(z0))) → c52(INDX(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(indx(x0, s1(z0))) → c52(INDX(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(indx(x0, sel1(z0, z1))) → c52(INDX(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(indx(x0, quote(z0))) → c52(INDX(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(indx(dbl(z0), x1)) → c52(INDX(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(indx(s(z0), x1)) → c52(INDX(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(indx(dbls(z0), x1)) → c52(INDX(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(indx(cons(z0, z1), x1)) → c52(INDX(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(indx(sel(z0, z1), x1)) → c52(INDX(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(indx(indx(z0, z1), x1)) → c52(INDX(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(indx(from(z0), x1)) → c52(INDX(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(indx(dbl1(z0), x1)) → c52(INDX(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(indx(s1(z0), x1)) → c52(INDX(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(indx(sel1(z0, z1), x1)) → c52(INDX(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(indx(quote(z0), x1)) → c52(INDX(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(indx(x0, 0)) → c52(INDX(proper(x0), ok(0)), PROPER(x0))
PROPER(indx(x0, nil)) → c52(INDX(proper(x0), ok(nil)), PROPER(x0))
PROPER(indx(x0, 01)) → c52(INDX(proper(x0), ok(01)), PROPER(x0))
PROPER(indx(0, x1)) → c52(INDX(ok(0), proper(x1)), PROPER(x1))
PROPER(indx(nil, x1)) → c52(INDX(ok(nil), proper(x1)), PROPER(x1))
PROPER(indx(01, x1)) → c52(INDX(ok(01), proper(x1)), PROPER(x1))
PROPER(from(dbl(z0))) → c53(FROM(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(from(s(z0))) → c53(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(dbls(z0))) → c53(FROM(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(from(cons(z0, z1))) → c53(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(sel(z0, z1))) → c53(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(from(indx(z0, z1))) → c53(FROM(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(from(from(z0))) → c53(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(dbl1(z0))) → c53(FROM(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(from(s1(z0))) → c53(FROM(s1(proper(z0))), PROPER(s1(z0)))
PROPER(from(sel1(z0, z1))) → c53(FROM(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(from(quote(z0))) → c53(FROM(quote(proper(z0))), PROPER(quote(z0)))
PROPER(from(0)) → c53(FROM(ok(0)))
PROPER(from(nil)) → c53(FROM(ok(nil)))
PROPER(from(01)) → c53(FROM(ok(01)))
PROPER(dbl1(dbl(z0))) → c54(DBL1(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbl1(s(z0))) → c54(DBL1(s(proper(z0))), PROPER(s(z0)))
PROPER(dbl1(dbls(z0))) → c54(DBL1(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbl1(cons(z0, z1))) → c54(DBL1(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbl1(sel(z0, z1))) → c54(DBL1(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbl1(indx(z0, z1))) → c54(DBL1(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbl1(from(z0))) → c54(DBL1(from(proper(z0))), PROPER(from(z0)))
PROPER(dbl1(dbl1(z0))) → c54(DBL1(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbl1(s1(z0))) → c54(DBL1(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbl1(sel1(z0, z1))) → c54(DBL1(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbl1(quote(z0))) → c54(DBL1(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbl1(0)) → c54(DBL1(ok(0)))
PROPER(dbl1(nil)) → c54(DBL1(ok(nil)))
PROPER(dbl1(01)) → c54(DBL1(ok(01)))
PROPER(s1(dbl(z0))) → c56(S1(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(s1(s(z0))) → c56(S1(s(proper(z0))), PROPER(s(z0)))
PROPER(s1(dbls(z0))) → c56(S1(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(s1(cons(z0, z1))) → c56(S1(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s1(sel(z0, z1))) → c56(S1(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(s1(indx(z0, z1))) → c56(S1(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(s1(from(z0))) → c56(S1(from(proper(z0))), PROPER(from(z0)))
PROPER(s1(dbl1(z0))) → c56(S1(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(s1(s1(z0))) → c56(S1(s1(proper(z0))), PROPER(s1(z0)))
PROPER(s1(sel1(z0, z1))) → c56(S1(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(s1(quote(z0))) → c56(S1(quote(proper(z0))), PROPER(quote(z0)))
PROPER(s1(0)) → c56(S1(ok(0)))
PROPER(s1(nil)) → c56(S1(ok(nil)))
PROPER(s1(01)) → c56(S1(ok(01)))
S tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(sel1(z0, z1)) → c57(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)))
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0))))))
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0))))))
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0)))
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(indx(sel1(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(indx(sel1(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel1(z0, z2)), x1), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(indx(quote(dbl(z0)), x1)) → c21(INDX(mark(dbl1(z0)), x1), ACTIVE(quote(dbl(z0))))
ACTIVE(indx(quote(sel(z0, z1)), x1)) → c21(INDX(mark(sel1(z0, z1)), x1), ACTIVE(quote(sel(z0, z1))))
ACTIVE(indx(dbl(z0), x1)) → c21(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
ACTIVE(indx(dbls(z0), x1)) → c21(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(indx(z0, z1), x1)) → c21(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1)))
ACTIVE(indx(dbl1(z0), x1)) → c21(INDX(dbl1(active(z0)), x1), ACTIVE(dbl1(z0)))
ACTIVE(indx(s1(z0), x1)) → c21(INDX(s1(active(z0)), x1), ACTIVE(s1(z0)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(active(z0), z1), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(z0, active(z1)), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(quote(z0), x1)) → c21(INDX(quote(active(z0)), x1), ACTIVE(quote(z0)))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)))
ACTIVE(indx(dbl(0), x1)) → c21(INDX(mark(0), x1))
ACTIVE(indx(dbls(nil), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(indx(indx(nil, z0), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0))))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1))
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0)))
ACTIVE(dbl1(sel(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl1(sel(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl1(sel1(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl1(sel1(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl1(quote(dbl(z0)))) → c22(DBL1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl1(quote(sel(z0, z1)))) → c22(DBL1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl1(dbl(z0))) → c22(DBL1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl1(dbls(z0))) → c22(DBL1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(indx(z0, z1))) → c22(DBL1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl1(dbl1(z0))) → c22(DBL1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl1(s1(z0))) → c22(DBL1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(quote(z0))) → c22(DBL1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(dbl1(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(dbl(0))) → c22(DBL1(mark(0)))
ACTIVE(dbl1(dbls(nil))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(indx(nil, z0))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(dbl1(0))) → c22(DBL1(mark(01)))
ACTIVE(dbl(dbl1(s(z0)))) → c4(DBL(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(DBLS(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(INDX(mark(s1(s1(dbl1(z0)))), x1))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(DBL1(mark(s(s(dbl(z0))))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(ACTIVE(dbl(s(z0))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(DBL1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(DBL1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl1(from(z0))) → c4(DBL1(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl1(from(z0))) → c4(ACTIVE(from(z0)))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(DBL1(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(s1(sel(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(s1(sel(s(z0), cons(z1, z2)))) → c23(S1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(s1(sel1(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(s1(sel1(s(z0), cons(z1, z2)))) → c23(S1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(s1(quote(dbl(z0)))) → c23(S1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(s1(quote(sel(z0, z1)))) → c23(S1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(s1(dbl(z0))) → c23(S1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(s1(dbls(z0))) → c23(S1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(s1(indx(z0, z1))) → c23(S1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(s1(dbl1(z0))) → c23(S1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(s1(s1(z0))) → c23(S1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(quote(z0))) → c23(S1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(s1(dbl(0))) → c23(S1(mark(0)))
ACTIVE(s1(dbls(nil))) → c23(S1(mark(nil)))
ACTIVE(s1(indx(nil, z0))) → c23(S1(mark(nil)))
ACTIVE(s1(dbl1(0))) → c23(S1(mark(01)))
ACTIVE(s1(dbl(s(z0)))) → c6(S1(mark(s(s(dbl(z0))))))
ACTIVE(s1(dbl(s(z0)))) → c6(ACTIVE(dbl(s(z0))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(S1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(S1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(s1(from(z0))) → c6(S1(mark(cons(z0, from(s(z0))))))
ACTIVE(s1(from(z0))) → c6(ACTIVE(from(z0)))
ACTIVE(s1(dbl1(s(z0)))) → c6(S1(mark(s1(s1(dbl1(z0))))))
ACTIVE(s1(dbl1(s(z0)))) → c6(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(sel(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(quote(sel(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(quote(sel1(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(quote(sel1(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(quote(quote(dbl(z0)))) → c26(QUOTE(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(quote(quote(sel(z0, z1)))) → c26(QUOTE(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(quote(dbl(z0))) → c26(QUOTE(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(quote(dbls(z0))) → c26(QUOTE(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(quote(indx(z0, z1))) → c26(QUOTE(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(quote(dbl1(z0))) → c26(QUOTE(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(quote(s1(z0))) → c26(QUOTE(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(quote(z0))) → c26(QUOTE(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(quote(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(quote(0))) → c22(DBL1(mark(01)))
ACTIVE(s1(quote(0))) → c23(S1(mark(01)))
ACTIVE(quote(dbl(0))) → c26(QUOTE(mark(0)))
ACTIVE(quote(dbls(nil))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(indx(nil, z0))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(dbl1(0))) → c26(QUOTE(mark(01)))
ACTIVE(quote(quote(0))) → c26(QUOTE(mark(01)))
ACTIVE(dbl(quote(s(z0)))) → c7(DBL(mark(s1(quote(z0)))))
ACTIVE(dbl(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(s(z0)))) → c7(DBLS(mark(s1(quote(z0)))))
ACTIVE(dbls(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(indx(quote(s(z0)), x1)) → c7(INDX(mark(s1(quote(z0))), x1))
ACTIVE(indx(quote(s(z0)), x1)) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbl1(quote(s(z0)))) → c7(DBL1(mark(s1(quote(z0)))))
ACTIVE(dbl1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(s1(quote(s(z0)))) → c7(S1(mark(s1(quote(z0)))))
ACTIVE(s1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(quote(dbl(s(z0)))) → c7(QUOTE(mark(s(s(dbl(z0))))))
ACTIVE(quote(dbl(s(z0)))) → c7(ACTIVE(dbl(s(z0))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(QUOTE(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(QUOTE(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(quote(from(z0))) → c7(QUOTE(mark(cons(z0, from(s(z0))))))
ACTIVE(quote(from(z0))) → c7(ACTIVE(from(z0)))
ACTIVE(quote(dbl1(s(z0)))) → c7(QUOTE(mark(s1(s1(dbl1(z0))))))
ACTIVE(quote(dbl1(s(z0)))) → c7(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(quote(s(z0)))) → c7(QUOTE(mark(s1(quote(z0)))))
ACTIVE(quote(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
PROPER(dbl(dbl(z0))) → c45(DBL(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbl(s(z0))) → c45(DBL(s(proper(z0))), PROPER(s(z0)))
PROPER(dbl(dbls(z0))) → c45(DBL(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbl(cons(z0, z1))) → c45(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbl(sel(z0, z1))) → c45(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbl(indx(z0, z1))) → c45(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbl(from(z0))) → c45(DBL(from(proper(z0))), PROPER(from(z0)))
PROPER(dbl(dbl1(z0))) → c45(DBL(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbl(s1(z0))) → c45(DBL(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbl(sel1(z0, z1))) → c45(DBL(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbl(quote(z0))) → c45(DBL(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbl(0)) → c45(DBL(ok(0)))
PROPER(dbl(nil)) → c45(DBL(ok(nil)))
PROPER(dbl(01)) → c45(DBL(ok(01)))
PROPER(s(dbl(z0))) → c47(S(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(s(s(z0))) → c47(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(dbls(z0))) → c47(S(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(s(cons(z0, z1))) → c47(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(sel(z0, z1))) → c47(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(s(indx(z0, z1))) → c47(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(s(from(z0))) → c47(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(dbl1(z0))) → c47(S(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(s(s1(z0))) → c47(S(s1(proper(z0))), PROPER(s1(z0)))
PROPER(s(sel1(z0, z1))) → c47(S(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(s(quote(z0))) → c47(S(quote(proper(z0))), PROPER(quote(z0)))
PROPER(s(0)) → c47(S(ok(0)))
PROPER(s(nil)) → c47(S(ok(nil)))
PROPER(s(01)) → c47(S(ok(01)))
PROPER(dbls(dbl(z0))) → c48(DBLS(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbls(s(z0))) → c48(DBLS(s(proper(z0))), PROPER(s(z0)))
PROPER(dbls(dbls(z0))) → c48(DBLS(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbls(cons(z0, z1))) → c48(DBLS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbls(sel(z0, z1))) → c48(DBLS(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbls(indx(z0, z1))) → c48(DBLS(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbls(from(z0))) → c48(DBLS(from(proper(z0))), PROPER(from(z0)))
PROPER(dbls(dbl1(z0))) → c48(DBLS(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbls(s1(z0))) → c48(DBLS(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbls(sel1(z0, z1))) → c48(DBLS(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbls(quote(z0))) → c48(DBLS(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbls(0)) → c48(DBLS(ok(0)))
PROPER(dbls(nil)) → c48(DBLS(ok(nil)))
PROPER(dbls(01)) → c48(DBLS(ok(01)))
PROPER(cons(x0, dbl(z0))) → c50(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(cons(x0, s(z0))) → c50(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, dbls(z0))) → c50(CONS(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(cons(x0, cons(z0, z1))) → c50(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, sel(z0, z1))) → c50(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(cons(x0, indx(z0, z1))) → c50(CONS(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(cons(x0, from(z0))) → c50(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, dbl1(z0))) → c50(CONS(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(cons(x0, s1(z0))) → c50(CONS(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(cons(x0, sel1(z0, z1))) → c50(CONS(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(cons(x0, quote(z0))) → c50(CONS(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(cons(dbl(z0), x1)) → c50(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(cons(s(z0), x1)) → c50(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(dbls(z0), x1)) → c50(CONS(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c50(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(sel(z0, z1), x1)) → c50(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(cons(indx(z0, z1), x1)) → c50(CONS(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c50(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(dbl1(z0), x1)) → c50(CONS(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(cons(s1(z0), x1)) → c50(CONS(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(cons(sel1(z0, z1), x1)) → c50(CONS(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(cons(quote(z0), x1)) → c50(CONS(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c50(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c50(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, 01)) → c50(CONS(proper(x0), ok(01)), PROPER(x0))
PROPER(cons(0, x1)) → c50(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c50(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(01, x1)) → c50(CONS(ok(01), proper(x1)), PROPER(x1))
PROPER(sel(x0, dbl(z0))) → c51(SEL(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(sel(x0, s(z0))) → c51(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(sel(x0, dbls(z0))) → c51(SEL(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(sel(x0, cons(z0, z1))) → c51(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(sel(x0, sel(z0, z1))) → c51(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(sel(x0, indx(z0, z1))) → c51(SEL(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(sel(x0, from(z0))) → c51(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(sel(x0, dbl1(z0))) → c51(SEL(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(sel(x0, s1(z0))) → c51(SEL(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(sel(x0, sel1(z0, z1))) → c51(SEL(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(sel(x0, quote(z0))) → c51(SEL(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(sel(dbl(z0), x1)) → c51(SEL(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(sel(s(z0), x1)) → c51(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(sel(dbls(z0), x1)) → c51(SEL(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(sel(cons(z0, z1), x1)) → c51(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(sel(sel(z0, z1), x1)) → c51(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(sel(indx(z0, z1), x1)) → c51(SEL(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(sel(from(z0), x1)) → c51(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(sel(dbl1(z0), x1)) → c51(SEL(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(sel(s1(z0), x1)) → c51(SEL(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(sel(sel1(z0, z1), x1)) → c51(SEL(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(sel(quote(z0), x1)) → c51(SEL(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(sel(x0, 0)) → c51(SEL(proper(x0), ok(0)), PROPER(x0))
PROPER(sel(x0, nil)) → c51(SEL(proper(x0), ok(nil)), PROPER(x0))
PROPER(sel(x0, 01)) → c51(SEL(proper(x0), ok(01)), PROPER(x0))
PROPER(sel(0, x1)) → c51(SEL(ok(0), proper(x1)), PROPER(x1))
PROPER(sel(nil, x1)) → c51(SEL(ok(nil), proper(x1)), PROPER(x1))
PROPER(sel(01, x1)) → c51(SEL(ok(01), proper(x1)), PROPER(x1))
PROPER(indx(x0, dbl(z0))) → c52(INDX(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(indx(x0, s(z0))) → c52(INDX(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(indx(x0, dbls(z0))) → c52(INDX(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(indx(x0, cons(z0, z1))) → c52(INDX(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(indx(x0, sel(z0, z1))) → c52(INDX(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(indx(x0, indx(z0, z1))) → c52(INDX(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(indx(x0, from(z0))) → c52(INDX(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(indx(x0, dbl1(z0))) → c52(INDX(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(indx(x0, s1(z0))) → c52(INDX(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(indx(x0, sel1(z0, z1))) → c52(INDX(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(indx(x0, quote(z0))) → c52(INDX(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(indx(dbl(z0), x1)) → c52(INDX(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(indx(s(z0), x1)) → c52(INDX(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(indx(dbls(z0), x1)) → c52(INDX(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(indx(cons(z0, z1), x1)) → c52(INDX(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(indx(sel(z0, z1), x1)) → c52(INDX(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(indx(indx(z0, z1), x1)) → c52(INDX(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(indx(from(z0), x1)) → c52(INDX(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(indx(dbl1(z0), x1)) → c52(INDX(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(indx(s1(z0), x1)) → c52(INDX(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(indx(sel1(z0, z1), x1)) → c52(INDX(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(indx(quote(z0), x1)) → c52(INDX(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(indx(x0, 0)) → c52(INDX(proper(x0), ok(0)), PROPER(x0))
PROPER(indx(x0, nil)) → c52(INDX(proper(x0), ok(nil)), PROPER(x0))
PROPER(indx(x0, 01)) → c52(INDX(proper(x0), ok(01)), PROPER(x0))
PROPER(indx(0, x1)) → c52(INDX(ok(0), proper(x1)), PROPER(x1))
PROPER(indx(nil, x1)) → c52(INDX(ok(nil), proper(x1)), PROPER(x1))
PROPER(indx(01, x1)) → c52(INDX(ok(01), proper(x1)), PROPER(x1))
PROPER(from(dbl(z0))) → c53(FROM(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(from(s(z0))) → c53(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(dbls(z0))) → c53(FROM(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(from(cons(z0, z1))) → c53(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(sel(z0, z1))) → c53(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(from(indx(z0, z1))) → c53(FROM(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(from(from(z0))) → c53(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(dbl1(z0))) → c53(FROM(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(from(s1(z0))) → c53(FROM(s1(proper(z0))), PROPER(s1(z0)))
PROPER(from(sel1(z0, z1))) → c53(FROM(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(from(quote(z0))) → c53(FROM(quote(proper(z0))), PROPER(quote(z0)))
PROPER(from(0)) → c53(FROM(ok(0)))
PROPER(from(nil)) → c53(FROM(ok(nil)))
PROPER(from(01)) → c53(FROM(ok(01)))
PROPER(dbl1(dbl(z0))) → c54(DBL1(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbl1(s(z0))) → c54(DBL1(s(proper(z0))), PROPER(s(z0)))
PROPER(dbl1(dbls(z0))) → c54(DBL1(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbl1(cons(z0, z1))) → c54(DBL1(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbl1(sel(z0, z1))) → c54(DBL1(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbl1(indx(z0, z1))) → c54(DBL1(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbl1(from(z0))) → c54(DBL1(from(proper(z0))), PROPER(from(z0)))
PROPER(dbl1(dbl1(z0))) → c54(DBL1(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbl1(s1(z0))) → c54(DBL1(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbl1(sel1(z0, z1))) → c54(DBL1(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbl1(quote(z0))) → c54(DBL1(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbl1(0)) → c54(DBL1(ok(0)))
PROPER(dbl1(nil)) → c54(DBL1(ok(nil)))
PROPER(dbl1(01)) → c54(DBL1(ok(01)))
PROPER(s1(dbl(z0))) → c56(S1(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(s1(s(z0))) → c56(S1(s(proper(z0))), PROPER(s(z0)))
PROPER(s1(dbls(z0))) → c56(S1(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(s1(cons(z0, z1))) → c56(S1(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s1(sel(z0, z1))) → c56(S1(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(s1(indx(z0, z1))) → c56(S1(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(s1(from(z0))) → c56(S1(from(proper(z0))), PROPER(from(z0)))
PROPER(s1(dbl1(z0))) → c56(S1(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(s1(s1(z0))) → c56(S1(s1(proper(z0))), PROPER(s1(z0)))
PROPER(s1(sel1(z0, z1))) → c56(S1(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(s1(quote(z0))) → c56(S1(quote(proper(z0))), PROPER(quote(z0)))
PROPER(s1(0)) → c56(S1(ok(0)))
PROPER(s1(nil)) → c56(S1(ok(nil)))
PROPER(s1(01)) → c56(S1(ok(01)))
K tuples:none
Defined Rule Symbols:
active, s, dbl, cons, dbls, sel, indx, s1, dbl1, sel1, quote, proper, from
Defined Pair Symbols:
ACTIVE, DBL, DBLS, SEL, INDX, DBL1, S1, SEL1, QUOTE, PROPER, S, CONS, FROM, TOP
Compound Symbols:
c5, c12, c15, c16, c19, c20, c24, c25, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c57, c58, c59, c60, c61, c62, c63, c8, c, c17, c17, c1, c18, c18, c2, c21, c21, c3, c22, c22, c4, c23, c23, c6, c26, c26, c7, c45, c45, c47, c47, c48, c48, c50, c50, c51, c51, c52, c52, c53, c53, c54, c54, c56, c56
(83) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
PROPER(
sel1(
z0,
z1)) →
c57(
SEL1(
proper(
z0),
proper(
z1)),
PROPER(
z0),
PROPER(
z1)) by
PROPER(sel1(x0, dbl(z0))) → c57(SEL1(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(sel1(x0, 0)) → c57(SEL1(proper(x0), ok(0)), PROPER(x0), PROPER(0))
PROPER(sel1(x0, s(z0))) → c57(SEL1(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(sel1(x0, dbls(z0))) → c57(SEL1(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(sel1(x0, nil)) → c57(SEL1(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
PROPER(sel1(x0, cons(z0, z1))) → c57(SEL1(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(sel1(x0, sel(z0, z1))) → c57(SEL1(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(sel1(x0, indx(z0, z1))) → c57(SEL1(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(sel1(x0, from(z0))) → c57(SEL1(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(sel1(x0, dbl1(z0))) → c57(SEL1(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(sel1(x0, 01)) → c57(SEL1(proper(x0), ok(01)), PROPER(x0), PROPER(01))
PROPER(sel1(x0, s1(z0))) → c57(SEL1(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(sel1(x0, sel1(z0, z1))) → c57(SEL1(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(sel1(x0, quote(z0))) → c57(SEL1(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(sel1(dbl(z0), x1)) → c57(SEL1(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(sel1(0, x1)) → c57(SEL1(ok(0), proper(x1)), PROPER(0), PROPER(x1))
PROPER(sel1(s(z0), x1)) → c57(SEL1(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(sel1(dbls(z0), x1)) → c57(SEL1(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(sel1(nil, x1)) → c57(SEL1(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
PROPER(sel1(cons(z0, z1), x1)) → c57(SEL1(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(sel1(sel(z0, z1), x1)) → c57(SEL1(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(sel1(indx(z0, z1), x1)) → c57(SEL1(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(sel1(from(z0), x1)) → c57(SEL1(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(sel1(dbl1(z0), x1)) → c57(SEL1(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(sel1(01, x1)) → c57(SEL1(ok(01), proper(x1)), PROPER(01), PROPER(x1))
PROPER(sel1(s1(z0), x1)) → c57(SEL1(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(sel1(sel1(z0, z1), x1)) → c57(SEL1(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(sel1(quote(z0), x1)) → c57(SEL1(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
(84) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(dbl(0)) → mark(0)
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
active(dbls(nil)) → mark(nil)
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1)))
active(sel(0, cons(z0, z1))) → mark(z0)
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
active(indx(nil, z0)) → mark(nil)
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2)))
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(dbl1(0)) → mark(01)
active(dbl1(s(z0))) → mark(s1(s1(dbl1(z0))))
active(sel1(0, cons(z0, z1))) → mark(z0)
active(sel1(s(z0), cons(z1, z2))) → mark(sel1(z0, z2))
active(quote(0)) → mark(01)
active(quote(s(z0))) → mark(s1(quote(z0)))
active(quote(dbl(z0))) → mark(dbl1(z0))
active(quote(sel(z0, z1))) → mark(sel1(z0, z1))
active(dbl(z0)) → dbl(active(z0))
active(dbls(z0)) → dbls(active(z0))
active(sel(z0, z1)) → sel(active(z0), z1)
active(sel(z0, z1)) → sel(z0, active(z1))
active(indx(z0, z1)) → indx(active(z0), z1)
active(dbl1(z0)) → dbl1(active(z0))
active(s1(z0)) → s1(active(z0))
active(sel1(z0, z1)) → sel1(active(z0), z1)
active(sel1(z0, z1)) → sel1(z0, active(z1))
active(quote(z0)) → quote(active(z0))
s(ok(z0)) → ok(s(z0))
dbl(mark(z0)) → mark(dbl(z0))
dbl(ok(z0)) → ok(dbl(z0))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
dbls(mark(z0)) → mark(dbls(z0))
dbls(ok(z0)) → ok(dbls(z0))
sel(mark(z0), z1) → mark(sel(z0, z1))
sel(z0, mark(z1)) → mark(sel(z0, z1))
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
indx(mark(z0), z1) → mark(indx(z0, z1))
indx(ok(z0), ok(z1)) → ok(indx(z0, z1))
s1(mark(z0)) → mark(s1(z0))
s1(ok(z0)) → ok(s1(z0))
dbl1(mark(z0)) → mark(dbl1(z0))
dbl1(ok(z0)) → ok(dbl1(z0))
sel1(mark(z0), z1) → mark(sel1(z0, z1))
sel1(z0, mark(z1)) → mark(sel1(z0, z1))
sel1(ok(z0), ok(z1)) → ok(sel1(z0, z1))
quote(mark(z0)) → mark(quote(z0))
quote(ok(z0)) → ok(quote(z0))
proper(dbl(z0)) → dbl(proper(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(dbls(z0)) → dbls(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
proper(indx(z0, z1)) → indx(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(dbl1(z0)) → dbl1(proper(z0))
proper(01) → ok(01)
proper(s1(z0)) → s1(proper(z0))
proper(sel1(z0, z1)) → sel1(proper(z0), proper(z1))
proper(quote(z0)) → quote(proper(z0))
from(ok(z0)) → ok(from(z0))
Tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)))
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0))))))
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0))))))
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0)))
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(indx(sel1(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(indx(sel1(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel1(z0, z2)), x1), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(indx(quote(dbl(z0)), x1)) → c21(INDX(mark(dbl1(z0)), x1), ACTIVE(quote(dbl(z0))))
ACTIVE(indx(quote(sel(z0, z1)), x1)) → c21(INDX(mark(sel1(z0, z1)), x1), ACTIVE(quote(sel(z0, z1))))
ACTIVE(indx(dbl(z0), x1)) → c21(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
ACTIVE(indx(dbls(z0), x1)) → c21(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(indx(z0, z1), x1)) → c21(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1)))
ACTIVE(indx(dbl1(z0), x1)) → c21(INDX(dbl1(active(z0)), x1), ACTIVE(dbl1(z0)))
ACTIVE(indx(s1(z0), x1)) → c21(INDX(s1(active(z0)), x1), ACTIVE(s1(z0)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(active(z0), z1), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(z0, active(z1)), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(quote(z0), x1)) → c21(INDX(quote(active(z0)), x1), ACTIVE(quote(z0)))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)))
ACTIVE(indx(dbl(0), x1)) → c21(INDX(mark(0), x1))
ACTIVE(indx(dbls(nil), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(indx(indx(nil, z0), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0))))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1))
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0)))
ACTIVE(dbl1(sel(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl1(sel(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl1(sel1(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl1(sel1(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl1(quote(dbl(z0)))) → c22(DBL1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl1(quote(sel(z0, z1)))) → c22(DBL1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl1(dbl(z0))) → c22(DBL1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl1(dbls(z0))) → c22(DBL1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(indx(z0, z1))) → c22(DBL1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl1(dbl1(z0))) → c22(DBL1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl1(s1(z0))) → c22(DBL1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(quote(z0))) → c22(DBL1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(dbl1(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(dbl(0))) → c22(DBL1(mark(0)))
ACTIVE(dbl1(dbls(nil))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(indx(nil, z0))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(dbl1(0))) → c22(DBL1(mark(01)))
ACTIVE(dbl(dbl1(s(z0)))) → c4(DBL(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(DBLS(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(INDX(mark(s1(s1(dbl1(z0)))), x1))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(DBL1(mark(s(s(dbl(z0))))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(ACTIVE(dbl(s(z0))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(DBL1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(DBL1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl1(from(z0))) → c4(DBL1(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl1(from(z0))) → c4(ACTIVE(from(z0)))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(DBL1(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(s1(sel(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(s1(sel(s(z0), cons(z1, z2)))) → c23(S1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(s1(sel1(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(s1(sel1(s(z0), cons(z1, z2)))) → c23(S1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(s1(quote(dbl(z0)))) → c23(S1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(s1(quote(sel(z0, z1)))) → c23(S1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(s1(dbl(z0))) → c23(S1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(s1(dbls(z0))) → c23(S1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(s1(indx(z0, z1))) → c23(S1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(s1(dbl1(z0))) → c23(S1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(s1(s1(z0))) → c23(S1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(quote(z0))) → c23(S1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(s1(dbl(0))) → c23(S1(mark(0)))
ACTIVE(s1(dbls(nil))) → c23(S1(mark(nil)))
ACTIVE(s1(indx(nil, z0))) → c23(S1(mark(nil)))
ACTIVE(s1(dbl1(0))) → c23(S1(mark(01)))
ACTIVE(s1(dbl(s(z0)))) → c6(S1(mark(s(s(dbl(z0))))))
ACTIVE(s1(dbl(s(z0)))) → c6(ACTIVE(dbl(s(z0))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(S1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(S1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(s1(from(z0))) → c6(S1(mark(cons(z0, from(s(z0))))))
ACTIVE(s1(from(z0))) → c6(ACTIVE(from(z0)))
ACTIVE(s1(dbl1(s(z0)))) → c6(S1(mark(s1(s1(dbl1(z0))))))
ACTIVE(s1(dbl1(s(z0)))) → c6(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(sel(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(quote(sel(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(quote(sel1(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(quote(sel1(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(quote(quote(dbl(z0)))) → c26(QUOTE(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(quote(quote(sel(z0, z1)))) → c26(QUOTE(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(quote(dbl(z0))) → c26(QUOTE(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(quote(dbls(z0))) → c26(QUOTE(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(quote(indx(z0, z1))) → c26(QUOTE(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(quote(dbl1(z0))) → c26(QUOTE(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(quote(s1(z0))) → c26(QUOTE(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(quote(z0))) → c26(QUOTE(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(quote(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(quote(0))) → c22(DBL1(mark(01)))
ACTIVE(s1(quote(0))) → c23(S1(mark(01)))
ACTIVE(quote(dbl(0))) → c26(QUOTE(mark(0)))
ACTIVE(quote(dbls(nil))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(indx(nil, z0))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(dbl1(0))) → c26(QUOTE(mark(01)))
ACTIVE(quote(quote(0))) → c26(QUOTE(mark(01)))
ACTIVE(dbl(quote(s(z0)))) → c7(DBL(mark(s1(quote(z0)))))
ACTIVE(dbl(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(s(z0)))) → c7(DBLS(mark(s1(quote(z0)))))
ACTIVE(dbls(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(indx(quote(s(z0)), x1)) → c7(INDX(mark(s1(quote(z0))), x1))
ACTIVE(indx(quote(s(z0)), x1)) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbl1(quote(s(z0)))) → c7(DBL1(mark(s1(quote(z0)))))
ACTIVE(dbl1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(s1(quote(s(z0)))) → c7(S1(mark(s1(quote(z0)))))
ACTIVE(s1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(quote(dbl(s(z0)))) → c7(QUOTE(mark(s(s(dbl(z0))))))
ACTIVE(quote(dbl(s(z0)))) → c7(ACTIVE(dbl(s(z0))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(QUOTE(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(QUOTE(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(quote(from(z0))) → c7(QUOTE(mark(cons(z0, from(s(z0))))))
ACTIVE(quote(from(z0))) → c7(ACTIVE(from(z0)))
ACTIVE(quote(dbl1(s(z0)))) → c7(QUOTE(mark(s1(s1(dbl1(z0))))))
ACTIVE(quote(dbl1(s(z0)))) → c7(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(quote(s(z0)))) → c7(QUOTE(mark(s1(quote(z0)))))
ACTIVE(quote(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
PROPER(dbl(dbl(z0))) → c45(DBL(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbl(s(z0))) → c45(DBL(s(proper(z0))), PROPER(s(z0)))
PROPER(dbl(dbls(z0))) → c45(DBL(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbl(cons(z0, z1))) → c45(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbl(sel(z0, z1))) → c45(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbl(indx(z0, z1))) → c45(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbl(from(z0))) → c45(DBL(from(proper(z0))), PROPER(from(z0)))
PROPER(dbl(dbl1(z0))) → c45(DBL(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbl(s1(z0))) → c45(DBL(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbl(sel1(z0, z1))) → c45(DBL(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbl(quote(z0))) → c45(DBL(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbl(0)) → c45(DBL(ok(0)))
PROPER(dbl(nil)) → c45(DBL(ok(nil)))
PROPER(dbl(01)) → c45(DBL(ok(01)))
PROPER(s(dbl(z0))) → c47(S(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(s(s(z0))) → c47(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(dbls(z0))) → c47(S(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(s(cons(z0, z1))) → c47(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(sel(z0, z1))) → c47(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(s(indx(z0, z1))) → c47(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(s(from(z0))) → c47(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(dbl1(z0))) → c47(S(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(s(s1(z0))) → c47(S(s1(proper(z0))), PROPER(s1(z0)))
PROPER(s(sel1(z0, z1))) → c47(S(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(s(quote(z0))) → c47(S(quote(proper(z0))), PROPER(quote(z0)))
PROPER(s(0)) → c47(S(ok(0)))
PROPER(s(nil)) → c47(S(ok(nil)))
PROPER(s(01)) → c47(S(ok(01)))
PROPER(dbls(dbl(z0))) → c48(DBLS(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbls(s(z0))) → c48(DBLS(s(proper(z0))), PROPER(s(z0)))
PROPER(dbls(dbls(z0))) → c48(DBLS(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbls(cons(z0, z1))) → c48(DBLS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbls(sel(z0, z1))) → c48(DBLS(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbls(indx(z0, z1))) → c48(DBLS(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbls(from(z0))) → c48(DBLS(from(proper(z0))), PROPER(from(z0)))
PROPER(dbls(dbl1(z0))) → c48(DBLS(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbls(s1(z0))) → c48(DBLS(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbls(sel1(z0, z1))) → c48(DBLS(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbls(quote(z0))) → c48(DBLS(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbls(0)) → c48(DBLS(ok(0)))
PROPER(dbls(nil)) → c48(DBLS(ok(nil)))
PROPER(dbls(01)) → c48(DBLS(ok(01)))
PROPER(cons(x0, dbl(z0))) → c50(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(cons(x0, s(z0))) → c50(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, dbls(z0))) → c50(CONS(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(cons(x0, cons(z0, z1))) → c50(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, sel(z0, z1))) → c50(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(cons(x0, indx(z0, z1))) → c50(CONS(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(cons(x0, from(z0))) → c50(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, dbl1(z0))) → c50(CONS(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(cons(x0, s1(z0))) → c50(CONS(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(cons(x0, sel1(z0, z1))) → c50(CONS(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(cons(x0, quote(z0))) → c50(CONS(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(cons(dbl(z0), x1)) → c50(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(cons(s(z0), x1)) → c50(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(dbls(z0), x1)) → c50(CONS(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c50(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(sel(z0, z1), x1)) → c50(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(cons(indx(z0, z1), x1)) → c50(CONS(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c50(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(dbl1(z0), x1)) → c50(CONS(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(cons(s1(z0), x1)) → c50(CONS(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(cons(sel1(z0, z1), x1)) → c50(CONS(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(cons(quote(z0), x1)) → c50(CONS(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c50(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c50(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, 01)) → c50(CONS(proper(x0), ok(01)), PROPER(x0))
PROPER(cons(0, x1)) → c50(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c50(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(01, x1)) → c50(CONS(ok(01), proper(x1)), PROPER(x1))
PROPER(sel(x0, dbl(z0))) → c51(SEL(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(sel(x0, s(z0))) → c51(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(sel(x0, dbls(z0))) → c51(SEL(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(sel(x0, cons(z0, z1))) → c51(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(sel(x0, sel(z0, z1))) → c51(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(sel(x0, indx(z0, z1))) → c51(SEL(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(sel(x0, from(z0))) → c51(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(sel(x0, dbl1(z0))) → c51(SEL(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(sel(x0, s1(z0))) → c51(SEL(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(sel(x0, sel1(z0, z1))) → c51(SEL(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(sel(x0, quote(z0))) → c51(SEL(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(sel(dbl(z0), x1)) → c51(SEL(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(sel(s(z0), x1)) → c51(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(sel(dbls(z0), x1)) → c51(SEL(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(sel(cons(z0, z1), x1)) → c51(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(sel(sel(z0, z1), x1)) → c51(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(sel(indx(z0, z1), x1)) → c51(SEL(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(sel(from(z0), x1)) → c51(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(sel(dbl1(z0), x1)) → c51(SEL(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(sel(s1(z0), x1)) → c51(SEL(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(sel(sel1(z0, z1), x1)) → c51(SEL(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(sel(quote(z0), x1)) → c51(SEL(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(sel(x0, 0)) → c51(SEL(proper(x0), ok(0)), PROPER(x0))
PROPER(sel(x0, nil)) → c51(SEL(proper(x0), ok(nil)), PROPER(x0))
PROPER(sel(x0, 01)) → c51(SEL(proper(x0), ok(01)), PROPER(x0))
PROPER(sel(0, x1)) → c51(SEL(ok(0), proper(x1)), PROPER(x1))
PROPER(sel(nil, x1)) → c51(SEL(ok(nil), proper(x1)), PROPER(x1))
PROPER(sel(01, x1)) → c51(SEL(ok(01), proper(x1)), PROPER(x1))
PROPER(indx(x0, dbl(z0))) → c52(INDX(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(indx(x0, s(z0))) → c52(INDX(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(indx(x0, dbls(z0))) → c52(INDX(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(indx(x0, cons(z0, z1))) → c52(INDX(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(indx(x0, sel(z0, z1))) → c52(INDX(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(indx(x0, indx(z0, z1))) → c52(INDX(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(indx(x0, from(z0))) → c52(INDX(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(indx(x0, dbl1(z0))) → c52(INDX(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(indx(x0, s1(z0))) → c52(INDX(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(indx(x0, sel1(z0, z1))) → c52(INDX(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(indx(x0, quote(z0))) → c52(INDX(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(indx(dbl(z0), x1)) → c52(INDX(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(indx(s(z0), x1)) → c52(INDX(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(indx(dbls(z0), x1)) → c52(INDX(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(indx(cons(z0, z1), x1)) → c52(INDX(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(indx(sel(z0, z1), x1)) → c52(INDX(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(indx(indx(z0, z1), x1)) → c52(INDX(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(indx(from(z0), x1)) → c52(INDX(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(indx(dbl1(z0), x1)) → c52(INDX(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(indx(s1(z0), x1)) → c52(INDX(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(indx(sel1(z0, z1), x1)) → c52(INDX(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(indx(quote(z0), x1)) → c52(INDX(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(indx(x0, 0)) → c52(INDX(proper(x0), ok(0)), PROPER(x0))
PROPER(indx(x0, nil)) → c52(INDX(proper(x0), ok(nil)), PROPER(x0))
PROPER(indx(x0, 01)) → c52(INDX(proper(x0), ok(01)), PROPER(x0))
PROPER(indx(0, x1)) → c52(INDX(ok(0), proper(x1)), PROPER(x1))
PROPER(indx(nil, x1)) → c52(INDX(ok(nil), proper(x1)), PROPER(x1))
PROPER(indx(01, x1)) → c52(INDX(ok(01), proper(x1)), PROPER(x1))
PROPER(from(dbl(z0))) → c53(FROM(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(from(s(z0))) → c53(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(dbls(z0))) → c53(FROM(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(from(cons(z0, z1))) → c53(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(sel(z0, z1))) → c53(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(from(indx(z0, z1))) → c53(FROM(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(from(from(z0))) → c53(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(dbl1(z0))) → c53(FROM(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(from(s1(z0))) → c53(FROM(s1(proper(z0))), PROPER(s1(z0)))
PROPER(from(sel1(z0, z1))) → c53(FROM(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(from(quote(z0))) → c53(FROM(quote(proper(z0))), PROPER(quote(z0)))
PROPER(from(0)) → c53(FROM(ok(0)))
PROPER(from(nil)) → c53(FROM(ok(nil)))
PROPER(from(01)) → c53(FROM(ok(01)))
PROPER(dbl1(dbl(z0))) → c54(DBL1(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbl1(s(z0))) → c54(DBL1(s(proper(z0))), PROPER(s(z0)))
PROPER(dbl1(dbls(z0))) → c54(DBL1(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbl1(cons(z0, z1))) → c54(DBL1(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbl1(sel(z0, z1))) → c54(DBL1(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbl1(indx(z0, z1))) → c54(DBL1(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbl1(from(z0))) → c54(DBL1(from(proper(z0))), PROPER(from(z0)))
PROPER(dbl1(dbl1(z0))) → c54(DBL1(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbl1(s1(z0))) → c54(DBL1(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbl1(sel1(z0, z1))) → c54(DBL1(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbl1(quote(z0))) → c54(DBL1(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbl1(0)) → c54(DBL1(ok(0)))
PROPER(dbl1(nil)) → c54(DBL1(ok(nil)))
PROPER(dbl1(01)) → c54(DBL1(ok(01)))
PROPER(s1(dbl(z0))) → c56(S1(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(s1(s(z0))) → c56(S1(s(proper(z0))), PROPER(s(z0)))
PROPER(s1(dbls(z0))) → c56(S1(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(s1(cons(z0, z1))) → c56(S1(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s1(sel(z0, z1))) → c56(S1(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(s1(indx(z0, z1))) → c56(S1(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(s1(from(z0))) → c56(S1(from(proper(z0))), PROPER(from(z0)))
PROPER(s1(dbl1(z0))) → c56(S1(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(s1(s1(z0))) → c56(S1(s1(proper(z0))), PROPER(s1(z0)))
PROPER(s1(sel1(z0, z1))) → c56(S1(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(s1(quote(z0))) → c56(S1(quote(proper(z0))), PROPER(quote(z0)))
PROPER(s1(0)) → c56(S1(ok(0)))
PROPER(s1(nil)) → c56(S1(ok(nil)))
PROPER(s1(01)) → c56(S1(ok(01)))
PROPER(sel1(x0, dbl(z0))) → c57(SEL1(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(sel1(x0, 0)) → c57(SEL1(proper(x0), ok(0)), PROPER(x0), PROPER(0))
PROPER(sel1(x0, s(z0))) → c57(SEL1(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(sel1(x0, dbls(z0))) → c57(SEL1(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(sel1(x0, nil)) → c57(SEL1(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
PROPER(sel1(x0, cons(z0, z1))) → c57(SEL1(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(sel1(x0, sel(z0, z1))) → c57(SEL1(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(sel1(x0, indx(z0, z1))) → c57(SEL1(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(sel1(x0, from(z0))) → c57(SEL1(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(sel1(x0, dbl1(z0))) → c57(SEL1(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(sel1(x0, 01)) → c57(SEL1(proper(x0), ok(01)), PROPER(x0), PROPER(01))
PROPER(sel1(x0, s1(z0))) → c57(SEL1(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(sel1(x0, sel1(z0, z1))) → c57(SEL1(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(sel1(x0, quote(z0))) → c57(SEL1(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(sel1(dbl(z0), x1)) → c57(SEL1(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(sel1(0, x1)) → c57(SEL1(ok(0), proper(x1)), PROPER(0), PROPER(x1))
PROPER(sel1(s(z0), x1)) → c57(SEL1(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(sel1(dbls(z0), x1)) → c57(SEL1(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(sel1(nil, x1)) → c57(SEL1(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
PROPER(sel1(cons(z0, z1), x1)) → c57(SEL1(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(sel1(sel(z0, z1), x1)) → c57(SEL1(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(sel1(indx(z0, z1), x1)) → c57(SEL1(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(sel1(from(z0), x1)) → c57(SEL1(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(sel1(dbl1(z0), x1)) → c57(SEL1(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(sel1(01, x1)) → c57(SEL1(ok(01), proper(x1)), PROPER(01), PROPER(x1))
PROPER(sel1(s1(z0), x1)) → c57(SEL1(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(sel1(sel1(z0, z1), x1)) → c57(SEL1(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(sel1(quote(z0), x1)) → c57(SEL1(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
S tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)))
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0))))))
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0))))))
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0)))
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(indx(sel1(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(indx(sel1(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel1(z0, z2)), x1), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(indx(quote(dbl(z0)), x1)) → c21(INDX(mark(dbl1(z0)), x1), ACTIVE(quote(dbl(z0))))
ACTIVE(indx(quote(sel(z0, z1)), x1)) → c21(INDX(mark(sel1(z0, z1)), x1), ACTIVE(quote(sel(z0, z1))))
ACTIVE(indx(dbl(z0), x1)) → c21(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
ACTIVE(indx(dbls(z0), x1)) → c21(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(indx(z0, z1), x1)) → c21(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1)))
ACTIVE(indx(dbl1(z0), x1)) → c21(INDX(dbl1(active(z0)), x1), ACTIVE(dbl1(z0)))
ACTIVE(indx(s1(z0), x1)) → c21(INDX(s1(active(z0)), x1), ACTIVE(s1(z0)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(active(z0), z1), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(z0, active(z1)), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(quote(z0), x1)) → c21(INDX(quote(active(z0)), x1), ACTIVE(quote(z0)))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)))
ACTIVE(indx(dbl(0), x1)) → c21(INDX(mark(0), x1))
ACTIVE(indx(dbls(nil), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(indx(indx(nil, z0), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0))))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1))
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0)))
ACTIVE(dbl1(sel(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl1(sel(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl1(sel1(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl1(sel1(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl1(quote(dbl(z0)))) → c22(DBL1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl1(quote(sel(z0, z1)))) → c22(DBL1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl1(dbl(z0))) → c22(DBL1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl1(dbls(z0))) → c22(DBL1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(indx(z0, z1))) → c22(DBL1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl1(dbl1(z0))) → c22(DBL1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl1(s1(z0))) → c22(DBL1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(quote(z0))) → c22(DBL1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(dbl1(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(dbl(0))) → c22(DBL1(mark(0)))
ACTIVE(dbl1(dbls(nil))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(indx(nil, z0))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(dbl1(0))) → c22(DBL1(mark(01)))
ACTIVE(dbl(dbl1(s(z0)))) → c4(DBL(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(DBLS(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(INDX(mark(s1(s1(dbl1(z0)))), x1))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(DBL1(mark(s(s(dbl(z0))))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(ACTIVE(dbl(s(z0))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(DBL1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(DBL1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl1(from(z0))) → c4(DBL1(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl1(from(z0))) → c4(ACTIVE(from(z0)))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(DBL1(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(s1(sel(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(s1(sel(s(z0), cons(z1, z2)))) → c23(S1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(s1(sel1(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(s1(sel1(s(z0), cons(z1, z2)))) → c23(S1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(s1(quote(dbl(z0)))) → c23(S1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(s1(quote(sel(z0, z1)))) → c23(S1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(s1(dbl(z0))) → c23(S1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(s1(dbls(z0))) → c23(S1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(s1(indx(z0, z1))) → c23(S1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(s1(dbl1(z0))) → c23(S1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(s1(s1(z0))) → c23(S1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(quote(z0))) → c23(S1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(s1(dbl(0))) → c23(S1(mark(0)))
ACTIVE(s1(dbls(nil))) → c23(S1(mark(nil)))
ACTIVE(s1(indx(nil, z0))) → c23(S1(mark(nil)))
ACTIVE(s1(dbl1(0))) → c23(S1(mark(01)))
ACTIVE(s1(dbl(s(z0)))) → c6(S1(mark(s(s(dbl(z0))))))
ACTIVE(s1(dbl(s(z0)))) → c6(ACTIVE(dbl(s(z0))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(S1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(S1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(s1(from(z0))) → c6(S1(mark(cons(z0, from(s(z0))))))
ACTIVE(s1(from(z0))) → c6(ACTIVE(from(z0)))
ACTIVE(s1(dbl1(s(z0)))) → c6(S1(mark(s1(s1(dbl1(z0))))))
ACTIVE(s1(dbl1(s(z0)))) → c6(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(sel(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(quote(sel(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(quote(sel1(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(quote(sel1(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(quote(quote(dbl(z0)))) → c26(QUOTE(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(quote(quote(sel(z0, z1)))) → c26(QUOTE(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(quote(dbl(z0))) → c26(QUOTE(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(quote(dbls(z0))) → c26(QUOTE(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(quote(indx(z0, z1))) → c26(QUOTE(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(quote(dbl1(z0))) → c26(QUOTE(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(quote(s1(z0))) → c26(QUOTE(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(quote(z0))) → c26(QUOTE(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(quote(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(quote(0))) → c22(DBL1(mark(01)))
ACTIVE(s1(quote(0))) → c23(S1(mark(01)))
ACTIVE(quote(dbl(0))) → c26(QUOTE(mark(0)))
ACTIVE(quote(dbls(nil))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(indx(nil, z0))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(dbl1(0))) → c26(QUOTE(mark(01)))
ACTIVE(quote(quote(0))) → c26(QUOTE(mark(01)))
ACTIVE(dbl(quote(s(z0)))) → c7(DBL(mark(s1(quote(z0)))))
ACTIVE(dbl(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(s(z0)))) → c7(DBLS(mark(s1(quote(z0)))))
ACTIVE(dbls(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(indx(quote(s(z0)), x1)) → c7(INDX(mark(s1(quote(z0))), x1))
ACTIVE(indx(quote(s(z0)), x1)) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbl1(quote(s(z0)))) → c7(DBL1(mark(s1(quote(z0)))))
ACTIVE(dbl1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(s1(quote(s(z0)))) → c7(S1(mark(s1(quote(z0)))))
ACTIVE(s1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(quote(dbl(s(z0)))) → c7(QUOTE(mark(s(s(dbl(z0))))))
ACTIVE(quote(dbl(s(z0)))) → c7(ACTIVE(dbl(s(z0))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(QUOTE(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(QUOTE(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(quote(from(z0))) → c7(QUOTE(mark(cons(z0, from(s(z0))))))
ACTIVE(quote(from(z0))) → c7(ACTIVE(from(z0)))
ACTIVE(quote(dbl1(s(z0)))) → c7(QUOTE(mark(s1(s1(dbl1(z0))))))
ACTIVE(quote(dbl1(s(z0)))) → c7(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(quote(s(z0)))) → c7(QUOTE(mark(s1(quote(z0)))))
ACTIVE(quote(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
PROPER(dbl(dbl(z0))) → c45(DBL(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbl(s(z0))) → c45(DBL(s(proper(z0))), PROPER(s(z0)))
PROPER(dbl(dbls(z0))) → c45(DBL(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbl(cons(z0, z1))) → c45(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbl(sel(z0, z1))) → c45(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbl(indx(z0, z1))) → c45(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbl(from(z0))) → c45(DBL(from(proper(z0))), PROPER(from(z0)))
PROPER(dbl(dbl1(z0))) → c45(DBL(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbl(s1(z0))) → c45(DBL(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbl(sel1(z0, z1))) → c45(DBL(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbl(quote(z0))) → c45(DBL(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbl(0)) → c45(DBL(ok(0)))
PROPER(dbl(nil)) → c45(DBL(ok(nil)))
PROPER(dbl(01)) → c45(DBL(ok(01)))
PROPER(s(dbl(z0))) → c47(S(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(s(s(z0))) → c47(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(dbls(z0))) → c47(S(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(s(cons(z0, z1))) → c47(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(sel(z0, z1))) → c47(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(s(indx(z0, z1))) → c47(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(s(from(z0))) → c47(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(dbl1(z0))) → c47(S(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(s(s1(z0))) → c47(S(s1(proper(z0))), PROPER(s1(z0)))
PROPER(s(sel1(z0, z1))) → c47(S(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(s(quote(z0))) → c47(S(quote(proper(z0))), PROPER(quote(z0)))
PROPER(s(0)) → c47(S(ok(0)))
PROPER(s(nil)) → c47(S(ok(nil)))
PROPER(s(01)) → c47(S(ok(01)))
PROPER(dbls(dbl(z0))) → c48(DBLS(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbls(s(z0))) → c48(DBLS(s(proper(z0))), PROPER(s(z0)))
PROPER(dbls(dbls(z0))) → c48(DBLS(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbls(cons(z0, z1))) → c48(DBLS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbls(sel(z0, z1))) → c48(DBLS(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbls(indx(z0, z1))) → c48(DBLS(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbls(from(z0))) → c48(DBLS(from(proper(z0))), PROPER(from(z0)))
PROPER(dbls(dbl1(z0))) → c48(DBLS(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbls(s1(z0))) → c48(DBLS(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbls(sel1(z0, z1))) → c48(DBLS(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbls(quote(z0))) → c48(DBLS(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbls(0)) → c48(DBLS(ok(0)))
PROPER(dbls(nil)) → c48(DBLS(ok(nil)))
PROPER(dbls(01)) → c48(DBLS(ok(01)))
PROPER(cons(x0, dbl(z0))) → c50(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(cons(x0, s(z0))) → c50(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, dbls(z0))) → c50(CONS(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(cons(x0, cons(z0, z1))) → c50(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, sel(z0, z1))) → c50(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(cons(x0, indx(z0, z1))) → c50(CONS(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(cons(x0, from(z0))) → c50(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, dbl1(z0))) → c50(CONS(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(cons(x0, s1(z0))) → c50(CONS(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(cons(x0, sel1(z0, z1))) → c50(CONS(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(cons(x0, quote(z0))) → c50(CONS(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(cons(dbl(z0), x1)) → c50(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(cons(s(z0), x1)) → c50(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(dbls(z0), x1)) → c50(CONS(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c50(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(sel(z0, z1), x1)) → c50(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(cons(indx(z0, z1), x1)) → c50(CONS(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c50(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(dbl1(z0), x1)) → c50(CONS(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(cons(s1(z0), x1)) → c50(CONS(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(cons(sel1(z0, z1), x1)) → c50(CONS(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(cons(quote(z0), x1)) → c50(CONS(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c50(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c50(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, 01)) → c50(CONS(proper(x0), ok(01)), PROPER(x0))
PROPER(cons(0, x1)) → c50(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c50(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(01, x1)) → c50(CONS(ok(01), proper(x1)), PROPER(x1))
PROPER(sel(x0, dbl(z0))) → c51(SEL(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(sel(x0, s(z0))) → c51(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(sel(x0, dbls(z0))) → c51(SEL(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(sel(x0, cons(z0, z1))) → c51(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(sel(x0, sel(z0, z1))) → c51(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(sel(x0, indx(z0, z1))) → c51(SEL(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(sel(x0, from(z0))) → c51(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(sel(x0, dbl1(z0))) → c51(SEL(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(sel(x0, s1(z0))) → c51(SEL(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(sel(x0, sel1(z0, z1))) → c51(SEL(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(sel(x0, quote(z0))) → c51(SEL(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(sel(dbl(z0), x1)) → c51(SEL(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(sel(s(z0), x1)) → c51(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(sel(dbls(z0), x1)) → c51(SEL(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(sel(cons(z0, z1), x1)) → c51(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(sel(sel(z0, z1), x1)) → c51(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(sel(indx(z0, z1), x1)) → c51(SEL(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(sel(from(z0), x1)) → c51(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(sel(dbl1(z0), x1)) → c51(SEL(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(sel(s1(z0), x1)) → c51(SEL(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(sel(sel1(z0, z1), x1)) → c51(SEL(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(sel(quote(z0), x1)) → c51(SEL(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(sel(x0, 0)) → c51(SEL(proper(x0), ok(0)), PROPER(x0))
PROPER(sel(x0, nil)) → c51(SEL(proper(x0), ok(nil)), PROPER(x0))
PROPER(sel(x0, 01)) → c51(SEL(proper(x0), ok(01)), PROPER(x0))
PROPER(sel(0, x1)) → c51(SEL(ok(0), proper(x1)), PROPER(x1))
PROPER(sel(nil, x1)) → c51(SEL(ok(nil), proper(x1)), PROPER(x1))
PROPER(sel(01, x1)) → c51(SEL(ok(01), proper(x1)), PROPER(x1))
PROPER(indx(x0, dbl(z0))) → c52(INDX(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(indx(x0, s(z0))) → c52(INDX(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(indx(x0, dbls(z0))) → c52(INDX(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(indx(x0, cons(z0, z1))) → c52(INDX(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(indx(x0, sel(z0, z1))) → c52(INDX(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(indx(x0, indx(z0, z1))) → c52(INDX(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(indx(x0, from(z0))) → c52(INDX(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(indx(x0, dbl1(z0))) → c52(INDX(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(indx(x0, s1(z0))) → c52(INDX(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(indx(x0, sel1(z0, z1))) → c52(INDX(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(indx(x0, quote(z0))) → c52(INDX(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(indx(dbl(z0), x1)) → c52(INDX(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(indx(s(z0), x1)) → c52(INDX(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(indx(dbls(z0), x1)) → c52(INDX(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(indx(cons(z0, z1), x1)) → c52(INDX(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(indx(sel(z0, z1), x1)) → c52(INDX(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(indx(indx(z0, z1), x1)) → c52(INDX(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(indx(from(z0), x1)) → c52(INDX(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(indx(dbl1(z0), x1)) → c52(INDX(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(indx(s1(z0), x1)) → c52(INDX(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(indx(sel1(z0, z1), x1)) → c52(INDX(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(indx(quote(z0), x1)) → c52(INDX(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(indx(x0, 0)) → c52(INDX(proper(x0), ok(0)), PROPER(x0))
PROPER(indx(x0, nil)) → c52(INDX(proper(x0), ok(nil)), PROPER(x0))
PROPER(indx(x0, 01)) → c52(INDX(proper(x0), ok(01)), PROPER(x0))
PROPER(indx(0, x1)) → c52(INDX(ok(0), proper(x1)), PROPER(x1))
PROPER(indx(nil, x1)) → c52(INDX(ok(nil), proper(x1)), PROPER(x1))
PROPER(indx(01, x1)) → c52(INDX(ok(01), proper(x1)), PROPER(x1))
PROPER(from(dbl(z0))) → c53(FROM(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(from(s(z0))) → c53(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(dbls(z0))) → c53(FROM(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(from(cons(z0, z1))) → c53(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(sel(z0, z1))) → c53(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(from(indx(z0, z1))) → c53(FROM(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(from(from(z0))) → c53(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(dbl1(z0))) → c53(FROM(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(from(s1(z0))) → c53(FROM(s1(proper(z0))), PROPER(s1(z0)))
PROPER(from(sel1(z0, z1))) → c53(FROM(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(from(quote(z0))) → c53(FROM(quote(proper(z0))), PROPER(quote(z0)))
PROPER(from(0)) → c53(FROM(ok(0)))
PROPER(from(nil)) → c53(FROM(ok(nil)))
PROPER(from(01)) → c53(FROM(ok(01)))
PROPER(dbl1(dbl(z0))) → c54(DBL1(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbl1(s(z0))) → c54(DBL1(s(proper(z0))), PROPER(s(z0)))
PROPER(dbl1(dbls(z0))) → c54(DBL1(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbl1(cons(z0, z1))) → c54(DBL1(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbl1(sel(z0, z1))) → c54(DBL1(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbl1(indx(z0, z1))) → c54(DBL1(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbl1(from(z0))) → c54(DBL1(from(proper(z0))), PROPER(from(z0)))
PROPER(dbl1(dbl1(z0))) → c54(DBL1(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbl1(s1(z0))) → c54(DBL1(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbl1(sel1(z0, z1))) → c54(DBL1(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbl1(quote(z0))) → c54(DBL1(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbl1(0)) → c54(DBL1(ok(0)))
PROPER(dbl1(nil)) → c54(DBL1(ok(nil)))
PROPER(dbl1(01)) → c54(DBL1(ok(01)))
PROPER(s1(dbl(z0))) → c56(S1(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(s1(s(z0))) → c56(S1(s(proper(z0))), PROPER(s(z0)))
PROPER(s1(dbls(z0))) → c56(S1(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(s1(cons(z0, z1))) → c56(S1(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s1(sel(z0, z1))) → c56(S1(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(s1(indx(z0, z1))) → c56(S1(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(s1(from(z0))) → c56(S1(from(proper(z0))), PROPER(from(z0)))
PROPER(s1(dbl1(z0))) → c56(S1(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(s1(s1(z0))) → c56(S1(s1(proper(z0))), PROPER(s1(z0)))
PROPER(s1(sel1(z0, z1))) → c56(S1(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(s1(quote(z0))) → c56(S1(quote(proper(z0))), PROPER(quote(z0)))
PROPER(s1(0)) → c56(S1(ok(0)))
PROPER(s1(nil)) → c56(S1(ok(nil)))
PROPER(s1(01)) → c56(S1(ok(01)))
PROPER(sel1(x0, dbl(z0))) → c57(SEL1(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(sel1(x0, 0)) → c57(SEL1(proper(x0), ok(0)), PROPER(x0), PROPER(0))
PROPER(sel1(x0, s(z0))) → c57(SEL1(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(sel1(x0, dbls(z0))) → c57(SEL1(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(sel1(x0, nil)) → c57(SEL1(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
PROPER(sel1(x0, cons(z0, z1))) → c57(SEL1(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(sel1(x0, sel(z0, z1))) → c57(SEL1(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(sel1(x0, indx(z0, z1))) → c57(SEL1(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(sel1(x0, from(z0))) → c57(SEL1(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(sel1(x0, dbl1(z0))) → c57(SEL1(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(sel1(x0, 01)) → c57(SEL1(proper(x0), ok(01)), PROPER(x0), PROPER(01))
PROPER(sel1(x0, s1(z0))) → c57(SEL1(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(sel1(x0, sel1(z0, z1))) → c57(SEL1(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(sel1(x0, quote(z0))) → c57(SEL1(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(sel1(dbl(z0), x1)) → c57(SEL1(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(sel1(0, x1)) → c57(SEL1(ok(0), proper(x1)), PROPER(0), PROPER(x1))
PROPER(sel1(s(z0), x1)) → c57(SEL1(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(sel1(dbls(z0), x1)) → c57(SEL1(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(sel1(nil, x1)) → c57(SEL1(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
PROPER(sel1(cons(z0, z1), x1)) → c57(SEL1(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(sel1(sel(z0, z1), x1)) → c57(SEL1(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(sel1(indx(z0, z1), x1)) → c57(SEL1(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(sel1(from(z0), x1)) → c57(SEL1(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(sel1(dbl1(z0), x1)) → c57(SEL1(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(sel1(01, x1)) → c57(SEL1(ok(01), proper(x1)), PROPER(01), PROPER(x1))
PROPER(sel1(s1(z0), x1)) → c57(SEL1(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(sel1(sel1(z0, z1), x1)) → c57(SEL1(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(sel1(quote(z0), x1)) → c57(SEL1(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
K tuples:none
Defined Rule Symbols:
active, s, dbl, cons, dbls, sel, indx, s1, dbl1, sel1, quote, proper, from
Defined Pair Symbols:
ACTIVE, DBL, DBLS, SEL, INDX, DBL1, S1, SEL1, QUOTE, PROPER, S, CONS, FROM, TOP
Compound Symbols:
c5, c12, c15, c16, c19, c20, c24, c25, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c58, c59, c60, c61, c62, c63, c8, c, c17, c17, c1, c18, c18, c2, c21, c21, c3, c22, c22, c4, c23, c23, c6, c26, c26, c7, c45, c45, c47, c47, c48, c48, c50, c50, c51, c51, c52, c52, c53, c53, c54, c54, c56, c56, c57
(85) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 6 trailing tuple parts
(86) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(dbl(0)) → mark(0)
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
active(dbls(nil)) → mark(nil)
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1)))
active(sel(0, cons(z0, z1))) → mark(z0)
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
active(indx(nil, z0)) → mark(nil)
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2)))
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(dbl1(0)) → mark(01)
active(dbl1(s(z0))) → mark(s1(s1(dbl1(z0))))
active(sel1(0, cons(z0, z1))) → mark(z0)
active(sel1(s(z0), cons(z1, z2))) → mark(sel1(z0, z2))
active(quote(0)) → mark(01)
active(quote(s(z0))) → mark(s1(quote(z0)))
active(quote(dbl(z0))) → mark(dbl1(z0))
active(quote(sel(z0, z1))) → mark(sel1(z0, z1))
active(dbl(z0)) → dbl(active(z0))
active(dbls(z0)) → dbls(active(z0))
active(sel(z0, z1)) → sel(active(z0), z1)
active(sel(z0, z1)) → sel(z0, active(z1))
active(indx(z0, z1)) → indx(active(z0), z1)
active(dbl1(z0)) → dbl1(active(z0))
active(s1(z0)) → s1(active(z0))
active(sel1(z0, z1)) → sel1(active(z0), z1)
active(sel1(z0, z1)) → sel1(z0, active(z1))
active(quote(z0)) → quote(active(z0))
s(ok(z0)) → ok(s(z0))
dbl(mark(z0)) → mark(dbl(z0))
dbl(ok(z0)) → ok(dbl(z0))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
dbls(mark(z0)) → mark(dbls(z0))
dbls(ok(z0)) → ok(dbls(z0))
sel(mark(z0), z1) → mark(sel(z0, z1))
sel(z0, mark(z1)) → mark(sel(z0, z1))
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
indx(mark(z0), z1) → mark(indx(z0, z1))
indx(ok(z0), ok(z1)) → ok(indx(z0, z1))
s1(mark(z0)) → mark(s1(z0))
s1(ok(z0)) → ok(s1(z0))
dbl1(mark(z0)) → mark(dbl1(z0))
dbl1(ok(z0)) → ok(dbl1(z0))
sel1(mark(z0), z1) → mark(sel1(z0, z1))
sel1(z0, mark(z1)) → mark(sel1(z0, z1))
sel1(ok(z0), ok(z1)) → ok(sel1(z0, z1))
quote(mark(z0)) → mark(quote(z0))
quote(ok(z0)) → ok(quote(z0))
proper(dbl(z0)) → dbl(proper(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(dbls(z0)) → dbls(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
proper(indx(z0, z1)) → indx(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(dbl1(z0)) → dbl1(proper(z0))
proper(01) → ok(01)
proper(s1(z0)) → s1(proper(z0))
proper(sel1(z0, z1)) → sel1(proper(z0), proper(z1))
proper(quote(z0)) → quote(proper(z0))
from(ok(z0)) → ok(from(z0))
Tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)))
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0))))))
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0))))))
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0)))
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(indx(sel1(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(indx(sel1(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel1(z0, z2)), x1), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(indx(quote(dbl(z0)), x1)) → c21(INDX(mark(dbl1(z0)), x1), ACTIVE(quote(dbl(z0))))
ACTIVE(indx(quote(sel(z0, z1)), x1)) → c21(INDX(mark(sel1(z0, z1)), x1), ACTIVE(quote(sel(z0, z1))))
ACTIVE(indx(dbl(z0), x1)) → c21(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
ACTIVE(indx(dbls(z0), x1)) → c21(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(indx(z0, z1), x1)) → c21(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1)))
ACTIVE(indx(dbl1(z0), x1)) → c21(INDX(dbl1(active(z0)), x1), ACTIVE(dbl1(z0)))
ACTIVE(indx(s1(z0), x1)) → c21(INDX(s1(active(z0)), x1), ACTIVE(s1(z0)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(active(z0), z1), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(z0, active(z1)), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(quote(z0), x1)) → c21(INDX(quote(active(z0)), x1), ACTIVE(quote(z0)))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)))
ACTIVE(indx(dbl(0), x1)) → c21(INDX(mark(0), x1))
ACTIVE(indx(dbls(nil), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(indx(indx(nil, z0), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0))))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1))
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0)))
ACTIVE(dbl1(sel(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl1(sel(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl1(sel1(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl1(sel1(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl1(quote(dbl(z0)))) → c22(DBL1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl1(quote(sel(z0, z1)))) → c22(DBL1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl1(dbl(z0))) → c22(DBL1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl1(dbls(z0))) → c22(DBL1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(indx(z0, z1))) → c22(DBL1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl1(dbl1(z0))) → c22(DBL1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl1(s1(z0))) → c22(DBL1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(quote(z0))) → c22(DBL1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(dbl1(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(dbl(0))) → c22(DBL1(mark(0)))
ACTIVE(dbl1(dbls(nil))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(indx(nil, z0))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(dbl1(0))) → c22(DBL1(mark(01)))
ACTIVE(dbl(dbl1(s(z0)))) → c4(DBL(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(DBLS(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(INDX(mark(s1(s1(dbl1(z0)))), x1))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(DBL1(mark(s(s(dbl(z0))))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(ACTIVE(dbl(s(z0))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(DBL1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(DBL1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl1(from(z0))) → c4(DBL1(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl1(from(z0))) → c4(ACTIVE(from(z0)))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(DBL1(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(s1(sel(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(s1(sel(s(z0), cons(z1, z2)))) → c23(S1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(s1(sel1(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(s1(sel1(s(z0), cons(z1, z2)))) → c23(S1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(s1(quote(dbl(z0)))) → c23(S1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(s1(quote(sel(z0, z1)))) → c23(S1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(s1(dbl(z0))) → c23(S1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(s1(dbls(z0))) → c23(S1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(s1(indx(z0, z1))) → c23(S1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(s1(dbl1(z0))) → c23(S1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(s1(s1(z0))) → c23(S1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(quote(z0))) → c23(S1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(s1(dbl(0))) → c23(S1(mark(0)))
ACTIVE(s1(dbls(nil))) → c23(S1(mark(nil)))
ACTIVE(s1(indx(nil, z0))) → c23(S1(mark(nil)))
ACTIVE(s1(dbl1(0))) → c23(S1(mark(01)))
ACTIVE(s1(dbl(s(z0)))) → c6(S1(mark(s(s(dbl(z0))))))
ACTIVE(s1(dbl(s(z0)))) → c6(ACTIVE(dbl(s(z0))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(S1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(S1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(s1(from(z0))) → c6(S1(mark(cons(z0, from(s(z0))))))
ACTIVE(s1(from(z0))) → c6(ACTIVE(from(z0)))
ACTIVE(s1(dbl1(s(z0)))) → c6(S1(mark(s1(s1(dbl1(z0))))))
ACTIVE(s1(dbl1(s(z0)))) → c6(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(sel(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(quote(sel(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(quote(sel1(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(quote(sel1(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(quote(quote(dbl(z0)))) → c26(QUOTE(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(quote(quote(sel(z0, z1)))) → c26(QUOTE(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(quote(dbl(z0))) → c26(QUOTE(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(quote(dbls(z0))) → c26(QUOTE(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(quote(indx(z0, z1))) → c26(QUOTE(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(quote(dbl1(z0))) → c26(QUOTE(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(quote(s1(z0))) → c26(QUOTE(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(quote(z0))) → c26(QUOTE(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(quote(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(quote(0))) → c22(DBL1(mark(01)))
ACTIVE(s1(quote(0))) → c23(S1(mark(01)))
ACTIVE(quote(dbl(0))) → c26(QUOTE(mark(0)))
ACTIVE(quote(dbls(nil))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(indx(nil, z0))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(dbl1(0))) → c26(QUOTE(mark(01)))
ACTIVE(quote(quote(0))) → c26(QUOTE(mark(01)))
ACTIVE(dbl(quote(s(z0)))) → c7(DBL(mark(s1(quote(z0)))))
ACTIVE(dbl(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(s(z0)))) → c7(DBLS(mark(s1(quote(z0)))))
ACTIVE(dbls(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(indx(quote(s(z0)), x1)) → c7(INDX(mark(s1(quote(z0))), x1))
ACTIVE(indx(quote(s(z0)), x1)) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbl1(quote(s(z0)))) → c7(DBL1(mark(s1(quote(z0)))))
ACTIVE(dbl1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(s1(quote(s(z0)))) → c7(S1(mark(s1(quote(z0)))))
ACTIVE(s1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(quote(dbl(s(z0)))) → c7(QUOTE(mark(s(s(dbl(z0))))))
ACTIVE(quote(dbl(s(z0)))) → c7(ACTIVE(dbl(s(z0))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(QUOTE(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(QUOTE(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(quote(from(z0))) → c7(QUOTE(mark(cons(z0, from(s(z0))))))
ACTIVE(quote(from(z0))) → c7(ACTIVE(from(z0)))
ACTIVE(quote(dbl1(s(z0)))) → c7(QUOTE(mark(s1(s1(dbl1(z0))))))
ACTIVE(quote(dbl1(s(z0)))) → c7(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(quote(s(z0)))) → c7(QUOTE(mark(s1(quote(z0)))))
ACTIVE(quote(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
PROPER(dbl(dbl(z0))) → c45(DBL(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbl(s(z0))) → c45(DBL(s(proper(z0))), PROPER(s(z0)))
PROPER(dbl(dbls(z0))) → c45(DBL(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbl(cons(z0, z1))) → c45(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbl(sel(z0, z1))) → c45(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbl(indx(z0, z1))) → c45(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbl(from(z0))) → c45(DBL(from(proper(z0))), PROPER(from(z0)))
PROPER(dbl(dbl1(z0))) → c45(DBL(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbl(s1(z0))) → c45(DBL(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbl(sel1(z0, z1))) → c45(DBL(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbl(quote(z0))) → c45(DBL(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbl(0)) → c45(DBL(ok(0)))
PROPER(dbl(nil)) → c45(DBL(ok(nil)))
PROPER(dbl(01)) → c45(DBL(ok(01)))
PROPER(s(dbl(z0))) → c47(S(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(s(s(z0))) → c47(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(dbls(z0))) → c47(S(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(s(cons(z0, z1))) → c47(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(sel(z0, z1))) → c47(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(s(indx(z0, z1))) → c47(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(s(from(z0))) → c47(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(dbl1(z0))) → c47(S(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(s(s1(z0))) → c47(S(s1(proper(z0))), PROPER(s1(z0)))
PROPER(s(sel1(z0, z1))) → c47(S(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(s(quote(z0))) → c47(S(quote(proper(z0))), PROPER(quote(z0)))
PROPER(s(0)) → c47(S(ok(0)))
PROPER(s(nil)) → c47(S(ok(nil)))
PROPER(s(01)) → c47(S(ok(01)))
PROPER(dbls(dbl(z0))) → c48(DBLS(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbls(s(z0))) → c48(DBLS(s(proper(z0))), PROPER(s(z0)))
PROPER(dbls(dbls(z0))) → c48(DBLS(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbls(cons(z0, z1))) → c48(DBLS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbls(sel(z0, z1))) → c48(DBLS(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbls(indx(z0, z1))) → c48(DBLS(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbls(from(z0))) → c48(DBLS(from(proper(z0))), PROPER(from(z0)))
PROPER(dbls(dbl1(z0))) → c48(DBLS(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbls(s1(z0))) → c48(DBLS(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbls(sel1(z0, z1))) → c48(DBLS(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbls(quote(z0))) → c48(DBLS(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbls(0)) → c48(DBLS(ok(0)))
PROPER(dbls(nil)) → c48(DBLS(ok(nil)))
PROPER(dbls(01)) → c48(DBLS(ok(01)))
PROPER(cons(x0, dbl(z0))) → c50(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(cons(x0, s(z0))) → c50(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, dbls(z0))) → c50(CONS(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(cons(x0, cons(z0, z1))) → c50(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, sel(z0, z1))) → c50(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(cons(x0, indx(z0, z1))) → c50(CONS(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(cons(x0, from(z0))) → c50(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, dbl1(z0))) → c50(CONS(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(cons(x0, s1(z0))) → c50(CONS(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(cons(x0, sel1(z0, z1))) → c50(CONS(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(cons(x0, quote(z0))) → c50(CONS(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(cons(dbl(z0), x1)) → c50(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(cons(s(z0), x1)) → c50(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(dbls(z0), x1)) → c50(CONS(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c50(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(sel(z0, z1), x1)) → c50(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(cons(indx(z0, z1), x1)) → c50(CONS(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c50(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(dbl1(z0), x1)) → c50(CONS(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(cons(s1(z0), x1)) → c50(CONS(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(cons(sel1(z0, z1), x1)) → c50(CONS(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(cons(quote(z0), x1)) → c50(CONS(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c50(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c50(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, 01)) → c50(CONS(proper(x0), ok(01)), PROPER(x0))
PROPER(cons(0, x1)) → c50(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c50(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(01, x1)) → c50(CONS(ok(01), proper(x1)), PROPER(x1))
PROPER(sel(x0, dbl(z0))) → c51(SEL(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(sel(x0, s(z0))) → c51(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(sel(x0, dbls(z0))) → c51(SEL(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(sel(x0, cons(z0, z1))) → c51(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(sel(x0, sel(z0, z1))) → c51(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(sel(x0, indx(z0, z1))) → c51(SEL(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(sel(x0, from(z0))) → c51(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(sel(x0, dbl1(z0))) → c51(SEL(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(sel(x0, s1(z0))) → c51(SEL(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(sel(x0, sel1(z0, z1))) → c51(SEL(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(sel(x0, quote(z0))) → c51(SEL(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(sel(dbl(z0), x1)) → c51(SEL(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(sel(s(z0), x1)) → c51(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(sel(dbls(z0), x1)) → c51(SEL(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(sel(cons(z0, z1), x1)) → c51(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(sel(sel(z0, z1), x1)) → c51(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(sel(indx(z0, z1), x1)) → c51(SEL(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(sel(from(z0), x1)) → c51(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(sel(dbl1(z0), x1)) → c51(SEL(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(sel(s1(z0), x1)) → c51(SEL(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(sel(sel1(z0, z1), x1)) → c51(SEL(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(sel(quote(z0), x1)) → c51(SEL(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(sel(x0, 0)) → c51(SEL(proper(x0), ok(0)), PROPER(x0))
PROPER(sel(x0, nil)) → c51(SEL(proper(x0), ok(nil)), PROPER(x0))
PROPER(sel(x0, 01)) → c51(SEL(proper(x0), ok(01)), PROPER(x0))
PROPER(sel(0, x1)) → c51(SEL(ok(0), proper(x1)), PROPER(x1))
PROPER(sel(nil, x1)) → c51(SEL(ok(nil), proper(x1)), PROPER(x1))
PROPER(sel(01, x1)) → c51(SEL(ok(01), proper(x1)), PROPER(x1))
PROPER(indx(x0, dbl(z0))) → c52(INDX(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(indx(x0, s(z0))) → c52(INDX(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(indx(x0, dbls(z0))) → c52(INDX(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(indx(x0, cons(z0, z1))) → c52(INDX(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(indx(x0, sel(z0, z1))) → c52(INDX(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(indx(x0, indx(z0, z1))) → c52(INDX(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(indx(x0, from(z0))) → c52(INDX(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(indx(x0, dbl1(z0))) → c52(INDX(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(indx(x0, s1(z0))) → c52(INDX(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(indx(x0, sel1(z0, z1))) → c52(INDX(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(indx(x0, quote(z0))) → c52(INDX(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(indx(dbl(z0), x1)) → c52(INDX(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(indx(s(z0), x1)) → c52(INDX(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(indx(dbls(z0), x1)) → c52(INDX(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(indx(cons(z0, z1), x1)) → c52(INDX(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(indx(sel(z0, z1), x1)) → c52(INDX(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(indx(indx(z0, z1), x1)) → c52(INDX(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(indx(from(z0), x1)) → c52(INDX(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(indx(dbl1(z0), x1)) → c52(INDX(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(indx(s1(z0), x1)) → c52(INDX(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(indx(sel1(z0, z1), x1)) → c52(INDX(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(indx(quote(z0), x1)) → c52(INDX(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(indx(x0, 0)) → c52(INDX(proper(x0), ok(0)), PROPER(x0))
PROPER(indx(x0, nil)) → c52(INDX(proper(x0), ok(nil)), PROPER(x0))
PROPER(indx(x0, 01)) → c52(INDX(proper(x0), ok(01)), PROPER(x0))
PROPER(indx(0, x1)) → c52(INDX(ok(0), proper(x1)), PROPER(x1))
PROPER(indx(nil, x1)) → c52(INDX(ok(nil), proper(x1)), PROPER(x1))
PROPER(indx(01, x1)) → c52(INDX(ok(01), proper(x1)), PROPER(x1))
PROPER(from(dbl(z0))) → c53(FROM(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(from(s(z0))) → c53(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(dbls(z0))) → c53(FROM(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(from(cons(z0, z1))) → c53(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(sel(z0, z1))) → c53(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(from(indx(z0, z1))) → c53(FROM(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(from(from(z0))) → c53(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(dbl1(z0))) → c53(FROM(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(from(s1(z0))) → c53(FROM(s1(proper(z0))), PROPER(s1(z0)))
PROPER(from(sel1(z0, z1))) → c53(FROM(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(from(quote(z0))) → c53(FROM(quote(proper(z0))), PROPER(quote(z0)))
PROPER(from(0)) → c53(FROM(ok(0)))
PROPER(from(nil)) → c53(FROM(ok(nil)))
PROPER(from(01)) → c53(FROM(ok(01)))
PROPER(dbl1(dbl(z0))) → c54(DBL1(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbl1(s(z0))) → c54(DBL1(s(proper(z0))), PROPER(s(z0)))
PROPER(dbl1(dbls(z0))) → c54(DBL1(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbl1(cons(z0, z1))) → c54(DBL1(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbl1(sel(z0, z1))) → c54(DBL1(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbl1(indx(z0, z1))) → c54(DBL1(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbl1(from(z0))) → c54(DBL1(from(proper(z0))), PROPER(from(z0)))
PROPER(dbl1(dbl1(z0))) → c54(DBL1(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbl1(s1(z0))) → c54(DBL1(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbl1(sel1(z0, z1))) → c54(DBL1(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbl1(quote(z0))) → c54(DBL1(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbl1(0)) → c54(DBL1(ok(0)))
PROPER(dbl1(nil)) → c54(DBL1(ok(nil)))
PROPER(dbl1(01)) → c54(DBL1(ok(01)))
PROPER(s1(dbl(z0))) → c56(S1(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(s1(s(z0))) → c56(S1(s(proper(z0))), PROPER(s(z0)))
PROPER(s1(dbls(z0))) → c56(S1(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(s1(cons(z0, z1))) → c56(S1(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s1(sel(z0, z1))) → c56(S1(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(s1(indx(z0, z1))) → c56(S1(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(s1(from(z0))) → c56(S1(from(proper(z0))), PROPER(from(z0)))
PROPER(s1(dbl1(z0))) → c56(S1(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(s1(s1(z0))) → c56(S1(s1(proper(z0))), PROPER(s1(z0)))
PROPER(s1(sel1(z0, z1))) → c56(S1(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(s1(quote(z0))) → c56(S1(quote(proper(z0))), PROPER(quote(z0)))
PROPER(s1(0)) → c56(S1(ok(0)))
PROPER(s1(nil)) → c56(S1(ok(nil)))
PROPER(s1(01)) → c56(S1(ok(01)))
PROPER(sel1(x0, dbl(z0))) → c57(SEL1(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(sel1(x0, s(z0))) → c57(SEL1(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(sel1(x0, dbls(z0))) → c57(SEL1(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(sel1(x0, cons(z0, z1))) → c57(SEL1(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(sel1(x0, sel(z0, z1))) → c57(SEL1(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(sel1(x0, indx(z0, z1))) → c57(SEL1(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(sel1(x0, from(z0))) → c57(SEL1(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(sel1(x0, dbl1(z0))) → c57(SEL1(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(sel1(x0, s1(z0))) → c57(SEL1(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(sel1(x0, sel1(z0, z1))) → c57(SEL1(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(sel1(x0, quote(z0))) → c57(SEL1(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(sel1(dbl(z0), x1)) → c57(SEL1(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(sel1(s(z0), x1)) → c57(SEL1(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(sel1(dbls(z0), x1)) → c57(SEL1(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(sel1(cons(z0, z1), x1)) → c57(SEL1(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(sel1(sel(z0, z1), x1)) → c57(SEL1(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(sel1(indx(z0, z1), x1)) → c57(SEL1(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(sel1(from(z0), x1)) → c57(SEL1(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(sel1(dbl1(z0), x1)) → c57(SEL1(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(sel1(s1(z0), x1)) → c57(SEL1(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(sel1(sel1(z0, z1), x1)) → c57(SEL1(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(sel1(quote(z0), x1)) → c57(SEL1(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(sel1(x0, 0)) → c57(SEL1(proper(x0), ok(0)), PROPER(x0))
PROPER(sel1(x0, nil)) → c57(SEL1(proper(x0), ok(nil)), PROPER(x0))
PROPER(sel1(x0, 01)) → c57(SEL1(proper(x0), ok(01)), PROPER(x0))
PROPER(sel1(0, x1)) → c57(SEL1(ok(0), proper(x1)), PROPER(x1))
PROPER(sel1(nil, x1)) → c57(SEL1(ok(nil), proper(x1)), PROPER(x1))
PROPER(sel1(01, x1)) → c57(SEL1(ok(01), proper(x1)), PROPER(x1))
S tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
PROPER(quote(z0)) → c58(QUOTE(proper(z0)), PROPER(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)))
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0))))))
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0))))))
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0)))
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(indx(sel1(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(indx(sel1(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel1(z0, z2)), x1), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(indx(quote(dbl(z0)), x1)) → c21(INDX(mark(dbl1(z0)), x1), ACTIVE(quote(dbl(z0))))
ACTIVE(indx(quote(sel(z0, z1)), x1)) → c21(INDX(mark(sel1(z0, z1)), x1), ACTIVE(quote(sel(z0, z1))))
ACTIVE(indx(dbl(z0), x1)) → c21(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
ACTIVE(indx(dbls(z0), x1)) → c21(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(indx(z0, z1), x1)) → c21(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1)))
ACTIVE(indx(dbl1(z0), x1)) → c21(INDX(dbl1(active(z0)), x1), ACTIVE(dbl1(z0)))
ACTIVE(indx(s1(z0), x1)) → c21(INDX(s1(active(z0)), x1), ACTIVE(s1(z0)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(active(z0), z1), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(z0, active(z1)), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(quote(z0), x1)) → c21(INDX(quote(active(z0)), x1), ACTIVE(quote(z0)))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)))
ACTIVE(indx(dbl(0), x1)) → c21(INDX(mark(0), x1))
ACTIVE(indx(dbls(nil), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(indx(indx(nil, z0), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0))))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1))
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0)))
ACTIVE(dbl1(sel(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl1(sel(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl1(sel1(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl1(sel1(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl1(quote(dbl(z0)))) → c22(DBL1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl1(quote(sel(z0, z1)))) → c22(DBL1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl1(dbl(z0))) → c22(DBL1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl1(dbls(z0))) → c22(DBL1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(indx(z0, z1))) → c22(DBL1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl1(dbl1(z0))) → c22(DBL1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl1(s1(z0))) → c22(DBL1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(quote(z0))) → c22(DBL1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(dbl1(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(dbl(0))) → c22(DBL1(mark(0)))
ACTIVE(dbl1(dbls(nil))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(indx(nil, z0))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(dbl1(0))) → c22(DBL1(mark(01)))
ACTIVE(dbl(dbl1(s(z0)))) → c4(DBL(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(DBLS(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(INDX(mark(s1(s1(dbl1(z0)))), x1))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(DBL1(mark(s(s(dbl(z0))))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(ACTIVE(dbl(s(z0))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(DBL1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(DBL1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl1(from(z0))) → c4(DBL1(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl1(from(z0))) → c4(ACTIVE(from(z0)))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(DBL1(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(s1(sel(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(s1(sel(s(z0), cons(z1, z2)))) → c23(S1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(s1(sel1(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(s1(sel1(s(z0), cons(z1, z2)))) → c23(S1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(s1(quote(dbl(z0)))) → c23(S1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(s1(quote(sel(z0, z1)))) → c23(S1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(s1(dbl(z0))) → c23(S1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(s1(dbls(z0))) → c23(S1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(s1(indx(z0, z1))) → c23(S1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(s1(dbl1(z0))) → c23(S1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(s1(s1(z0))) → c23(S1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(quote(z0))) → c23(S1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(s1(dbl(0))) → c23(S1(mark(0)))
ACTIVE(s1(dbls(nil))) → c23(S1(mark(nil)))
ACTIVE(s1(indx(nil, z0))) → c23(S1(mark(nil)))
ACTIVE(s1(dbl1(0))) → c23(S1(mark(01)))
ACTIVE(s1(dbl(s(z0)))) → c6(S1(mark(s(s(dbl(z0))))))
ACTIVE(s1(dbl(s(z0)))) → c6(ACTIVE(dbl(s(z0))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(S1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(S1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(s1(from(z0))) → c6(S1(mark(cons(z0, from(s(z0))))))
ACTIVE(s1(from(z0))) → c6(ACTIVE(from(z0)))
ACTIVE(s1(dbl1(s(z0)))) → c6(S1(mark(s1(s1(dbl1(z0))))))
ACTIVE(s1(dbl1(s(z0)))) → c6(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(sel(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(quote(sel(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(quote(sel1(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(quote(sel1(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(quote(quote(dbl(z0)))) → c26(QUOTE(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(quote(quote(sel(z0, z1)))) → c26(QUOTE(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(quote(dbl(z0))) → c26(QUOTE(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(quote(dbls(z0))) → c26(QUOTE(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(quote(indx(z0, z1))) → c26(QUOTE(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(quote(dbl1(z0))) → c26(QUOTE(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(quote(s1(z0))) → c26(QUOTE(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(quote(z0))) → c26(QUOTE(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(quote(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(quote(0))) → c22(DBL1(mark(01)))
ACTIVE(s1(quote(0))) → c23(S1(mark(01)))
ACTIVE(quote(dbl(0))) → c26(QUOTE(mark(0)))
ACTIVE(quote(dbls(nil))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(indx(nil, z0))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(dbl1(0))) → c26(QUOTE(mark(01)))
ACTIVE(quote(quote(0))) → c26(QUOTE(mark(01)))
ACTIVE(dbl(quote(s(z0)))) → c7(DBL(mark(s1(quote(z0)))))
ACTIVE(dbl(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(s(z0)))) → c7(DBLS(mark(s1(quote(z0)))))
ACTIVE(dbls(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(indx(quote(s(z0)), x1)) → c7(INDX(mark(s1(quote(z0))), x1))
ACTIVE(indx(quote(s(z0)), x1)) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbl1(quote(s(z0)))) → c7(DBL1(mark(s1(quote(z0)))))
ACTIVE(dbl1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(s1(quote(s(z0)))) → c7(S1(mark(s1(quote(z0)))))
ACTIVE(s1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(quote(dbl(s(z0)))) → c7(QUOTE(mark(s(s(dbl(z0))))))
ACTIVE(quote(dbl(s(z0)))) → c7(ACTIVE(dbl(s(z0))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(QUOTE(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(QUOTE(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(quote(from(z0))) → c7(QUOTE(mark(cons(z0, from(s(z0))))))
ACTIVE(quote(from(z0))) → c7(ACTIVE(from(z0)))
ACTIVE(quote(dbl1(s(z0)))) → c7(QUOTE(mark(s1(s1(dbl1(z0))))))
ACTIVE(quote(dbl1(s(z0)))) → c7(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(quote(s(z0)))) → c7(QUOTE(mark(s1(quote(z0)))))
ACTIVE(quote(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
PROPER(dbl(dbl(z0))) → c45(DBL(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbl(s(z0))) → c45(DBL(s(proper(z0))), PROPER(s(z0)))
PROPER(dbl(dbls(z0))) → c45(DBL(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbl(cons(z0, z1))) → c45(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbl(sel(z0, z1))) → c45(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbl(indx(z0, z1))) → c45(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbl(from(z0))) → c45(DBL(from(proper(z0))), PROPER(from(z0)))
PROPER(dbl(dbl1(z0))) → c45(DBL(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbl(s1(z0))) → c45(DBL(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbl(sel1(z0, z1))) → c45(DBL(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbl(quote(z0))) → c45(DBL(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbl(0)) → c45(DBL(ok(0)))
PROPER(dbl(nil)) → c45(DBL(ok(nil)))
PROPER(dbl(01)) → c45(DBL(ok(01)))
PROPER(s(dbl(z0))) → c47(S(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(s(s(z0))) → c47(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(dbls(z0))) → c47(S(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(s(cons(z0, z1))) → c47(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(sel(z0, z1))) → c47(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(s(indx(z0, z1))) → c47(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(s(from(z0))) → c47(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(dbl1(z0))) → c47(S(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(s(s1(z0))) → c47(S(s1(proper(z0))), PROPER(s1(z0)))
PROPER(s(sel1(z0, z1))) → c47(S(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(s(quote(z0))) → c47(S(quote(proper(z0))), PROPER(quote(z0)))
PROPER(s(0)) → c47(S(ok(0)))
PROPER(s(nil)) → c47(S(ok(nil)))
PROPER(s(01)) → c47(S(ok(01)))
PROPER(dbls(dbl(z0))) → c48(DBLS(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbls(s(z0))) → c48(DBLS(s(proper(z0))), PROPER(s(z0)))
PROPER(dbls(dbls(z0))) → c48(DBLS(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbls(cons(z0, z1))) → c48(DBLS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbls(sel(z0, z1))) → c48(DBLS(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbls(indx(z0, z1))) → c48(DBLS(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbls(from(z0))) → c48(DBLS(from(proper(z0))), PROPER(from(z0)))
PROPER(dbls(dbl1(z0))) → c48(DBLS(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbls(s1(z0))) → c48(DBLS(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbls(sel1(z0, z1))) → c48(DBLS(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbls(quote(z0))) → c48(DBLS(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbls(0)) → c48(DBLS(ok(0)))
PROPER(dbls(nil)) → c48(DBLS(ok(nil)))
PROPER(dbls(01)) → c48(DBLS(ok(01)))
PROPER(cons(x0, dbl(z0))) → c50(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(cons(x0, s(z0))) → c50(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, dbls(z0))) → c50(CONS(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(cons(x0, cons(z0, z1))) → c50(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, sel(z0, z1))) → c50(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(cons(x0, indx(z0, z1))) → c50(CONS(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(cons(x0, from(z0))) → c50(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, dbl1(z0))) → c50(CONS(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(cons(x0, s1(z0))) → c50(CONS(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(cons(x0, sel1(z0, z1))) → c50(CONS(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(cons(x0, quote(z0))) → c50(CONS(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(cons(dbl(z0), x1)) → c50(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(cons(s(z0), x1)) → c50(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(dbls(z0), x1)) → c50(CONS(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c50(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(sel(z0, z1), x1)) → c50(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(cons(indx(z0, z1), x1)) → c50(CONS(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c50(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(dbl1(z0), x1)) → c50(CONS(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(cons(s1(z0), x1)) → c50(CONS(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(cons(sel1(z0, z1), x1)) → c50(CONS(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(cons(quote(z0), x1)) → c50(CONS(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c50(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c50(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, 01)) → c50(CONS(proper(x0), ok(01)), PROPER(x0))
PROPER(cons(0, x1)) → c50(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c50(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(01, x1)) → c50(CONS(ok(01), proper(x1)), PROPER(x1))
PROPER(sel(x0, dbl(z0))) → c51(SEL(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(sel(x0, s(z0))) → c51(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(sel(x0, dbls(z0))) → c51(SEL(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(sel(x0, cons(z0, z1))) → c51(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(sel(x0, sel(z0, z1))) → c51(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(sel(x0, indx(z0, z1))) → c51(SEL(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(sel(x0, from(z0))) → c51(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(sel(x0, dbl1(z0))) → c51(SEL(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(sel(x0, s1(z0))) → c51(SEL(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(sel(x0, sel1(z0, z1))) → c51(SEL(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(sel(x0, quote(z0))) → c51(SEL(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(sel(dbl(z0), x1)) → c51(SEL(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(sel(s(z0), x1)) → c51(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(sel(dbls(z0), x1)) → c51(SEL(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(sel(cons(z0, z1), x1)) → c51(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(sel(sel(z0, z1), x1)) → c51(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(sel(indx(z0, z1), x1)) → c51(SEL(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(sel(from(z0), x1)) → c51(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(sel(dbl1(z0), x1)) → c51(SEL(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(sel(s1(z0), x1)) → c51(SEL(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(sel(sel1(z0, z1), x1)) → c51(SEL(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(sel(quote(z0), x1)) → c51(SEL(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(sel(x0, 0)) → c51(SEL(proper(x0), ok(0)), PROPER(x0))
PROPER(sel(x0, nil)) → c51(SEL(proper(x0), ok(nil)), PROPER(x0))
PROPER(sel(x0, 01)) → c51(SEL(proper(x0), ok(01)), PROPER(x0))
PROPER(sel(0, x1)) → c51(SEL(ok(0), proper(x1)), PROPER(x1))
PROPER(sel(nil, x1)) → c51(SEL(ok(nil), proper(x1)), PROPER(x1))
PROPER(sel(01, x1)) → c51(SEL(ok(01), proper(x1)), PROPER(x1))
PROPER(indx(x0, dbl(z0))) → c52(INDX(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(indx(x0, s(z0))) → c52(INDX(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(indx(x0, dbls(z0))) → c52(INDX(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(indx(x0, cons(z0, z1))) → c52(INDX(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(indx(x0, sel(z0, z1))) → c52(INDX(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(indx(x0, indx(z0, z1))) → c52(INDX(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(indx(x0, from(z0))) → c52(INDX(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(indx(x0, dbl1(z0))) → c52(INDX(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(indx(x0, s1(z0))) → c52(INDX(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(indx(x0, sel1(z0, z1))) → c52(INDX(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(indx(x0, quote(z0))) → c52(INDX(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(indx(dbl(z0), x1)) → c52(INDX(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(indx(s(z0), x1)) → c52(INDX(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(indx(dbls(z0), x1)) → c52(INDX(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(indx(cons(z0, z1), x1)) → c52(INDX(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(indx(sel(z0, z1), x1)) → c52(INDX(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(indx(indx(z0, z1), x1)) → c52(INDX(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(indx(from(z0), x1)) → c52(INDX(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(indx(dbl1(z0), x1)) → c52(INDX(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(indx(s1(z0), x1)) → c52(INDX(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(indx(sel1(z0, z1), x1)) → c52(INDX(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(indx(quote(z0), x1)) → c52(INDX(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(indx(x0, 0)) → c52(INDX(proper(x0), ok(0)), PROPER(x0))
PROPER(indx(x0, nil)) → c52(INDX(proper(x0), ok(nil)), PROPER(x0))
PROPER(indx(x0, 01)) → c52(INDX(proper(x0), ok(01)), PROPER(x0))
PROPER(indx(0, x1)) → c52(INDX(ok(0), proper(x1)), PROPER(x1))
PROPER(indx(nil, x1)) → c52(INDX(ok(nil), proper(x1)), PROPER(x1))
PROPER(indx(01, x1)) → c52(INDX(ok(01), proper(x1)), PROPER(x1))
PROPER(from(dbl(z0))) → c53(FROM(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(from(s(z0))) → c53(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(dbls(z0))) → c53(FROM(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(from(cons(z0, z1))) → c53(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(sel(z0, z1))) → c53(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(from(indx(z0, z1))) → c53(FROM(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(from(from(z0))) → c53(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(dbl1(z0))) → c53(FROM(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(from(s1(z0))) → c53(FROM(s1(proper(z0))), PROPER(s1(z0)))
PROPER(from(sel1(z0, z1))) → c53(FROM(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(from(quote(z0))) → c53(FROM(quote(proper(z0))), PROPER(quote(z0)))
PROPER(from(0)) → c53(FROM(ok(0)))
PROPER(from(nil)) → c53(FROM(ok(nil)))
PROPER(from(01)) → c53(FROM(ok(01)))
PROPER(dbl1(dbl(z0))) → c54(DBL1(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbl1(s(z0))) → c54(DBL1(s(proper(z0))), PROPER(s(z0)))
PROPER(dbl1(dbls(z0))) → c54(DBL1(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbl1(cons(z0, z1))) → c54(DBL1(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbl1(sel(z0, z1))) → c54(DBL1(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbl1(indx(z0, z1))) → c54(DBL1(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbl1(from(z0))) → c54(DBL1(from(proper(z0))), PROPER(from(z0)))
PROPER(dbl1(dbl1(z0))) → c54(DBL1(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbl1(s1(z0))) → c54(DBL1(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbl1(sel1(z0, z1))) → c54(DBL1(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbl1(quote(z0))) → c54(DBL1(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbl1(0)) → c54(DBL1(ok(0)))
PROPER(dbl1(nil)) → c54(DBL1(ok(nil)))
PROPER(dbl1(01)) → c54(DBL1(ok(01)))
PROPER(s1(dbl(z0))) → c56(S1(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(s1(s(z0))) → c56(S1(s(proper(z0))), PROPER(s(z0)))
PROPER(s1(dbls(z0))) → c56(S1(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(s1(cons(z0, z1))) → c56(S1(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s1(sel(z0, z1))) → c56(S1(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(s1(indx(z0, z1))) → c56(S1(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(s1(from(z0))) → c56(S1(from(proper(z0))), PROPER(from(z0)))
PROPER(s1(dbl1(z0))) → c56(S1(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(s1(s1(z0))) → c56(S1(s1(proper(z0))), PROPER(s1(z0)))
PROPER(s1(sel1(z0, z1))) → c56(S1(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(s1(quote(z0))) → c56(S1(quote(proper(z0))), PROPER(quote(z0)))
PROPER(s1(0)) → c56(S1(ok(0)))
PROPER(s1(nil)) → c56(S1(ok(nil)))
PROPER(s1(01)) → c56(S1(ok(01)))
PROPER(sel1(x0, dbl(z0))) → c57(SEL1(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(sel1(x0, s(z0))) → c57(SEL1(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(sel1(x0, dbls(z0))) → c57(SEL1(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(sel1(x0, cons(z0, z1))) → c57(SEL1(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(sel1(x0, sel(z0, z1))) → c57(SEL1(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(sel1(x0, indx(z0, z1))) → c57(SEL1(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(sel1(x0, from(z0))) → c57(SEL1(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(sel1(x0, dbl1(z0))) → c57(SEL1(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(sel1(x0, s1(z0))) → c57(SEL1(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(sel1(x0, sel1(z0, z1))) → c57(SEL1(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(sel1(x0, quote(z0))) → c57(SEL1(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(sel1(dbl(z0), x1)) → c57(SEL1(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(sel1(s(z0), x1)) → c57(SEL1(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(sel1(dbls(z0), x1)) → c57(SEL1(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(sel1(cons(z0, z1), x1)) → c57(SEL1(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(sel1(sel(z0, z1), x1)) → c57(SEL1(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(sel1(indx(z0, z1), x1)) → c57(SEL1(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(sel1(from(z0), x1)) → c57(SEL1(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(sel1(dbl1(z0), x1)) → c57(SEL1(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(sel1(s1(z0), x1)) → c57(SEL1(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(sel1(sel1(z0, z1), x1)) → c57(SEL1(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(sel1(quote(z0), x1)) → c57(SEL1(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(sel1(x0, 0)) → c57(SEL1(proper(x0), ok(0)), PROPER(x0))
PROPER(sel1(x0, nil)) → c57(SEL1(proper(x0), ok(nil)), PROPER(x0))
PROPER(sel1(x0, 01)) → c57(SEL1(proper(x0), ok(01)), PROPER(x0))
PROPER(sel1(0, x1)) → c57(SEL1(ok(0), proper(x1)), PROPER(x1))
PROPER(sel1(nil, x1)) → c57(SEL1(ok(nil), proper(x1)), PROPER(x1))
PROPER(sel1(01, x1)) → c57(SEL1(ok(01), proper(x1)), PROPER(x1))
K tuples:none
Defined Rule Symbols:
active, s, dbl, cons, dbls, sel, indx, s1, dbl1, sel1, quote, proper, from
Defined Pair Symbols:
ACTIVE, DBL, DBLS, SEL, INDX, DBL1, S1, SEL1, QUOTE, PROPER, S, CONS, FROM, TOP
Compound Symbols:
c5, c12, c15, c16, c19, c20, c24, c25, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c58, c59, c60, c61, c62, c63, c8, c, c17, c17, c1, c18, c18, c2, c21, c21, c3, c22, c22, c4, c23, c23, c6, c26, c26, c7, c45, c45, c47, c47, c48, c48, c50, c50, c51, c51, c52, c52, c53, c53, c54, c54, c56, c56, c57, c57
(87) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
PROPER(
quote(
z0)) →
c58(
QUOTE(
proper(
z0)),
PROPER(
z0)) by
PROPER(quote(dbl(z0))) → c58(QUOTE(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(quote(0)) → c58(QUOTE(ok(0)), PROPER(0))
PROPER(quote(s(z0))) → c58(QUOTE(s(proper(z0))), PROPER(s(z0)))
PROPER(quote(dbls(z0))) → c58(QUOTE(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(quote(nil)) → c58(QUOTE(ok(nil)), PROPER(nil))
PROPER(quote(cons(z0, z1))) → c58(QUOTE(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(quote(sel(z0, z1))) → c58(QUOTE(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(quote(indx(z0, z1))) → c58(QUOTE(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(quote(from(z0))) → c58(QUOTE(from(proper(z0))), PROPER(from(z0)))
PROPER(quote(dbl1(z0))) → c58(QUOTE(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(quote(01)) → c58(QUOTE(ok(01)), PROPER(01))
PROPER(quote(s1(z0))) → c58(QUOTE(s1(proper(z0))), PROPER(s1(z0)))
PROPER(quote(sel1(z0, z1))) → c58(QUOTE(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(quote(quote(z0))) → c58(QUOTE(quote(proper(z0))), PROPER(quote(z0)))
(88) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(dbl(0)) → mark(0)
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
active(dbls(nil)) → mark(nil)
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1)))
active(sel(0, cons(z0, z1))) → mark(z0)
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
active(indx(nil, z0)) → mark(nil)
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2)))
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(dbl1(0)) → mark(01)
active(dbl1(s(z0))) → mark(s1(s1(dbl1(z0))))
active(sel1(0, cons(z0, z1))) → mark(z0)
active(sel1(s(z0), cons(z1, z2))) → mark(sel1(z0, z2))
active(quote(0)) → mark(01)
active(quote(s(z0))) → mark(s1(quote(z0)))
active(quote(dbl(z0))) → mark(dbl1(z0))
active(quote(sel(z0, z1))) → mark(sel1(z0, z1))
active(dbl(z0)) → dbl(active(z0))
active(dbls(z0)) → dbls(active(z0))
active(sel(z0, z1)) → sel(active(z0), z1)
active(sel(z0, z1)) → sel(z0, active(z1))
active(indx(z0, z1)) → indx(active(z0), z1)
active(dbl1(z0)) → dbl1(active(z0))
active(s1(z0)) → s1(active(z0))
active(sel1(z0, z1)) → sel1(active(z0), z1)
active(sel1(z0, z1)) → sel1(z0, active(z1))
active(quote(z0)) → quote(active(z0))
s(ok(z0)) → ok(s(z0))
dbl(mark(z0)) → mark(dbl(z0))
dbl(ok(z0)) → ok(dbl(z0))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
dbls(mark(z0)) → mark(dbls(z0))
dbls(ok(z0)) → ok(dbls(z0))
sel(mark(z0), z1) → mark(sel(z0, z1))
sel(z0, mark(z1)) → mark(sel(z0, z1))
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
indx(mark(z0), z1) → mark(indx(z0, z1))
indx(ok(z0), ok(z1)) → ok(indx(z0, z1))
s1(mark(z0)) → mark(s1(z0))
s1(ok(z0)) → ok(s1(z0))
dbl1(mark(z0)) → mark(dbl1(z0))
dbl1(ok(z0)) → ok(dbl1(z0))
sel1(mark(z0), z1) → mark(sel1(z0, z1))
sel1(z0, mark(z1)) → mark(sel1(z0, z1))
sel1(ok(z0), ok(z1)) → ok(sel1(z0, z1))
quote(mark(z0)) → mark(quote(z0))
quote(ok(z0)) → ok(quote(z0))
proper(dbl(z0)) → dbl(proper(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(dbls(z0)) → dbls(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
proper(indx(z0, z1)) → indx(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(dbl1(z0)) → dbl1(proper(z0))
proper(01) → ok(01)
proper(s1(z0)) → s1(proper(z0))
proper(sel1(z0, z1)) → sel1(proper(z0), proper(z1))
proper(quote(z0)) → quote(proper(z0))
from(ok(z0)) → ok(from(z0))
Tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)))
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0))))))
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0))))))
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0)))
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(indx(sel1(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(indx(sel1(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel1(z0, z2)), x1), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(indx(quote(dbl(z0)), x1)) → c21(INDX(mark(dbl1(z0)), x1), ACTIVE(quote(dbl(z0))))
ACTIVE(indx(quote(sel(z0, z1)), x1)) → c21(INDX(mark(sel1(z0, z1)), x1), ACTIVE(quote(sel(z0, z1))))
ACTIVE(indx(dbl(z0), x1)) → c21(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
ACTIVE(indx(dbls(z0), x1)) → c21(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(indx(z0, z1), x1)) → c21(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1)))
ACTIVE(indx(dbl1(z0), x1)) → c21(INDX(dbl1(active(z0)), x1), ACTIVE(dbl1(z0)))
ACTIVE(indx(s1(z0), x1)) → c21(INDX(s1(active(z0)), x1), ACTIVE(s1(z0)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(active(z0), z1), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(z0, active(z1)), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(quote(z0), x1)) → c21(INDX(quote(active(z0)), x1), ACTIVE(quote(z0)))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)))
ACTIVE(indx(dbl(0), x1)) → c21(INDX(mark(0), x1))
ACTIVE(indx(dbls(nil), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(indx(indx(nil, z0), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0))))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1))
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0)))
ACTIVE(dbl1(sel(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl1(sel(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl1(sel1(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl1(sel1(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl1(quote(dbl(z0)))) → c22(DBL1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl1(quote(sel(z0, z1)))) → c22(DBL1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl1(dbl(z0))) → c22(DBL1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl1(dbls(z0))) → c22(DBL1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(indx(z0, z1))) → c22(DBL1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl1(dbl1(z0))) → c22(DBL1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl1(s1(z0))) → c22(DBL1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(quote(z0))) → c22(DBL1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(dbl1(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(dbl(0))) → c22(DBL1(mark(0)))
ACTIVE(dbl1(dbls(nil))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(indx(nil, z0))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(dbl1(0))) → c22(DBL1(mark(01)))
ACTIVE(dbl(dbl1(s(z0)))) → c4(DBL(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(DBLS(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(INDX(mark(s1(s1(dbl1(z0)))), x1))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(DBL1(mark(s(s(dbl(z0))))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(ACTIVE(dbl(s(z0))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(DBL1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(DBL1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl1(from(z0))) → c4(DBL1(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl1(from(z0))) → c4(ACTIVE(from(z0)))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(DBL1(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(s1(sel(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(s1(sel(s(z0), cons(z1, z2)))) → c23(S1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(s1(sel1(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(s1(sel1(s(z0), cons(z1, z2)))) → c23(S1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(s1(quote(dbl(z0)))) → c23(S1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(s1(quote(sel(z0, z1)))) → c23(S1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(s1(dbl(z0))) → c23(S1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(s1(dbls(z0))) → c23(S1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(s1(indx(z0, z1))) → c23(S1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(s1(dbl1(z0))) → c23(S1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(s1(s1(z0))) → c23(S1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(quote(z0))) → c23(S1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(s1(dbl(0))) → c23(S1(mark(0)))
ACTIVE(s1(dbls(nil))) → c23(S1(mark(nil)))
ACTIVE(s1(indx(nil, z0))) → c23(S1(mark(nil)))
ACTIVE(s1(dbl1(0))) → c23(S1(mark(01)))
ACTIVE(s1(dbl(s(z0)))) → c6(S1(mark(s(s(dbl(z0))))))
ACTIVE(s1(dbl(s(z0)))) → c6(ACTIVE(dbl(s(z0))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(S1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(S1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(s1(from(z0))) → c6(S1(mark(cons(z0, from(s(z0))))))
ACTIVE(s1(from(z0))) → c6(ACTIVE(from(z0)))
ACTIVE(s1(dbl1(s(z0)))) → c6(S1(mark(s1(s1(dbl1(z0))))))
ACTIVE(s1(dbl1(s(z0)))) → c6(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(sel(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(quote(sel(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(quote(sel1(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(quote(sel1(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(quote(quote(dbl(z0)))) → c26(QUOTE(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(quote(quote(sel(z0, z1)))) → c26(QUOTE(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(quote(dbl(z0))) → c26(QUOTE(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(quote(dbls(z0))) → c26(QUOTE(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(quote(indx(z0, z1))) → c26(QUOTE(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(quote(dbl1(z0))) → c26(QUOTE(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(quote(s1(z0))) → c26(QUOTE(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(quote(z0))) → c26(QUOTE(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(quote(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(quote(0))) → c22(DBL1(mark(01)))
ACTIVE(s1(quote(0))) → c23(S1(mark(01)))
ACTIVE(quote(dbl(0))) → c26(QUOTE(mark(0)))
ACTIVE(quote(dbls(nil))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(indx(nil, z0))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(dbl1(0))) → c26(QUOTE(mark(01)))
ACTIVE(quote(quote(0))) → c26(QUOTE(mark(01)))
ACTIVE(dbl(quote(s(z0)))) → c7(DBL(mark(s1(quote(z0)))))
ACTIVE(dbl(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(s(z0)))) → c7(DBLS(mark(s1(quote(z0)))))
ACTIVE(dbls(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(indx(quote(s(z0)), x1)) → c7(INDX(mark(s1(quote(z0))), x1))
ACTIVE(indx(quote(s(z0)), x1)) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbl1(quote(s(z0)))) → c7(DBL1(mark(s1(quote(z0)))))
ACTIVE(dbl1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(s1(quote(s(z0)))) → c7(S1(mark(s1(quote(z0)))))
ACTIVE(s1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(quote(dbl(s(z0)))) → c7(QUOTE(mark(s(s(dbl(z0))))))
ACTIVE(quote(dbl(s(z0)))) → c7(ACTIVE(dbl(s(z0))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(QUOTE(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(QUOTE(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(quote(from(z0))) → c7(QUOTE(mark(cons(z0, from(s(z0))))))
ACTIVE(quote(from(z0))) → c7(ACTIVE(from(z0)))
ACTIVE(quote(dbl1(s(z0)))) → c7(QUOTE(mark(s1(s1(dbl1(z0))))))
ACTIVE(quote(dbl1(s(z0)))) → c7(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(quote(s(z0)))) → c7(QUOTE(mark(s1(quote(z0)))))
ACTIVE(quote(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
PROPER(dbl(dbl(z0))) → c45(DBL(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbl(s(z0))) → c45(DBL(s(proper(z0))), PROPER(s(z0)))
PROPER(dbl(dbls(z0))) → c45(DBL(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbl(cons(z0, z1))) → c45(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbl(sel(z0, z1))) → c45(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbl(indx(z0, z1))) → c45(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbl(from(z0))) → c45(DBL(from(proper(z0))), PROPER(from(z0)))
PROPER(dbl(dbl1(z0))) → c45(DBL(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbl(s1(z0))) → c45(DBL(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbl(sel1(z0, z1))) → c45(DBL(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbl(quote(z0))) → c45(DBL(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbl(0)) → c45(DBL(ok(0)))
PROPER(dbl(nil)) → c45(DBL(ok(nil)))
PROPER(dbl(01)) → c45(DBL(ok(01)))
PROPER(s(dbl(z0))) → c47(S(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(s(s(z0))) → c47(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(dbls(z0))) → c47(S(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(s(cons(z0, z1))) → c47(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(sel(z0, z1))) → c47(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(s(indx(z0, z1))) → c47(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(s(from(z0))) → c47(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(dbl1(z0))) → c47(S(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(s(s1(z0))) → c47(S(s1(proper(z0))), PROPER(s1(z0)))
PROPER(s(sel1(z0, z1))) → c47(S(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(s(quote(z0))) → c47(S(quote(proper(z0))), PROPER(quote(z0)))
PROPER(s(0)) → c47(S(ok(0)))
PROPER(s(nil)) → c47(S(ok(nil)))
PROPER(s(01)) → c47(S(ok(01)))
PROPER(dbls(dbl(z0))) → c48(DBLS(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbls(s(z0))) → c48(DBLS(s(proper(z0))), PROPER(s(z0)))
PROPER(dbls(dbls(z0))) → c48(DBLS(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbls(cons(z0, z1))) → c48(DBLS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbls(sel(z0, z1))) → c48(DBLS(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbls(indx(z0, z1))) → c48(DBLS(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbls(from(z0))) → c48(DBLS(from(proper(z0))), PROPER(from(z0)))
PROPER(dbls(dbl1(z0))) → c48(DBLS(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbls(s1(z0))) → c48(DBLS(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbls(sel1(z0, z1))) → c48(DBLS(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbls(quote(z0))) → c48(DBLS(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbls(0)) → c48(DBLS(ok(0)))
PROPER(dbls(nil)) → c48(DBLS(ok(nil)))
PROPER(dbls(01)) → c48(DBLS(ok(01)))
PROPER(cons(x0, dbl(z0))) → c50(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(cons(x0, s(z0))) → c50(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, dbls(z0))) → c50(CONS(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(cons(x0, cons(z0, z1))) → c50(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, sel(z0, z1))) → c50(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(cons(x0, indx(z0, z1))) → c50(CONS(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(cons(x0, from(z0))) → c50(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, dbl1(z0))) → c50(CONS(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(cons(x0, s1(z0))) → c50(CONS(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(cons(x0, sel1(z0, z1))) → c50(CONS(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(cons(x0, quote(z0))) → c50(CONS(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(cons(dbl(z0), x1)) → c50(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(cons(s(z0), x1)) → c50(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(dbls(z0), x1)) → c50(CONS(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c50(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(sel(z0, z1), x1)) → c50(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(cons(indx(z0, z1), x1)) → c50(CONS(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c50(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(dbl1(z0), x1)) → c50(CONS(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(cons(s1(z0), x1)) → c50(CONS(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(cons(sel1(z0, z1), x1)) → c50(CONS(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(cons(quote(z0), x1)) → c50(CONS(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c50(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c50(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, 01)) → c50(CONS(proper(x0), ok(01)), PROPER(x0))
PROPER(cons(0, x1)) → c50(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c50(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(01, x1)) → c50(CONS(ok(01), proper(x1)), PROPER(x1))
PROPER(sel(x0, dbl(z0))) → c51(SEL(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(sel(x0, s(z0))) → c51(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(sel(x0, dbls(z0))) → c51(SEL(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(sel(x0, cons(z0, z1))) → c51(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(sel(x0, sel(z0, z1))) → c51(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(sel(x0, indx(z0, z1))) → c51(SEL(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(sel(x0, from(z0))) → c51(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(sel(x0, dbl1(z0))) → c51(SEL(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(sel(x0, s1(z0))) → c51(SEL(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(sel(x0, sel1(z0, z1))) → c51(SEL(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(sel(x0, quote(z0))) → c51(SEL(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(sel(dbl(z0), x1)) → c51(SEL(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(sel(s(z0), x1)) → c51(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(sel(dbls(z0), x1)) → c51(SEL(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(sel(cons(z0, z1), x1)) → c51(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(sel(sel(z0, z1), x1)) → c51(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(sel(indx(z0, z1), x1)) → c51(SEL(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(sel(from(z0), x1)) → c51(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(sel(dbl1(z0), x1)) → c51(SEL(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(sel(s1(z0), x1)) → c51(SEL(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(sel(sel1(z0, z1), x1)) → c51(SEL(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(sel(quote(z0), x1)) → c51(SEL(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(sel(x0, 0)) → c51(SEL(proper(x0), ok(0)), PROPER(x0))
PROPER(sel(x0, nil)) → c51(SEL(proper(x0), ok(nil)), PROPER(x0))
PROPER(sel(x0, 01)) → c51(SEL(proper(x0), ok(01)), PROPER(x0))
PROPER(sel(0, x1)) → c51(SEL(ok(0), proper(x1)), PROPER(x1))
PROPER(sel(nil, x1)) → c51(SEL(ok(nil), proper(x1)), PROPER(x1))
PROPER(sel(01, x1)) → c51(SEL(ok(01), proper(x1)), PROPER(x1))
PROPER(indx(x0, dbl(z0))) → c52(INDX(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(indx(x0, s(z0))) → c52(INDX(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(indx(x0, dbls(z0))) → c52(INDX(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(indx(x0, cons(z0, z1))) → c52(INDX(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(indx(x0, sel(z0, z1))) → c52(INDX(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(indx(x0, indx(z0, z1))) → c52(INDX(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(indx(x0, from(z0))) → c52(INDX(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(indx(x0, dbl1(z0))) → c52(INDX(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(indx(x0, s1(z0))) → c52(INDX(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(indx(x0, sel1(z0, z1))) → c52(INDX(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(indx(x0, quote(z0))) → c52(INDX(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(indx(dbl(z0), x1)) → c52(INDX(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(indx(s(z0), x1)) → c52(INDX(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(indx(dbls(z0), x1)) → c52(INDX(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(indx(cons(z0, z1), x1)) → c52(INDX(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(indx(sel(z0, z1), x1)) → c52(INDX(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(indx(indx(z0, z1), x1)) → c52(INDX(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(indx(from(z0), x1)) → c52(INDX(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(indx(dbl1(z0), x1)) → c52(INDX(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(indx(s1(z0), x1)) → c52(INDX(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(indx(sel1(z0, z1), x1)) → c52(INDX(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(indx(quote(z0), x1)) → c52(INDX(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(indx(x0, 0)) → c52(INDX(proper(x0), ok(0)), PROPER(x0))
PROPER(indx(x0, nil)) → c52(INDX(proper(x0), ok(nil)), PROPER(x0))
PROPER(indx(x0, 01)) → c52(INDX(proper(x0), ok(01)), PROPER(x0))
PROPER(indx(0, x1)) → c52(INDX(ok(0), proper(x1)), PROPER(x1))
PROPER(indx(nil, x1)) → c52(INDX(ok(nil), proper(x1)), PROPER(x1))
PROPER(indx(01, x1)) → c52(INDX(ok(01), proper(x1)), PROPER(x1))
PROPER(from(dbl(z0))) → c53(FROM(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(from(s(z0))) → c53(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(dbls(z0))) → c53(FROM(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(from(cons(z0, z1))) → c53(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(sel(z0, z1))) → c53(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(from(indx(z0, z1))) → c53(FROM(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(from(from(z0))) → c53(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(dbl1(z0))) → c53(FROM(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(from(s1(z0))) → c53(FROM(s1(proper(z0))), PROPER(s1(z0)))
PROPER(from(sel1(z0, z1))) → c53(FROM(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(from(quote(z0))) → c53(FROM(quote(proper(z0))), PROPER(quote(z0)))
PROPER(from(0)) → c53(FROM(ok(0)))
PROPER(from(nil)) → c53(FROM(ok(nil)))
PROPER(from(01)) → c53(FROM(ok(01)))
PROPER(dbl1(dbl(z0))) → c54(DBL1(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbl1(s(z0))) → c54(DBL1(s(proper(z0))), PROPER(s(z0)))
PROPER(dbl1(dbls(z0))) → c54(DBL1(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbl1(cons(z0, z1))) → c54(DBL1(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbl1(sel(z0, z1))) → c54(DBL1(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbl1(indx(z0, z1))) → c54(DBL1(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbl1(from(z0))) → c54(DBL1(from(proper(z0))), PROPER(from(z0)))
PROPER(dbl1(dbl1(z0))) → c54(DBL1(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbl1(s1(z0))) → c54(DBL1(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbl1(sel1(z0, z1))) → c54(DBL1(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbl1(quote(z0))) → c54(DBL1(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbl1(0)) → c54(DBL1(ok(0)))
PROPER(dbl1(nil)) → c54(DBL1(ok(nil)))
PROPER(dbl1(01)) → c54(DBL1(ok(01)))
PROPER(s1(dbl(z0))) → c56(S1(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(s1(s(z0))) → c56(S1(s(proper(z0))), PROPER(s(z0)))
PROPER(s1(dbls(z0))) → c56(S1(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(s1(cons(z0, z1))) → c56(S1(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s1(sel(z0, z1))) → c56(S1(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(s1(indx(z0, z1))) → c56(S1(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(s1(from(z0))) → c56(S1(from(proper(z0))), PROPER(from(z0)))
PROPER(s1(dbl1(z0))) → c56(S1(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(s1(s1(z0))) → c56(S1(s1(proper(z0))), PROPER(s1(z0)))
PROPER(s1(sel1(z0, z1))) → c56(S1(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(s1(quote(z0))) → c56(S1(quote(proper(z0))), PROPER(quote(z0)))
PROPER(s1(0)) → c56(S1(ok(0)))
PROPER(s1(nil)) → c56(S1(ok(nil)))
PROPER(s1(01)) → c56(S1(ok(01)))
PROPER(sel1(x0, dbl(z0))) → c57(SEL1(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(sel1(x0, s(z0))) → c57(SEL1(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(sel1(x0, dbls(z0))) → c57(SEL1(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(sel1(x0, cons(z0, z1))) → c57(SEL1(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(sel1(x0, sel(z0, z1))) → c57(SEL1(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(sel1(x0, indx(z0, z1))) → c57(SEL1(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(sel1(x0, from(z0))) → c57(SEL1(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(sel1(x0, dbl1(z0))) → c57(SEL1(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(sel1(x0, s1(z0))) → c57(SEL1(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(sel1(x0, sel1(z0, z1))) → c57(SEL1(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(sel1(x0, quote(z0))) → c57(SEL1(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(sel1(dbl(z0), x1)) → c57(SEL1(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(sel1(s(z0), x1)) → c57(SEL1(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(sel1(dbls(z0), x1)) → c57(SEL1(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(sel1(cons(z0, z1), x1)) → c57(SEL1(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(sel1(sel(z0, z1), x1)) → c57(SEL1(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(sel1(indx(z0, z1), x1)) → c57(SEL1(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(sel1(from(z0), x1)) → c57(SEL1(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(sel1(dbl1(z0), x1)) → c57(SEL1(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(sel1(s1(z0), x1)) → c57(SEL1(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(sel1(sel1(z0, z1), x1)) → c57(SEL1(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(sel1(quote(z0), x1)) → c57(SEL1(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(sel1(x0, 0)) → c57(SEL1(proper(x0), ok(0)), PROPER(x0))
PROPER(sel1(x0, nil)) → c57(SEL1(proper(x0), ok(nil)), PROPER(x0))
PROPER(sel1(x0, 01)) → c57(SEL1(proper(x0), ok(01)), PROPER(x0))
PROPER(sel1(0, x1)) → c57(SEL1(ok(0), proper(x1)), PROPER(x1))
PROPER(sel1(nil, x1)) → c57(SEL1(ok(nil), proper(x1)), PROPER(x1))
PROPER(sel1(01, x1)) → c57(SEL1(ok(01), proper(x1)), PROPER(x1))
PROPER(quote(dbl(z0))) → c58(QUOTE(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(quote(0)) → c58(QUOTE(ok(0)), PROPER(0))
PROPER(quote(s(z0))) → c58(QUOTE(s(proper(z0))), PROPER(s(z0)))
PROPER(quote(dbls(z0))) → c58(QUOTE(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(quote(nil)) → c58(QUOTE(ok(nil)), PROPER(nil))
PROPER(quote(cons(z0, z1))) → c58(QUOTE(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(quote(sel(z0, z1))) → c58(QUOTE(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(quote(indx(z0, z1))) → c58(QUOTE(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(quote(from(z0))) → c58(QUOTE(from(proper(z0))), PROPER(from(z0)))
PROPER(quote(dbl1(z0))) → c58(QUOTE(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(quote(01)) → c58(QUOTE(ok(01)), PROPER(01))
PROPER(quote(s1(z0))) → c58(QUOTE(s1(proper(z0))), PROPER(s1(z0)))
PROPER(quote(sel1(z0, z1))) → c58(QUOTE(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(quote(quote(z0))) → c58(QUOTE(quote(proper(z0))), PROPER(quote(z0)))
S tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)))
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0))))))
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0))))))
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0)))
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(indx(sel1(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(indx(sel1(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel1(z0, z2)), x1), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(indx(quote(dbl(z0)), x1)) → c21(INDX(mark(dbl1(z0)), x1), ACTIVE(quote(dbl(z0))))
ACTIVE(indx(quote(sel(z0, z1)), x1)) → c21(INDX(mark(sel1(z0, z1)), x1), ACTIVE(quote(sel(z0, z1))))
ACTIVE(indx(dbl(z0), x1)) → c21(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
ACTIVE(indx(dbls(z0), x1)) → c21(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(indx(z0, z1), x1)) → c21(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1)))
ACTIVE(indx(dbl1(z0), x1)) → c21(INDX(dbl1(active(z0)), x1), ACTIVE(dbl1(z0)))
ACTIVE(indx(s1(z0), x1)) → c21(INDX(s1(active(z0)), x1), ACTIVE(s1(z0)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(active(z0), z1), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(z0, active(z1)), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(quote(z0), x1)) → c21(INDX(quote(active(z0)), x1), ACTIVE(quote(z0)))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)))
ACTIVE(indx(dbl(0), x1)) → c21(INDX(mark(0), x1))
ACTIVE(indx(dbls(nil), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(indx(indx(nil, z0), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0))))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1))
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0)))
ACTIVE(dbl1(sel(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl1(sel(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl1(sel1(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl1(sel1(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl1(quote(dbl(z0)))) → c22(DBL1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl1(quote(sel(z0, z1)))) → c22(DBL1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl1(dbl(z0))) → c22(DBL1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl1(dbls(z0))) → c22(DBL1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(indx(z0, z1))) → c22(DBL1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl1(dbl1(z0))) → c22(DBL1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl1(s1(z0))) → c22(DBL1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(quote(z0))) → c22(DBL1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(dbl1(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(dbl(0))) → c22(DBL1(mark(0)))
ACTIVE(dbl1(dbls(nil))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(indx(nil, z0))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(dbl1(0))) → c22(DBL1(mark(01)))
ACTIVE(dbl(dbl1(s(z0)))) → c4(DBL(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(DBLS(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(INDX(mark(s1(s1(dbl1(z0)))), x1))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(DBL1(mark(s(s(dbl(z0))))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(ACTIVE(dbl(s(z0))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(DBL1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(DBL1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl1(from(z0))) → c4(DBL1(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl1(from(z0))) → c4(ACTIVE(from(z0)))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(DBL1(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(s1(sel(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(s1(sel(s(z0), cons(z1, z2)))) → c23(S1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(s1(sel1(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(s1(sel1(s(z0), cons(z1, z2)))) → c23(S1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(s1(quote(dbl(z0)))) → c23(S1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(s1(quote(sel(z0, z1)))) → c23(S1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(s1(dbl(z0))) → c23(S1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(s1(dbls(z0))) → c23(S1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(s1(indx(z0, z1))) → c23(S1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(s1(dbl1(z0))) → c23(S1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(s1(s1(z0))) → c23(S1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(quote(z0))) → c23(S1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(s1(dbl(0))) → c23(S1(mark(0)))
ACTIVE(s1(dbls(nil))) → c23(S1(mark(nil)))
ACTIVE(s1(indx(nil, z0))) → c23(S1(mark(nil)))
ACTIVE(s1(dbl1(0))) → c23(S1(mark(01)))
ACTIVE(s1(dbl(s(z0)))) → c6(S1(mark(s(s(dbl(z0))))))
ACTIVE(s1(dbl(s(z0)))) → c6(ACTIVE(dbl(s(z0))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(S1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(S1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(s1(from(z0))) → c6(S1(mark(cons(z0, from(s(z0))))))
ACTIVE(s1(from(z0))) → c6(ACTIVE(from(z0)))
ACTIVE(s1(dbl1(s(z0)))) → c6(S1(mark(s1(s1(dbl1(z0))))))
ACTIVE(s1(dbl1(s(z0)))) → c6(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(sel(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(quote(sel(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(quote(sel1(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(quote(sel1(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(quote(quote(dbl(z0)))) → c26(QUOTE(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(quote(quote(sel(z0, z1)))) → c26(QUOTE(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(quote(dbl(z0))) → c26(QUOTE(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(quote(dbls(z0))) → c26(QUOTE(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(quote(indx(z0, z1))) → c26(QUOTE(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(quote(dbl1(z0))) → c26(QUOTE(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(quote(s1(z0))) → c26(QUOTE(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(quote(z0))) → c26(QUOTE(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(quote(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(quote(0))) → c22(DBL1(mark(01)))
ACTIVE(s1(quote(0))) → c23(S1(mark(01)))
ACTIVE(quote(dbl(0))) → c26(QUOTE(mark(0)))
ACTIVE(quote(dbls(nil))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(indx(nil, z0))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(dbl1(0))) → c26(QUOTE(mark(01)))
ACTIVE(quote(quote(0))) → c26(QUOTE(mark(01)))
ACTIVE(dbl(quote(s(z0)))) → c7(DBL(mark(s1(quote(z0)))))
ACTIVE(dbl(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(s(z0)))) → c7(DBLS(mark(s1(quote(z0)))))
ACTIVE(dbls(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(indx(quote(s(z0)), x1)) → c7(INDX(mark(s1(quote(z0))), x1))
ACTIVE(indx(quote(s(z0)), x1)) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbl1(quote(s(z0)))) → c7(DBL1(mark(s1(quote(z0)))))
ACTIVE(dbl1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(s1(quote(s(z0)))) → c7(S1(mark(s1(quote(z0)))))
ACTIVE(s1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(quote(dbl(s(z0)))) → c7(QUOTE(mark(s(s(dbl(z0))))))
ACTIVE(quote(dbl(s(z0)))) → c7(ACTIVE(dbl(s(z0))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(QUOTE(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(QUOTE(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(quote(from(z0))) → c7(QUOTE(mark(cons(z0, from(s(z0))))))
ACTIVE(quote(from(z0))) → c7(ACTIVE(from(z0)))
ACTIVE(quote(dbl1(s(z0)))) → c7(QUOTE(mark(s1(s1(dbl1(z0))))))
ACTIVE(quote(dbl1(s(z0)))) → c7(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(quote(s(z0)))) → c7(QUOTE(mark(s1(quote(z0)))))
ACTIVE(quote(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
PROPER(dbl(dbl(z0))) → c45(DBL(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbl(s(z0))) → c45(DBL(s(proper(z0))), PROPER(s(z0)))
PROPER(dbl(dbls(z0))) → c45(DBL(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbl(cons(z0, z1))) → c45(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbl(sel(z0, z1))) → c45(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbl(indx(z0, z1))) → c45(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbl(from(z0))) → c45(DBL(from(proper(z0))), PROPER(from(z0)))
PROPER(dbl(dbl1(z0))) → c45(DBL(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbl(s1(z0))) → c45(DBL(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbl(sel1(z0, z1))) → c45(DBL(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbl(quote(z0))) → c45(DBL(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbl(0)) → c45(DBL(ok(0)))
PROPER(dbl(nil)) → c45(DBL(ok(nil)))
PROPER(dbl(01)) → c45(DBL(ok(01)))
PROPER(s(dbl(z0))) → c47(S(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(s(s(z0))) → c47(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(dbls(z0))) → c47(S(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(s(cons(z0, z1))) → c47(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(sel(z0, z1))) → c47(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(s(indx(z0, z1))) → c47(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(s(from(z0))) → c47(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(dbl1(z0))) → c47(S(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(s(s1(z0))) → c47(S(s1(proper(z0))), PROPER(s1(z0)))
PROPER(s(sel1(z0, z1))) → c47(S(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(s(quote(z0))) → c47(S(quote(proper(z0))), PROPER(quote(z0)))
PROPER(s(0)) → c47(S(ok(0)))
PROPER(s(nil)) → c47(S(ok(nil)))
PROPER(s(01)) → c47(S(ok(01)))
PROPER(dbls(dbl(z0))) → c48(DBLS(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbls(s(z0))) → c48(DBLS(s(proper(z0))), PROPER(s(z0)))
PROPER(dbls(dbls(z0))) → c48(DBLS(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbls(cons(z0, z1))) → c48(DBLS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbls(sel(z0, z1))) → c48(DBLS(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbls(indx(z0, z1))) → c48(DBLS(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbls(from(z0))) → c48(DBLS(from(proper(z0))), PROPER(from(z0)))
PROPER(dbls(dbl1(z0))) → c48(DBLS(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbls(s1(z0))) → c48(DBLS(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbls(sel1(z0, z1))) → c48(DBLS(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbls(quote(z0))) → c48(DBLS(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbls(0)) → c48(DBLS(ok(0)))
PROPER(dbls(nil)) → c48(DBLS(ok(nil)))
PROPER(dbls(01)) → c48(DBLS(ok(01)))
PROPER(cons(x0, dbl(z0))) → c50(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(cons(x0, s(z0))) → c50(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, dbls(z0))) → c50(CONS(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(cons(x0, cons(z0, z1))) → c50(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, sel(z0, z1))) → c50(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(cons(x0, indx(z0, z1))) → c50(CONS(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(cons(x0, from(z0))) → c50(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, dbl1(z0))) → c50(CONS(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(cons(x0, s1(z0))) → c50(CONS(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(cons(x0, sel1(z0, z1))) → c50(CONS(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(cons(x0, quote(z0))) → c50(CONS(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(cons(dbl(z0), x1)) → c50(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(cons(s(z0), x1)) → c50(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(dbls(z0), x1)) → c50(CONS(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c50(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(sel(z0, z1), x1)) → c50(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(cons(indx(z0, z1), x1)) → c50(CONS(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c50(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(dbl1(z0), x1)) → c50(CONS(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(cons(s1(z0), x1)) → c50(CONS(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(cons(sel1(z0, z1), x1)) → c50(CONS(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(cons(quote(z0), x1)) → c50(CONS(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c50(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c50(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, 01)) → c50(CONS(proper(x0), ok(01)), PROPER(x0))
PROPER(cons(0, x1)) → c50(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c50(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(01, x1)) → c50(CONS(ok(01), proper(x1)), PROPER(x1))
PROPER(sel(x0, dbl(z0))) → c51(SEL(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(sel(x0, s(z0))) → c51(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(sel(x0, dbls(z0))) → c51(SEL(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(sel(x0, cons(z0, z1))) → c51(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(sel(x0, sel(z0, z1))) → c51(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(sel(x0, indx(z0, z1))) → c51(SEL(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(sel(x0, from(z0))) → c51(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(sel(x0, dbl1(z0))) → c51(SEL(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(sel(x0, s1(z0))) → c51(SEL(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(sel(x0, sel1(z0, z1))) → c51(SEL(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(sel(x0, quote(z0))) → c51(SEL(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(sel(dbl(z0), x1)) → c51(SEL(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(sel(s(z0), x1)) → c51(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(sel(dbls(z0), x1)) → c51(SEL(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(sel(cons(z0, z1), x1)) → c51(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(sel(sel(z0, z1), x1)) → c51(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(sel(indx(z0, z1), x1)) → c51(SEL(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(sel(from(z0), x1)) → c51(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(sel(dbl1(z0), x1)) → c51(SEL(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(sel(s1(z0), x1)) → c51(SEL(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(sel(sel1(z0, z1), x1)) → c51(SEL(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(sel(quote(z0), x1)) → c51(SEL(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(sel(x0, 0)) → c51(SEL(proper(x0), ok(0)), PROPER(x0))
PROPER(sel(x0, nil)) → c51(SEL(proper(x0), ok(nil)), PROPER(x0))
PROPER(sel(x0, 01)) → c51(SEL(proper(x0), ok(01)), PROPER(x0))
PROPER(sel(0, x1)) → c51(SEL(ok(0), proper(x1)), PROPER(x1))
PROPER(sel(nil, x1)) → c51(SEL(ok(nil), proper(x1)), PROPER(x1))
PROPER(sel(01, x1)) → c51(SEL(ok(01), proper(x1)), PROPER(x1))
PROPER(indx(x0, dbl(z0))) → c52(INDX(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(indx(x0, s(z0))) → c52(INDX(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(indx(x0, dbls(z0))) → c52(INDX(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(indx(x0, cons(z0, z1))) → c52(INDX(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(indx(x0, sel(z0, z1))) → c52(INDX(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(indx(x0, indx(z0, z1))) → c52(INDX(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(indx(x0, from(z0))) → c52(INDX(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(indx(x0, dbl1(z0))) → c52(INDX(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(indx(x0, s1(z0))) → c52(INDX(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(indx(x0, sel1(z0, z1))) → c52(INDX(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(indx(x0, quote(z0))) → c52(INDX(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(indx(dbl(z0), x1)) → c52(INDX(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(indx(s(z0), x1)) → c52(INDX(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(indx(dbls(z0), x1)) → c52(INDX(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(indx(cons(z0, z1), x1)) → c52(INDX(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(indx(sel(z0, z1), x1)) → c52(INDX(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(indx(indx(z0, z1), x1)) → c52(INDX(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(indx(from(z0), x1)) → c52(INDX(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(indx(dbl1(z0), x1)) → c52(INDX(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(indx(s1(z0), x1)) → c52(INDX(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(indx(sel1(z0, z1), x1)) → c52(INDX(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(indx(quote(z0), x1)) → c52(INDX(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(indx(x0, 0)) → c52(INDX(proper(x0), ok(0)), PROPER(x0))
PROPER(indx(x0, nil)) → c52(INDX(proper(x0), ok(nil)), PROPER(x0))
PROPER(indx(x0, 01)) → c52(INDX(proper(x0), ok(01)), PROPER(x0))
PROPER(indx(0, x1)) → c52(INDX(ok(0), proper(x1)), PROPER(x1))
PROPER(indx(nil, x1)) → c52(INDX(ok(nil), proper(x1)), PROPER(x1))
PROPER(indx(01, x1)) → c52(INDX(ok(01), proper(x1)), PROPER(x1))
PROPER(from(dbl(z0))) → c53(FROM(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(from(s(z0))) → c53(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(dbls(z0))) → c53(FROM(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(from(cons(z0, z1))) → c53(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(sel(z0, z1))) → c53(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(from(indx(z0, z1))) → c53(FROM(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(from(from(z0))) → c53(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(dbl1(z0))) → c53(FROM(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(from(s1(z0))) → c53(FROM(s1(proper(z0))), PROPER(s1(z0)))
PROPER(from(sel1(z0, z1))) → c53(FROM(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(from(quote(z0))) → c53(FROM(quote(proper(z0))), PROPER(quote(z0)))
PROPER(from(0)) → c53(FROM(ok(0)))
PROPER(from(nil)) → c53(FROM(ok(nil)))
PROPER(from(01)) → c53(FROM(ok(01)))
PROPER(dbl1(dbl(z0))) → c54(DBL1(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbl1(s(z0))) → c54(DBL1(s(proper(z0))), PROPER(s(z0)))
PROPER(dbl1(dbls(z0))) → c54(DBL1(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbl1(cons(z0, z1))) → c54(DBL1(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbl1(sel(z0, z1))) → c54(DBL1(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbl1(indx(z0, z1))) → c54(DBL1(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbl1(from(z0))) → c54(DBL1(from(proper(z0))), PROPER(from(z0)))
PROPER(dbl1(dbl1(z0))) → c54(DBL1(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbl1(s1(z0))) → c54(DBL1(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbl1(sel1(z0, z1))) → c54(DBL1(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbl1(quote(z0))) → c54(DBL1(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbl1(0)) → c54(DBL1(ok(0)))
PROPER(dbl1(nil)) → c54(DBL1(ok(nil)))
PROPER(dbl1(01)) → c54(DBL1(ok(01)))
PROPER(s1(dbl(z0))) → c56(S1(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(s1(s(z0))) → c56(S1(s(proper(z0))), PROPER(s(z0)))
PROPER(s1(dbls(z0))) → c56(S1(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(s1(cons(z0, z1))) → c56(S1(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s1(sel(z0, z1))) → c56(S1(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(s1(indx(z0, z1))) → c56(S1(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(s1(from(z0))) → c56(S1(from(proper(z0))), PROPER(from(z0)))
PROPER(s1(dbl1(z0))) → c56(S1(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(s1(s1(z0))) → c56(S1(s1(proper(z0))), PROPER(s1(z0)))
PROPER(s1(sel1(z0, z1))) → c56(S1(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(s1(quote(z0))) → c56(S1(quote(proper(z0))), PROPER(quote(z0)))
PROPER(s1(0)) → c56(S1(ok(0)))
PROPER(s1(nil)) → c56(S1(ok(nil)))
PROPER(s1(01)) → c56(S1(ok(01)))
PROPER(sel1(x0, dbl(z0))) → c57(SEL1(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(sel1(x0, s(z0))) → c57(SEL1(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(sel1(x0, dbls(z0))) → c57(SEL1(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(sel1(x0, cons(z0, z1))) → c57(SEL1(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(sel1(x0, sel(z0, z1))) → c57(SEL1(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(sel1(x0, indx(z0, z1))) → c57(SEL1(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(sel1(x0, from(z0))) → c57(SEL1(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(sel1(x0, dbl1(z0))) → c57(SEL1(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(sel1(x0, s1(z0))) → c57(SEL1(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(sel1(x0, sel1(z0, z1))) → c57(SEL1(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(sel1(x0, quote(z0))) → c57(SEL1(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(sel1(dbl(z0), x1)) → c57(SEL1(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(sel1(s(z0), x1)) → c57(SEL1(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(sel1(dbls(z0), x1)) → c57(SEL1(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(sel1(cons(z0, z1), x1)) → c57(SEL1(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(sel1(sel(z0, z1), x1)) → c57(SEL1(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(sel1(indx(z0, z1), x1)) → c57(SEL1(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(sel1(from(z0), x1)) → c57(SEL1(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(sel1(dbl1(z0), x1)) → c57(SEL1(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(sel1(s1(z0), x1)) → c57(SEL1(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(sel1(sel1(z0, z1), x1)) → c57(SEL1(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(sel1(quote(z0), x1)) → c57(SEL1(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(sel1(x0, 0)) → c57(SEL1(proper(x0), ok(0)), PROPER(x0))
PROPER(sel1(x0, nil)) → c57(SEL1(proper(x0), ok(nil)), PROPER(x0))
PROPER(sel1(x0, 01)) → c57(SEL1(proper(x0), ok(01)), PROPER(x0))
PROPER(sel1(0, x1)) → c57(SEL1(ok(0), proper(x1)), PROPER(x1))
PROPER(sel1(nil, x1)) → c57(SEL1(ok(nil), proper(x1)), PROPER(x1))
PROPER(sel1(01, x1)) → c57(SEL1(ok(01), proper(x1)), PROPER(x1))
PROPER(quote(dbl(z0))) → c58(QUOTE(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(quote(0)) → c58(QUOTE(ok(0)), PROPER(0))
PROPER(quote(s(z0))) → c58(QUOTE(s(proper(z0))), PROPER(s(z0)))
PROPER(quote(dbls(z0))) → c58(QUOTE(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(quote(nil)) → c58(QUOTE(ok(nil)), PROPER(nil))
PROPER(quote(cons(z0, z1))) → c58(QUOTE(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(quote(sel(z0, z1))) → c58(QUOTE(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(quote(indx(z0, z1))) → c58(QUOTE(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(quote(from(z0))) → c58(QUOTE(from(proper(z0))), PROPER(from(z0)))
PROPER(quote(dbl1(z0))) → c58(QUOTE(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(quote(01)) → c58(QUOTE(ok(01)), PROPER(01))
PROPER(quote(s1(z0))) → c58(QUOTE(s1(proper(z0))), PROPER(s1(z0)))
PROPER(quote(sel1(z0, z1))) → c58(QUOTE(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(quote(quote(z0))) → c58(QUOTE(quote(proper(z0))), PROPER(quote(z0)))
K tuples:none
Defined Rule Symbols:
active, s, dbl, cons, dbls, sel, indx, s1, dbl1, sel1, quote, proper, from
Defined Pair Symbols:
ACTIVE, DBL, DBLS, SEL, INDX, DBL1, S1, SEL1, QUOTE, S, CONS, FROM, TOP, PROPER
Compound Symbols:
c5, c12, c15, c16, c19, c20, c24, c25, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c59, c60, c61, c62, c63, c8, c, c17, c17, c1, c18, c18, c2, c21, c21, c3, c22, c22, c4, c23, c23, c6, c26, c26, c7, c45, c45, c47, c47, c48, c48, c50, c50, c51, c51, c52, c52, c53, c53, c54, c54, c56, c56, c57, c57, c58
(89) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 3 trailing tuple parts
(90) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(dbl(0)) → mark(0)
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
active(dbls(nil)) → mark(nil)
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1)))
active(sel(0, cons(z0, z1))) → mark(z0)
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
active(indx(nil, z0)) → mark(nil)
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2)))
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(dbl1(0)) → mark(01)
active(dbl1(s(z0))) → mark(s1(s1(dbl1(z0))))
active(sel1(0, cons(z0, z1))) → mark(z0)
active(sel1(s(z0), cons(z1, z2))) → mark(sel1(z0, z2))
active(quote(0)) → mark(01)
active(quote(s(z0))) → mark(s1(quote(z0)))
active(quote(dbl(z0))) → mark(dbl1(z0))
active(quote(sel(z0, z1))) → mark(sel1(z0, z1))
active(dbl(z0)) → dbl(active(z0))
active(dbls(z0)) → dbls(active(z0))
active(sel(z0, z1)) → sel(active(z0), z1)
active(sel(z0, z1)) → sel(z0, active(z1))
active(indx(z0, z1)) → indx(active(z0), z1)
active(dbl1(z0)) → dbl1(active(z0))
active(s1(z0)) → s1(active(z0))
active(sel1(z0, z1)) → sel1(active(z0), z1)
active(sel1(z0, z1)) → sel1(z0, active(z1))
active(quote(z0)) → quote(active(z0))
s(ok(z0)) → ok(s(z0))
dbl(mark(z0)) → mark(dbl(z0))
dbl(ok(z0)) → ok(dbl(z0))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
dbls(mark(z0)) → mark(dbls(z0))
dbls(ok(z0)) → ok(dbls(z0))
sel(mark(z0), z1) → mark(sel(z0, z1))
sel(z0, mark(z1)) → mark(sel(z0, z1))
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
indx(mark(z0), z1) → mark(indx(z0, z1))
indx(ok(z0), ok(z1)) → ok(indx(z0, z1))
s1(mark(z0)) → mark(s1(z0))
s1(ok(z0)) → ok(s1(z0))
dbl1(mark(z0)) → mark(dbl1(z0))
dbl1(ok(z0)) → ok(dbl1(z0))
sel1(mark(z0), z1) → mark(sel1(z0, z1))
sel1(z0, mark(z1)) → mark(sel1(z0, z1))
sel1(ok(z0), ok(z1)) → ok(sel1(z0, z1))
quote(mark(z0)) → mark(quote(z0))
quote(ok(z0)) → ok(quote(z0))
proper(dbl(z0)) → dbl(proper(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(dbls(z0)) → dbls(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
proper(indx(z0, z1)) → indx(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(dbl1(z0)) → dbl1(proper(z0))
proper(01) → ok(01)
proper(s1(z0)) → s1(proper(z0))
proper(sel1(z0, z1)) → sel1(proper(z0), proper(z1))
proper(quote(z0)) → quote(proper(z0))
from(ok(z0)) → ok(from(z0))
Tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)))
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0))))))
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0))))))
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0)))
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(indx(sel1(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(indx(sel1(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel1(z0, z2)), x1), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(indx(quote(dbl(z0)), x1)) → c21(INDX(mark(dbl1(z0)), x1), ACTIVE(quote(dbl(z0))))
ACTIVE(indx(quote(sel(z0, z1)), x1)) → c21(INDX(mark(sel1(z0, z1)), x1), ACTIVE(quote(sel(z0, z1))))
ACTIVE(indx(dbl(z0), x1)) → c21(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
ACTIVE(indx(dbls(z0), x1)) → c21(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(indx(z0, z1), x1)) → c21(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1)))
ACTIVE(indx(dbl1(z0), x1)) → c21(INDX(dbl1(active(z0)), x1), ACTIVE(dbl1(z0)))
ACTIVE(indx(s1(z0), x1)) → c21(INDX(s1(active(z0)), x1), ACTIVE(s1(z0)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(active(z0), z1), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(z0, active(z1)), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(quote(z0), x1)) → c21(INDX(quote(active(z0)), x1), ACTIVE(quote(z0)))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)))
ACTIVE(indx(dbl(0), x1)) → c21(INDX(mark(0), x1))
ACTIVE(indx(dbls(nil), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(indx(indx(nil, z0), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0))))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1))
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0)))
ACTIVE(dbl1(sel(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl1(sel(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl1(sel1(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl1(sel1(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl1(quote(dbl(z0)))) → c22(DBL1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl1(quote(sel(z0, z1)))) → c22(DBL1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl1(dbl(z0))) → c22(DBL1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl1(dbls(z0))) → c22(DBL1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(indx(z0, z1))) → c22(DBL1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl1(dbl1(z0))) → c22(DBL1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl1(s1(z0))) → c22(DBL1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(quote(z0))) → c22(DBL1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(dbl1(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(dbl(0))) → c22(DBL1(mark(0)))
ACTIVE(dbl1(dbls(nil))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(indx(nil, z0))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(dbl1(0))) → c22(DBL1(mark(01)))
ACTIVE(dbl(dbl1(s(z0)))) → c4(DBL(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(DBLS(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(INDX(mark(s1(s1(dbl1(z0)))), x1))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(DBL1(mark(s(s(dbl(z0))))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(ACTIVE(dbl(s(z0))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(DBL1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(DBL1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl1(from(z0))) → c4(DBL1(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl1(from(z0))) → c4(ACTIVE(from(z0)))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(DBL1(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(s1(sel(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(s1(sel(s(z0), cons(z1, z2)))) → c23(S1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(s1(sel1(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(s1(sel1(s(z0), cons(z1, z2)))) → c23(S1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(s1(quote(dbl(z0)))) → c23(S1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(s1(quote(sel(z0, z1)))) → c23(S1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(s1(dbl(z0))) → c23(S1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(s1(dbls(z0))) → c23(S1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(s1(indx(z0, z1))) → c23(S1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(s1(dbl1(z0))) → c23(S1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(s1(s1(z0))) → c23(S1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(quote(z0))) → c23(S1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(s1(dbl(0))) → c23(S1(mark(0)))
ACTIVE(s1(dbls(nil))) → c23(S1(mark(nil)))
ACTIVE(s1(indx(nil, z0))) → c23(S1(mark(nil)))
ACTIVE(s1(dbl1(0))) → c23(S1(mark(01)))
ACTIVE(s1(dbl(s(z0)))) → c6(S1(mark(s(s(dbl(z0))))))
ACTIVE(s1(dbl(s(z0)))) → c6(ACTIVE(dbl(s(z0))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(S1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(S1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(s1(from(z0))) → c6(S1(mark(cons(z0, from(s(z0))))))
ACTIVE(s1(from(z0))) → c6(ACTIVE(from(z0)))
ACTIVE(s1(dbl1(s(z0)))) → c6(S1(mark(s1(s1(dbl1(z0))))))
ACTIVE(s1(dbl1(s(z0)))) → c6(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(sel(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(quote(sel(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(quote(sel1(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(quote(sel1(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(quote(quote(dbl(z0)))) → c26(QUOTE(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(quote(quote(sel(z0, z1)))) → c26(QUOTE(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(quote(dbl(z0))) → c26(QUOTE(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(quote(dbls(z0))) → c26(QUOTE(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(quote(indx(z0, z1))) → c26(QUOTE(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(quote(dbl1(z0))) → c26(QUOTE(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(quote(s1(z0))) → c26(QUOTE(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(quote(z0))) → c26(QUOTE(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(quote(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(quote(0))) → c22(DBL1(mark(01)))
ACTIVE(s1(quote(0))) → c23(S1(mark(01)))
ACTIVE(quote(dbl(0))) → c26(QUOTE(mark(0)))
ACTIVE(quote(dbls(nil))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(indx(nil, z0))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(dbl1(0))) → c26(QUOTE(mark(01)))
ACTIVE(quote(quote(0))) → c26(QUOTE(mark(01)))
ACTIVE(dbl(quote(s(z0)))) → c7(DBL(mark(s1(quote(z0)))))
ACTIVE(dbl(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(s(z0)))) → c7(DBLS(mark(s1(quote(z0)))))
ACTIVE(dbls(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(indx(quote(s(z0)), x1)) → c7(INDX(mark(s1(quote(z0))), x1))
ACTIVE(indx(quote(s(z0)), x1)) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbl1(quote(s(z0)))) → c7(DBL1(mark(s1(quote(z0)))))
ACTIVE(dbl1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(s1(quote(s(z0)))) → c7(S1(mark(s1(quote(z0)))))
ACTIVE(s1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(quote(dbl(s(z0)))) → c7(QUOTE(mark(s(s(dbl(z0))))))
ACTIVE(quote(dbl(s(z0)))) → c7(ACTIVE(dbl(s(z0))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(QUOTE(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(QUOTE(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(quote(from(z0))) → c7(QUOTE(mark(cons(z0, from(s(z0))))))
ACTIVE(quote(from(z0))) → c7(ACTIVE(from(z0)))
ACTIVE(quote(dbl1(s(z0)))) → c7(QUOTE(mark(s1(s1(dbl1(z0))))))
ACTIVE(quote(dbl1(s(z0)))) → c7(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(quote(s(z0)))) → c7(QUOTE(mark(s1(quote(z0)))))
ACTIVE(quote(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
PROPER(dbl(dbl(z0))) → c45(DBL(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbl(s(z0))) → c45(DBL(s(proper(z0))), PROPER(s(z0)))
PROPER(dbl(dbls(z0))) → c45(DBL(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbl(cons(z0, z1))) → c45(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbl(sel(z0, z1))) → c45(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbl(indx(z0, z1))) → c45(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbl(from(z0))) → c45(DBL(from(proper(z0))), PROPER(from(z0)))
PROPER(dbl(dbl1(z0))) → c45(DBL(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbl(s1(z0))) → c45(DBL(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbl(sel1(z0, z1))) → c45(DBL(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbl(quote(z0))) → c45(DBL(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbl(0)) → c45(DBL(ok(0)))
PROPER(dbl(nil)) → c45(DBL(ok(nil)))
PROPER(dbl(01)) → c45(DBL(ok(01)))
PROPER(s(dbl(z0))) → c47(S(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(s(s(z0))) → c47(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(dbls(z0))) → c47(S(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(s(cons(z0, z1))) → c47(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(sel(z0, z1))) → c47(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(s(indx(z0, z1))) → c47(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(s(from(z0))) → c47(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(dbl1(z0))) → c47(S(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(s(s1(z0))) → c47(S(s1(proper(z0))), PROPER(s1(z0)))
PROPER(s(sel1(z0, z1))) → c47(S(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(s(quote(z0))) → c47(S(quote(proper(z0))), PROPER(quote(z0)))
PROPER(s(0)) → c47(S(ok(0)))
PROPER(s(nil)) → c47(S(ok(nil)))
PROPER(s(01)) → c47(S(ok(01)))
PROPER(dbls(dbl(z0))) → c48(DBLS(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbls(s(z0))) → c48(DBLS(s(proper(z0))), PROPER(s(z0)))
PROPER(dbls(dbls(z0))) → c48(DBLS(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbls(cons(z0, z1))) → c48(DBLS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbls(sel(z0, z1))) → c48(DBLS(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbls(indx(z0, z1))) → c48(DBLS(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbls(from(z0))) → c48(DBLS(from(proper(z0))), PROPER(from(z0)))
PROPER(dbls(dbl1(z0))) → c48(DBLS(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbls(s1(z0))) → c48(DBLS(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbls(sel1(z0, z1))) → c48(DBLS(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbls(quote(z0))) → c48(DBLS(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbls(0)) → c48(DBLS(ok(0)))
PROPER(dbls(nil)) → c48(DBLS(ok(nil)))
PROPER(dbls(01)) → c48(DBLS(ok(01)))
PROPER(cons(x0, dbl(z0))) → c50(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(cons(x0, s(z0))) → c50(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, dbls(z0))) → c50(CONS(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(cons(x0, cons(z0, z1))) → c50(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, sel(z0, z1))) → c50(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(cons(x0, indx(z0, z1))) → c50(CONS(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(cons(x0, from(z0))) → c50(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, dbl1(z0))) → c50(CONS(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(cons(x0, s1(z0))) → c50(CONS(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(cons(x0, sel1(z0, z1))) → c50(CONS(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(cons(x0, quote(z0))) → c50(CONS(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(cons(dbl(z0), x1)) → c50(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(cons(s(z0), x1)) → c50(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(dbls(z0), x1)) → c50(CONS(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c50(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(sel(z0, z1), x1)) → c50(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(cons(indx(z0, z1), x1)) → c50(CONS(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c50(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(dbl1(z0), x1)) → c50(CONS(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(cons(s1(z0), x1)) → c50(CONS(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(cons(sel1(z0, z1), x1)) → c50(CONS(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(cons(quote(z0), x1)) → c50(CONS(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c50(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c50(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, 01)) → c50(CONS(proper(x0), ok(01)), PROPER(x0))
PROPER(cons(0, x1)) → c50(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c50(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(01, x1)) → c50(CONS(ok(01), proper(x1)), PROPER(x1))
PROPER(sel(x0, dbl(z0))) → c51(SEL(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(sel(x0, s(z0))) → c51(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(sel(x0, dbls(z0))) → c51(SEL(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(sel(x0, cons(z0, z1))) → c51(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(sel(x0, sel(z0, z1))) → c51(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(sel(x0, indx(z0, z1))) → c51(SEL(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(sel(x0, from(z0))) → c51(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(sel(x0, dbl1(z0))) → c51(SEL(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(sel(x0, s1(z0))) → c51(SEL(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(sel(x0, sel1(z0, z1))) → c51(SEL(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(sel(x0, quote(z0))) → c51(SEL(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(sel(dbl(z0), x1)) → c51(SEL(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(sel(s(z0), x1)) → c51(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(sel(dbls(z0), x1)) → c51(SEL(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(sel(cons(z0, z1), x1)) → c51(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(sel(sel(z0, z1), x1)) → c51(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(sel(indx(z0, z1), x1)) → c51(SEL(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(sel(from(z0), x1)) → c51(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(sel(dbl1(z0), x1)) → c51(SEL(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(sel(s1(z0), x1)) → c51(SEL(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(sel(sel1(z0, z1), x1)) → c51(SEL(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(sel(quote(z0), x1)) → c51(SEL(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(sel(x0, 0)) → c51(SEL(proper(x0), ok(0)), PROPER(x0))
PROPER(sel(x0, nil)) → c51(SEL(proper(x0), ok(nil)), PROPER(x0))
PROPER(sel(x0, 01)) → c51(SEL(proper(x0), ok(01)), PROPER(x0))
PROPER(sel(0, x1)) → c51(SEL(ok(0), proper(x1)), PROPER(x1))
PROPER(sel(nil, x1)) → c51(SEL(ok(nil), proper(x1)), PROPER(x1))
PROPER(sel(01, x1)) → c51(SEL(ok(01), proper(x1)), PROPER(x1))
PROPER(indx(x0, dbl(z0))) → c52(INDX(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(indx(x0, s(z0))) → c52(INDX(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(indx(x0, dbls(z0))) → c52(INDX(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(indx(x0, cons(z0, z1))) → c52(INDX(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(indx(x0, sel(z0, z1))) → c52(INDX(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(indx(x0, indx(z0, z1))) → c52(INDX(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(indx(x0, from(z0))) → c52(INDX(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(indx(x0, dbl1(z0))) → c52(INDX(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(indx(x0, s1(z0))) → c52(INDX(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(indx(x0, sel1(z0, z1))) → c52(INDX(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(indx(x0, quote(z0))) → c52(INDX(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(indx(dbl(z0), x1)) → c52(INDX(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(indx(s(z0), x1)) → c52(INDX(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(indx(dbls(z0), x1)) → c52(INDX(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(indx(cons(z0, z1), x1)) → c52(INDX(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(indx(sel(z0, z1), x1)) → c52(INDX(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(indx(indx(z0, z1), x1)) → c52(INDX(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(indx(from(z0), x1)) → c52(INDX(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(indx(dbl1(z0), x1)) → c52(INDX(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(indx(s1(z0), x1)) → c52(INDX(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(indx(sel1(z0, z1), x1)) → c52(INDX(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(indx(quote(z0), x1)) → c52(INDX(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(indx(x0, 0)) → c52(INDX(proper(x0), ok(0)), PROPER(x0))
PROPER(indx(x0, nil)) → c52(INDX(proper(x0), ok(nil)), PROPER(x0))
PROPER(indx(x0, 01)) → c52(INDX(proper(x0), ok(01)), PROPER(x0))
PROPER(indx(0, x1)) → c52(INDX(ok(0), proper(x1)), PROPER(x1))
PROPER(indx(nil, x1)) → c52(INDX(ok(nil), proper(x1)), PROPER(x1))
PROPER(indx(01, x1)) → c52(INDX(ok(01), proper(x1)), PROPER(x1))
PROPER(from(dbl(z0))) → c53(FROM(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(from(s(z0))) → c53(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(dbls(z0))) → c53(FROM(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(from(cons(z0, z1))) → c53(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(sel(z0, z1))) → c53(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(from(indx(z0, z1))) → c53(FROM(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(from(from(z0))) → c53(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(dbl1(z0))) → c53(FROM(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(from(s1(z0))) → c53(FROM(s1(proper(z0))), PROPER(s1(z0)))
PROPER(from(sel1(z0, z1))) → c53(FROM(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(from(quote(z0))) → c53(FROM(quote(proper(z0))), PROPER(quote(z0)))
PROPER(from(0)) → c53(FROM(ok(0)))
PROPER(from(nil)) → c53(FROM(ok(nil)))
PROPER(from(01)) → c53(FROM(ok(01)))
PROPER(dbl1(dbl(z0))) → c54(DBL1(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbl1(s(z0))) → c54(DBL1(s(proper(z0))), PROPER(s(z0)))
PROPER(dbl1(dbls(z0))) → c54(DBL1(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbl1(cons(z0, z1))) → c54(DBL1(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbl1(sel(z0, z1))) → c54(DBL1(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbl1(indx(z0, z1))) → c54(DBL1(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbl1(from(z0))) → c54(DBL1(from(proper(z0))), PROPER(from(z0)))
PROPER(dbl1(dbl1(z0))) → c54(DBL1(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbl1(s1(z0))) → c54(DBL1(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbl1(sel1(z0, z1))) → c54(DBL1(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbl1(quote(z0))) → c54(DBL1(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbl1(0)) → c54(DBL1(ok(0)))
PROPER(dbl1(nil)) → c54(DBL1(ok(nil)))
PROPER(dbl1(01)) → c54(DBL1(ok(01)))
PROPER(s1(dbl(z0))) → c56(S1(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(s1(s(z0))) → c56(S1(s(proper(z0))), PROPER(s(z0)))
PROPER(s1(dbls(z0))) → c56(S1(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(s1(cons(z0, z1))) → c56(S1(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s1(sel(z0, z1))) → c56(S1(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(s1(indx(z0, z1))) → c56(S1(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(s1(from(z0))) → c56(S1(from(proper(z0))), PROPER(from(z0)))
PROPER(s1(dbl1(z0))) → c56(S1(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(s1(s1(z0))) → c56(S1(s1(proper(z0))), PROPER(s1(z0)))
PROPER(s1(sel1(z0, z1))) → c56(S1(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(s1(quote(z0))) → c56(S1(quote(proper(z0))), PROPER(quote(z0)))
PROPER(s1(0)) → c56(S1(ok(0)))
PROPER(s1(nil)) → c56(S1(ok(nil)))
PROPER(s1(01)) → c56(S1(ok(01)))
PROPER(sel1(x0, dbl(z0))) → c57(SEL1(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(sel1(x0, s(z0))) → c57(SEL1(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(sel1(x0, dbls(z0))) → c57(SEL1(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(sel1(x0, cons(z0, z1))) → c57(SEL1(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(sel1(x0, sel(z0, z1))) → c57(SEL1(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(sel1(x0, indx(z0, z1))) → c57(SEL1(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(sel1(x0, from(z0))) → c57(SEL1(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(sel1(x0, dbl1(z0))) → c57(SEL1(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(sel1(x0, s1(z0))) → c57(SEL1(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(sel1(x0, sel1(z0, z1))) → c57(SEL1(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(sel1(x0, quote(z0))) → c57(SEL1(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(sel1(dbl(z0), x1)) → c57(SEL1(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(sel1(s(z0), x1)) → c57(SEL1(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(sel1(dbls(z0), x1)) → c57(SEL1(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(sel1(cons(z0, z1), x1)) → c57(SEL1(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(sel1(sel(z0, z1), x1)) → c57(SEL1(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(sel1(indx(z0, z1), x1)) → c57(SEL1(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(sel1(from(z0), x1)) → c57(SEL1(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(sel1(dbl1(z0), x1)) → c57(SEL1(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(sel1(s1(z0), x1)) → c57(SEL1(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(sel1(sel1(z0, z1), x1)) → c57(SEL1(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(sel1(quote(z0), x1)) → c57(SEL1(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(sel1(x0, 0)) → c57(SEL1(proper(x0), ok(0)), PROPER(x0))
PROPER(sel1(x0, nil)) → c57(SEL1(proper(x0), ok(nil)), PROPER(x0))
PROPER(sel1(x0, 01)) → c57(SEL1(proper(x0), ok(01)), PROPER(x0))
PROPER(sel1(0, x1)) → c57(SEL1(ok(0), proper(x1)), PROPER(x1))
PROPER(sel1(nil, x1)) → c57(SEL1(ok(nil), proper(x1)), PROPER(x1))
PROPER(sel1(01, x1)) → c57(SEL1(ok(01), proper(x1)), PROPER(x1))
PROPER(quote(dbl(z0))) → c58(QUOTE(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(quote(s(z0))) → c58(QUOTE(s(proper(z0))), PROPER(s(z0)))
PROPER(quote(dbls(z0))) → c58(QUOTE(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(quote(cons(z0, z1))) → c58(QUOTE(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(quote(sel(z0, z1))) → c58(QUOTE(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(quote(indx(z0, z1))) → c58(QUOTE(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(quote(from(z0))) → c58(QUOTE(from(proper(z0))), PROPER(from(z0)))
PROPER(quote(dbl1(z0))) → c58(QUOTE(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(quote(s1(z0))) → c58(QUOTE(s1(proper(z0))), PROPER(s1(z0)))
PROPER(quote(sel1(z0, z1))) → c58(QUOTE(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(quote(quote(z0))) → c58(QUOTE(quote(proper(z0))), PROPER(quote(z0)))
PROPER(quote(0)) → c58(QUOTE(ok(0)))
PROPER(quote(nil)) → c58(QUOTE(ok(nil)))
PROPER(quote(01)) → c58(QUOTE(ok(01)))
S tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(mark(z0)) → c62(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)))
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0))))))
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0))))))
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0)))
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(indx(sel1(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(indx(sel1(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel1(z0, z2)), x1), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(indx(quote(dbl(z0)), x1)) → c21(INDX(mark(dbl1(z0)), x1), ACTIVE(quote(dbl(z0))))
ACTIVE(indx(quote(sel(z0, z1)), x1)) → c21(INDX(mark(sel1(z0, z1)), x1), ACTIVE(quote(sel(z0, z1))))
ACTIVE(indx(dbl(z0), x1)) → c21(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
ACTIVE(indx(dbls(z0), x1)) → c21(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(indx(z0, z1), x1)) → c21(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1)))
ACTIVE(indx(dbl1(z0), x1)) → c21(INDX(dbl1(active(z0)), x1), ACTIVE(dbl1(z0)))
ACTIVE(indx(s1(z0), x1)) → c21(INDX(s1(active(z0)), x1), ACTIVE(s1(z0)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(active(z0), z1), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(z0, active(z1)), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(quote(z0), x1)) → c21(INDX(quote(active(z0)), x1), ACTIVE(quote(z0)))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)))
ACTIVE(indx(dbl(0), x1)) → c21(INDX(mark(0), x1))
ACTIVE(indx(dbls(nil), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(indx(indx(nil, z0), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0))))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1))
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0)))
ACTIVE(dbl1(sel(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl1(sel(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl1(sel1(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl1(sel1(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl1(quote(dbl(z0)))) → c22(DBL1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl1(quote(sel(z0, z1)))) → c22(DBL1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl1(dbl(z0))) → c22(DBL1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl1(dbls(z0))) → c22(DBL1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(indx(z0, z1))) → c22(DBL1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl1(dbl1(z0))) → c22(DBL1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl1(s1(z0))) → c22(DBL1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(quote(z0))) → c22(DBL1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(dbl1(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(dbl(0))) → c22(DBL1(mark(0)))
ACTIVE(dbl1(dbls(nil))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(indx(nil, z0))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(dbl1(0))) → c22(DBL1(mark(01)))
ACTIVE(dbl(dbl1(s(z0)))) → c4(DBL(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(DBLS(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(INDX(mark(s1(s1(dbl1(z0)))), x1))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(DBL1(mark(s(s(dbl(z0))))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(ACTIVE(dbl(s(z0))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(DBL1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(DBL1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl1(from(z0))) → c4(DBL1(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl1(from(z0))) → c4(ACTIVE(from(z0)))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(DBL1(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(s1(sel(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(s1(sel(s(z0), cons(z1, z2)))) → c23(S1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(s1(sel1(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(s1(sel1(s(z0), cons(z1, z2)))) → c23(S1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(s1(quote(dbl(z0)))) → c23(S1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(s1(quote(sel(z0, z1)))) → c23(S1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(s1(dbl(z0))) → c23(S1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(s1(dbls(z0))) → c23(S1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(s1(indx(z0, z1))) → c23(S1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(s1(dbl1(z0))) → c23(S1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(s1(s1(z0))) → c23(S1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(quote(z0))) → c23(S1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(s1(dbl(0))) → c23(S1(mark(0)))
ACTIVE(s1(dbls(nil))) → c23(S1(mark(nil)))
ACTIVE(s1(indx(nil, z0))) → c23(S1(mark(nil)))
ACTIVE(s1(dbl1(0))) → c23(S1(mark(01)))
ACTIVE(s1(dbl(s(z0)))) → c6(S1(mark(s(s(dbl(z0))))))
ACTIVE(s1(dbl(s(z0)))) → c6(ACTIVE(dbl(s(z0))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(S1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(S1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(s1(from(z0))) → c6(S1(mark(cons(z0, from(s(z0))))))
ACTIVE(s1(from(z0))) → c6(ACTIVE(from(z0)))
ACTIVE(s1(dbl1(s(z0)))) → c6(S1(mark(s1(s1(dbl1(z0))))))
ACTIVE(s1(dbl1(s(z0)))) → c6(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(sel(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(quote(sel(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(quote(sel1(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(quote(sel1(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(quote(quote(dbl(z0)))) → c26(QUOTE(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(quote(quote(sel(z0, z1)))) → c26(QUOTE(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(quote(dbl(z0))) → c26(QUOTE(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(quote(dbls(z0))) → c26(QUOTE(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(quote(indx(z0, z1))) → c26(QUOTE(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(quote(dbl1(z0))) → c26(QUOTE(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(quote(s1(z0))) → c26(QUOTE(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(quote(z0))) → c26(QUOTE(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(quote(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(quote(0))) → c22(DBL1(mark(01)))
ACTIVE(s1(quote(0))) → c23(S1(mark(01)))
ACTIVE(quote(dbl(0))) → c26(QUOTE(mark(0)))
ACTIVE(quote(dbls(nil))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(indx(nil, z0))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(dbl1(0))) → c26(QUOTE(mark(01)))
ACTIVE(quote(quote(0))) → c26(QUOTE(mark(01)))
ACTIVE(dbl(quote(s(z0)))) → c7(DBL(mark(s1(quote(z0)))))
ACTIVE(dbl(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(s(z0)))) → c7(DBLS(mark(s1(quote(z0)))))
ACTIVE(dbls(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(indx(quote(s(z0)), x1)) → c7(INDX(mark(s1(quote(z0))), x1))
ACTIVE(indx(quote(s(z0)), x1)) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbl1(quote(s(z0)))) → c7(DBL1(mark(s1(quote(z0)))))
ACTIVE(dbl1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(s1(quote(s(z0)))) → c7(S1(mark(s1(quote(z0)))))
ACTIVE(s1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(quote(dbl(s(z0)))) → c7(QUOTE(mark(s(s(dbl(z0))))))
ACTIVE(quote(dbl(s(z0)))) → c7(ACTIVE(dbl(s(z0))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(QUOTE(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(QUOTE(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(quote(from(z0))) → c7(QUOTE(mark(cons(z0, from(s(z0))))))
ACTIVE(quote(from(z0))) → c7(ACTIVE(from(z0)))
ACTIVE(quote(dbl1(s(z0)))) → c7(QUOTE(mark(s1(s1(dbl1(z0))))))
ACTIVE(quote(dbl1(s(z0)))) → c7(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(quote(s(z0)))) → c7(QUOTE(mark(s1(quote(z0)))))
ACTIVE(quote(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
PROPER(dbl(dbl(z0))) → c45(DBL(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbl(s(z0))) → c45(DBL(s(proper(z0))), PROPER(s(z0)))
PROPER(dbl(dbls(z0))) → c45(DBL(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbl(cons(z0, z1))) → c45(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbl(sel(z0, z1))) → c45(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbl(indx(z0, z1))) → c45(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbl(from(z0))) → c45(DBL(from(proper(z0))), PROPER(from(z0)))
PROPER(dbl(dbl1(z0))) → c45(DBL(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbl(s1(z0))) → c45(DBL(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbl(sel1(z0, z1))) → c45(DBL(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbl(quote(z0))) → c45(DBL(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbl(0)) → c45(DBL(ok(0)))
PROPER(dbl(nil)) → c45(DBL(ok(nil)))
PROPER(dbl(01)) → c45(DBL(ok(01)))
PROPER(s(dbl(z0))) → c47(S(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(s(s(z0))) → c47(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(dbls(z0))) → c47(S(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(s(cons(z0, z1))) → c47(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(sel(z0, z1))) → c47(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(s(indx(z0, z1))) → c47(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(s(from(z0))) → c47(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(dbl1(z0))) → c47(S(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(s(s1(z0))) → c47(S(s1(proper(z0))), PROPER(s1(z0)))
PROPER(s(sel1(z0, z1))) → c47(S(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(s(quote(z0))) → c47(S(quote(proper(z0))), PROPER(quote(z0)))
PROPER(s(0)) → c47(S(ok(0)))
PROPER(s(nil)) → c47(S(ok(nil)))
PROPER(s(01)) → c47(S(ok(01)))
PROPER(dbls(dbl(z0))) → c48(DBLS(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbls(s(z0))) → c48(DBLS(s(proper(z0))), PROPER(s(z0)))
PROPER(dbls(dbls(z0))) → c48(DBLS(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbls(cons(z0, z1))) → c48(DBLS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbls(sel(z0, z1))) → c48(DBLS(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbls(indx(z0, z1))) → c48(DBLS(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbls(from(z0))) → c48(DBLS(from(proper(z0))), PROPER(from(z0)))
PROPER(dbls(dbl1(z0))) → c48(DBLS(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbls(s1(z0))) → c48(DBLS(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbls(sel1(z0, z1))) → c48(DBLS(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbls(quote(z0))) → c48(DBLS(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbls(0)) → c48(DBLS(ok(0)))
PROPER(dbls(nil)) → c48(DBLS(ok(nil)))
PROPER(dbls(01)) → c48(DBLS(ok(01)))
PROPER(cons(x0, dbl(z0))) → c50(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(cons(x0, s(z0))) → c50(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, dbls(z0))) → c50(CONS(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(cons(x0, cons(z0, z1))) → c50(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, sel(z0, z1))) → c50(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(cons(x0, indx(z0, z1))) → c50(CONS(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(cons(x0, from(z0))) → c50(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, dbl1(z0))) → c50(CONS(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(cons(x0, s1(z0))) → c50(CONS(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(cons(x0, sel1(z0, z1))) → c50(CONS(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(cons(x0, quote(z0))) → c50(CONS(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(cons(dbl(z0), x1)) → c50(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(cons(s(z0), x1)) → c50(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(dbls(z0), x1)) → c50(CONS(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c50(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(sel(z0, z1), x1)) → c50(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(cons(indx(z0, z1), x1)) → c50(CONS(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c50(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(dbl1(z0), x1)) → c50(CONS(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(cons(s1(z0), x1)) → c50(CONS(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(cons(sel1(z0, z1), x1)) → c50(CONS(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(cons(quote(z0), x1)) → c50(CONS(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c50(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c50(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, 01)) → c50(CONS(proper(x0), ok(01)), PROPER(x0))
PROPER(cons(0, x1)) → c50(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c50(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(01, x1)) → c50(CONS(ok(01), proper(x1)), PROPER(x1))
PROPER(sel(x0, dbl(z0))) → c51(SEL(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(sel(x0, s(z0))) → c51(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(sel(x0, dbls(z0))) → c51(SEL(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(sel(x0, cons(z0, z1))) → c51(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(sel(x0, sel(z0, z1))) → c51(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(sel(x0, indx(z0, z1))) → c51(SEL(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(sel(x0, from(z0))) → c51(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(sel(x0, dbl1(z0))) → c51(SEL(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(sel(x0, s1(z0))) → c51(SEL(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(sel(x0, sel1(z0, z1))) → c51(SEL(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(sel(x0, quote(z0))) → c51(SEL(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(sel(dbl(z0), x1)) → c51(SEL(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(sel(s(z0), x1)) → c51(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(sel(dbls(z0), x1)) → c51(SEL(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(sel(cons(z0, z1), x1)) → c51(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(sel(sel(z0, z1), x1)) → c51(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(sel(indx(z0, z1), x1)) → c51(SEL(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(sel(from(z0), x1)) → c51(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(sel(dbl1(z0), x1)) → c51(SEL(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(sel(s1(z0), x1)) → c51(SEL(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(sel(sel1(z0, z1), x1)) → c51(SEL(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(sel(quote(z0), x1)) → c51(SEL(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(sel(x0, 0)) → c51(SEL(proper(x0), ok(0)), PROPER(x0))
PROPER(sel(x0, nil)) → c51(SEL(proper(x0), ok(nil)), PROPER(x0))
PROPER(sel(x0, 01)) → c51(SEL(proper(x0), ok(01)), PROPER(x0))
PROPER(sel(0, x1)) → c51(SEL(ok(0), proper(x1)), PROPER(x1))
PROPER(sel(nil, x1)) → c51(SEL(ok(nil), proper(x1)), PROPER(x1))
PROPER(sel(01, x1)) → c51(SEL(ok(01), proper(x1)), PROPER(x1))
PROPER(indx(x0, dbl(z0))) → c52(INDX(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(indx(x0, s(z0))) → c52(INDX(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(indx(x0, dbls(z0))) → c52(INDX(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(indx(x0, cons(z0, z1))) → c52(INDX(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(indx(x0, sel(z0, z1))) → c52(INDX(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(indx(x0, indx(z0, z1))) → c52(INDX(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(indx(x0, from(z0))) → c52(INDX(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(indx(x0, dbl1(z0))) → c52(INDX(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(indx(x0, s1(z0))) → c52(INDX(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(indx(x0, sel1(z0, z1))) → c52(INDX(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(indx(x0, quote(z0))) → c52(INDX(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(indx(dbl(z0), x1)) → c52(INDX(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(indx(s(z0), x1)) → c52(INDX(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(indx(dbls(z0), x1)) → c52(INDX(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(indx(cons(z0, z1), x1)) → c52(INDX(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(indx(sel(z0, z1), x1)) → c52(INDX(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(indx(indx(z0, z1), x1)) → c52(INDX(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(indx(from(z0), x1)) → c52(INDX(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(indx(dbl1(z0), x1)) → c52(INDX(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(indx(s1(z0), x1)) → c52(INDX(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(indx(sel1(z0, z1), x1)) → c52(INDX(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(indx(quote(z0), x1)) → c52(INDX(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(indx(x0, 0)) → c52(INDX(proper(x0), ok(0)), PROPER(x0))
PROPER(indx(x0, nil)) → c52(INDX(proper(x0), ok(nil)), PROPER(x0))
PROPER(indx(x0, 01)) → c52(INDX(proper(x0), ok(01)), PROPER(x0))
PROPER(indx(0, x1)) → c52(INDX(ok(0), proper(x1)), PROPER(x1))
PROPER(indx(nil, x1)) → c52(INDX(ok(nil), proper(x1)), PROPER(x1))
PROPER(indx(01, x1)) → c52(INDX(ok(01), proper(x1)), PROPER(x1))
PROPER(from(dbl(z0))) → c53(FROM(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(from(s(z0))) → c53(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(dbls(z0))) → c53(FROM(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(from(cons(z0, z1))) → c53(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(sel(z0, z1))) → c53(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(from(indx(z0, z1))) → c53(FROM(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(from(from(z0))) → c53(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(dbl1(z0))) → c53(FROM(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(from(s1(z0))) → c53(FROM(s1(proper(z0))), PROPER(s1(z0)))
PROPER(from(sel1(z0, z1))) → c53(FROM(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(from(quote(z0))) → c53(FROM(quote(proper(z0))), PROPER(quote(z0)))
PROPER(from(0)) → c53(FROM(ok(0)))
PROPER(from(nil)) → c53(FROM(ok(nil)))
PROPER(from(01)) → c53(FROM(ok(01)))
PROPER(dbl1(dbl(z0))) → c54(DBL1(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbl1(s(z0))) → c54(DBL1(s(proper(z0))), PROPER(s(z0)))
PROPER(dbl1(dbls(z0))) → c54(DBL1(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbl1(cons(z0, z1))) → c54(DBL1(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbl1(sel(z0, z1))) → c54(DBL1(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbl1(indx(z0, z1))) → c54(DBL1(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbl1(from(z0))) → c54(DBL1(from(proper(z0))), PROPER(from(z0)))
PROPER(dbl1(dbl1(z0))) → c54(DBL1(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbl1(s1(z0))) → c54(DBL1(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbl1(sel1(z0, z1))) → c54(DBL1(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbl1(quote(z0))) → c54(DBL1(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbl1(0)) → c54(DBL1(ok(0)))
PROPER(dbl1(nil)) → c54(DBL1(ok(nil)))
PROPER(dbl1(01)) → c54(DBL1(ok(01)))
PROPER(s1(dbl(z0))) → c56(S1(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(s1(s(z0))) → c56(S1(s(proper(z0))), PROPER(s(z0)))
PROPER(s1(dbls(z0))) → c56(S1(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(s1(cons(z0, z1))) → c56(S1(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s1(sel(z0, z1))) → c56(S1(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(s1(indx(z0, z1))) → c56(S1(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(s1(from(z0))) → c56(S1(from(proper(z0))), PROPER(from(z0)))
PROPER(s1(dbl1(z0))) → c56(S1(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(s1(s1(z0))) → c56(S1(s1(proper(z0))), PROPER(s1(z0)))
PROPER(s1(sel1(z0, z1))) → c56(S1(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(s1(quote(z0))) → c56(S1(quote(proper(z0))), PROPER(quote(z0)))
PROPER(s1(0)) → c56(S1(ok(0)))
PROPER(s1(nil)) → c56(S1(ok(nil)))
PROPER(s1(01)) → c56(S1(ok(01)))
PROPER(sel1(x0, dbl(z0))) → c57(SEL1(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(sel1(x0, s(z0))) → c57(SEL1(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(sel1(x0, dbls(z0))) → c57(SEL1(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(sel1(x0, cons(z0, z1))) → c57(SEL1(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(sel1(x0, sel(z0, z1))) → c57(SEL1(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(sel1(x0, indx(z0, z1))) → c57(SEL1(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(sel1(x0, from(z0))) → c57(SEL1(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(sel1(x0, dbl1(z0))) → c57(SEL1(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(sel1(x0, s1(z0))) → c57(SEL1(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(sel1(x0, sel1(z0, z1))) → c57(SEL1(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(sel1(x0, quote(z0))) → c57(SEL1(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(sel1(dbl(z0), x1)) → c57(SEL1(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(sel1(s(z0), x1)) → c57(SEL1(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(sel1(dbls(z0), x1)) → c57(SEL1(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(sel1(cons(z0, z1), x1)) → c57(SEL1(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(sel1(sel(z0, z1), x1)) → c57(SEL1(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(sel1(indx(z0, z1), x1)) → c57(SEL1(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(sel1(from(z0), x1)) → c57(SEL1(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(sel1(dbl1(z0), x1)) → c57(SEL1(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(sel1(s1(z0), x1)) → c57(SEL1(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(sel1(sel1(z0, z1), x1)) → c57(SEL1(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(sel1(quote(z0), x1)) → c57(SEL1(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(sel1(x0, 0)) → c57(SEL1(proper(x0), ok(0)), PROPER(x0))
PROPER(sel1(x0, nil)) → c57(SEL1(proper(x0), ok(nil)), PROPER(x0))
PROPER(sel1(x0, 01)) → c57(SEL1(proper(x0), ok(01)), PROPER(x0))
PROPER(sel1(0, x1)) → c57(SEL1(ok(0), proper(x1)), PROPER(x1))
PROPER(sel1(nil, x1)) → c57(SEL1(ok(nil), proper(x1)), PROPER(x1))
PROPER(sel1(01, x1)) → c57(SEL1(ok(01), proper(x1)), PROPER(x1))
PROPER(quote(dbl(z0))) → c58(QUOTE(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(quote(s(z0))) → c58(QUOTE(s(proper(z0))), PROPER(s(z0)))
PROPER(quote(dbls(z0))) → c58(QUOTE(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(quote(cons(z0, z1))) → c58(QUOTE(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(quote(sel(z0, z1))) → c58(QUOTE(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(quote(indx(z0, z1))) → c58(QUOTE(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(quote(from(z0))) → c58(QUOTE(from(proper(z0))), PROPER(from(z0)))
PROPER(quote(dbl1(z0))) → c58(QUOTE(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(quote(s1(z0))) → c58(QUOTE(s1(proper(z0))), PROPER(s1(z0)))
PROPER(quote(sel1(z0, z1))) → c58(QUOTE(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(quote(quote(z0))) → c58(QUOTE(quote(proper(z0))), PROPER(quote(z0)))
PROPER(quote(0)) → c58(QUOTE(ok(0)))
PROPER(quote(nil)) → c58(QUOTE(ok(nil)))
PROPER(quote(01)) → c58(QUOTE(ok(01)))
K tuples:none
Defined Rule Symbols:
active, s, dbl, cons, dbls, sel, indx, s1, dbl1, sel1, quote, proper, from
Defined Pair Symbols:
ACTIVE, DBL, DBLS, SEL, INDX, DBL1, S1, SEL1, QUOTE, S, CONS, FROM, TOP, PROPER
Compound Symbols:
c5, c12, c15, c16, c19, c20, c24, c25, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c59, c60, c61, c62, c63, c8, c, c17, c17, c1, c18, c18, c2, c21, c21, c3, c22, c22, c4, c23, c23, c6, c26, c26, c7, c45, c45, c47, c47, c48, c48, c50, c50, c51, c51, c52, c52, c53, c53, c54, c54, c56, c56, c57, c57, c58, c58
(91) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
TOP(
mark(
z0)) →
c62(
TOP(
proper(
z0)),
PROPER(
z0)) by
TOP(mark(dbl(z0))) → c62(TOP(dbl(proper(z0))), PROPER(dbl(z0)))
TOP(mark(0)) → c62(TOP(ok(0)), PROPER(0))
TOP(mark(s(z0))) → c62(TOP(s(proper(z0))), PROPER(s(z0)))
TOP(mark(dbls(z0))) → c62(TOP(dbls(proper(z0))), PROPER(dbls(z0)))
TOP(mark(nil)) → c62(TOP(ok(nil)), PROPER(nil))
TOP(mark(cons(z0, z1))) → c62(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
TOP(mark(sel(z0, z1))) → c62(TOP(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
TOP(mark(indx(z0, z1))) → c62(TOP(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
TOP(mark(from(z0))) → c62(TOP(from(proper(z0))), PROPER(from(z0)))
TOP(mark(dbl1(z0))) → c62(TOP(dbl1(proper(z0))), PROPER(dbl1(z0)))
TOP(mark(01)) → c62(TOP(ok(01)), PROPER(01))
TOP(mark(s1(z0))) → c62(TOP(s1(proper(z0))), PROPER(s1(z0)))
TOP(mark(sel1(z0, z1))) → c62(TOP(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
TOP(mark(quote(z0))) → c62(TOP(quote(proper(z0))), PROPER(quote(z0)))
(92) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(dbl(0)) → mark(0)
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
active(dbls(nil)) → mark(nil)
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1)))
active(sel(0, cons(z0, z1))) → mark(z0)
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
active(indx(nil, z0)) → mark(nil)
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2)))
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(dbl1(0)) → mark(01)
active(dbl1(s(z0))) → mark(s1(s1(dbl1(z0))))
active(sel1(0, cons(z0, z1))) → mark(z0)
active(sel1(s(z0), cons(z1, z2))) → mark(sel1(z0, z2))
active(quote(0)) → mark(01)
active(quote(s(z0))) → mark(s1(quote(z0)))
active(quote(dbl(z0))) → mark(dbl1(z0))
active(quote(sel(z0, z1))) → mark(sel1(z0, z1))
active(dbl(z0)) → dbl(active(z0))
active(dbls(z0)) → dbls(active(z0))
active(sel(z0, z1)) → sel(active(z0), z1)
active(sel(z0, z1)) → sel(z0, active(z1))
active(indx(z0, z1)) → indx(active(z0), z1)
active(dbl1(z0)) → dbl1(active(z0))
active(s1(z0)) → s1(active(z0))
active(sel1(z0, z1)) → sel1(active(z0), z1)
active(sel1(z0, z1)) → sel1(z0, active(z1))
active(quote(z0)) → quote(active(z0))
s(ok(z0)) → ok(s(z0))
dbl(mark(z0)) → mark(dbl(z0))
dbl(ok(z0)) → ok(dbl(z0))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
dbls(mark(z0)) → mark(dbls(z0))
dbls(ok(z0)) → ok(dbls(z0))
sel(mark(z0), z1) → mark(sel(z0, z1))
sel(z0, mark(z1)) → mark(sel(z0, z1))
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
indx(mark(z0), z1) → mark(indx(z0, z1))
indx(ok(z0), ok(z1)) → ok(indx(z0, z1))
s1(mark(z0)) → mark(s1(z0))
s1(ok(z0)) → ok(s1(z0))
dbl1(mark(z0)) → mark(dbl1(z0))
dbl1(ok(z0)) → ok(dbl1(z0))
sel1(mark(z0), z1) → mark(sel1(z0, z1))
sel1(z0, mark(z1)) → mark(sel1(z0, z1))
sel1(ok(z0), ok(z1)) → ok(sel1(z0, z1))
quote(mark(z0)) → mark(quote(z0))
quote(ok(z0)) → ok(quote(z0))
proper(dbl(z0)) → dbl(proper(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(dbls(z0)) → dbls(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
proper(indx(z0, z1)) → indx(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(dbl1(z0)) → dbl1(proper(z0))
proper(01) → ok(01)
proper(s1(z0)) → s1(proper(z0))
proper(sel1(z0, z1)) → sel1(proper(z0), proper(z1))
proper(quote(z0)) → quote(proper(z0))
from(ok(z0)) → ok(from(z0))
Tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)))
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0))))))
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0))))))
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0)))
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(indx(sel1(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(indx(sel1(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel1(z0, z2)), x1), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(indx(quote(dbl(z0)), x1)) → c21(INDX(mark(dbl1(z0)), x1), ACTIVE(quote(dbl(z0))))
ACTIVE(indx(quote(sel(z0, z1)), x1)) → c21(INDX(mark(sel1(z0, z1)), x1), ACTIVE(quote(sel(z0, z1))))
ACTIVE(indx(dbl(z0), x1)) → c21(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
ACTIVE(indx(dbls(z0), x1)) → c21(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(indx(z0, z1), x1)) → c21(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1)))
ACTIVE(indx(dbl1(z0), x1)) → c21(INDX(dbl1(active(z0)), x1), ACTIVE(dbl1(z0)))
ACTIVE(indx(s1(z0), x1)) → c21(INDX(s1(active(z0)), x1), ACTIVE(s1(z0)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(active(z0), z1), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(z0, active(z1)), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(quote(z0), x1)) → c21(INDX(quote(active(z0)), x1), ACTIVE(quote(z0)))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)))
ACTIVE(indx(dbl(0), x1)) → c21(INDX(mark(0), x1))
ACTIVE(indx(dbls(nil), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(indx(indx(nil, z0), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0))))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1))
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0)))
ACTIVE(dbl1(sel(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl1(sel(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl1(sel1(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl1(sel1(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl1(quote(dbl(z0)))) → c22(DBL1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl1(quote(sel(z0, z1)))) → c22(DBL1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl1(dbl(z0))) → c22(DBL1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl1(dbls(z0))) → c22(DBL1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(indx(z0, z1))) → c22(DBL1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl1(dbl1(z0))) → c22(DBL1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl1(s1(z0))) → c22(DBL1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(quote(z0))) → c22(DBL1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(dbl1(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(dbl(0))) → c22(DBL1(mark(0)))
ACTIVE(dbl1(dbls(nil))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(indx(nil, z0))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(dbl1(0))) → c22(DBL1(mark(01)))
ACTIVE(dbl(dbl1(s(z0)))) → c4(DBL(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(DBLS(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(INDX(mark(s1(s1(dbl1(z0)))), x1))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(DBL1(mark(s(s(dbl(z0))))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(ACTIVE(dbl(s(z0))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(DBL1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(DBL1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl1(from(z0))) → c4(DBL1(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl1(from(z0))) → c4(ACTIVE(from(z0)))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(DBL1(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(s1(sel(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(s1(sel(s(z0), cons(z1, z2)))) → c23(S1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(s1(sel1(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(s1(sel1(s(z0), cons(z1, z2)))) → c23(S1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(s1(quote(dbl(z0)))) → c23(S1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(s1(quote(sel(z0, z1)))) → c23(S1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(s1(dbl(z0))) → c23(S1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(s1(dbls(z0))) → c23(S1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(s1(indx(z0, z1))) → c23(S1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(s1(dbl1(z0))) → c23(S1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(s1(s1(z0))) → c23(S1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(quote(z0))) → c23(S1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(s1(dbl(0))) → c23(S1(mark(0)))
ACTIVE(s1(dbls(nil))) → c23(S1(mark(nil)))
ACTIVE(s1(indx(nil, z0))) → c23(S1(mark(nil)))
ACTIVE(s1(dbl1(0))) → c23(S1(mark(01)))
ACTIVE(s1(dbl(s(z0)))) → c6(S1(mark(s(s(dbl(z0))))))
ACTIVE(s1(dbl(s(z0)))) → c6(ACTIVE(dbl(s(z0))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(S1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(S1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(s1(from(z0))) → c6(S1(mark(cons(z0, from(s(z0))))))
ACTIVE(s1(from(z0))) → c6(ACTIVE(from(z0)))
ACTIVE(s1(dbl1(s(z0)))) → c6(S1(mark(s1(s1(dbl1(z0))))))
ACTIVE(s1(dbl1(s(z0)))) → c6(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(sel(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(quote(sel(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(quote(sel1(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(quote(sel1(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(quote(quote(dbl(z0)))) → c26(QUOTE(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(quote(quote(sel(z0, z1)))) → c26(QUOTE(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(quote(dbl(z0))) → c26(QUOTE(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(quote(dbls(z0))) → c26(QUOTE(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(quote(indx(z0, z1))) → c26(QUOTE(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(quote(dbl1(z0))) → c26(QUOTE(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(quote(s1(z0))) → c26(QUOTE(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(quote(z0))) → c26(QUOTE(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(quote(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(quote(0))) → c22(DBL1(mark(01)))
ACTIVE(s1(quote(0))) → c23(S1(mark(01)))
ACTIVE(quote(dbl(0))) → c26(QUOTE(mark(0)))
ACTIVE(quote(dbls(nil))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(indx(nil, z0))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(dbl1(0))) → c26(QUOTE(mark(01)))
ACTIVE(quote(quote(0))) → c26(QUOTE(mark(01)))
ACTIVE(dbl(quote(s(z0)))) → c7(DBL(mark(s1(quote(z0)))))
ACTIVE(dbl(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(s(z0)))) → c7(DBLS(mark(s1(quote(z0)))))
ACTIVE(dbls(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(indx(quote(s(z0)), x1)) → c7(INDX(mark(s1(quote(z0))), x1))
ACTIVE(indx(quote(s(z0)), x1)) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbl1(quote(s(z0)))) → c7(DBL1(mark(s1(quote(z0)))))
ACTIVE(dbl1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(s1(quote(s(z0)))) → c7(S1(mark(s1(quote(z0)))))
ACTIVE(s1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(quote(dbl(s(z0)))) → c7(QUOTE(mark(s(s(dbl(z0))))))
ACTIVE(quote(dbl(s(z0)))) → c7(ACTIVE(dbl(s(z0))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(QUOTE(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(QUOTE(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(quote(from(z0))) → c7(QUOTE(mark(cons(z0, from(s(z0))))))
ACTIVE(quote(from(z0))) → c7(ACTIVE(from(z0)))
ACTIVE(quote(dbl1(s(z0)))) → c7(QUOTE(mark(s1(s1(dbl1(z0))))))
ACTIVE(quote(dbl1(s(z0)))) → c7(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(quote(s(z0)))) → c7(QUOTE(mark(s1(quote(z0)))))
ACTIVE(quote(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
PROPER(dbl(dbl(z0))) → c45(DBL(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbl(s(z0))) → c45(DBL(s(proper(z0))), PROPER(s(z0)))
PROPER(dbl(dbls(z0))) → c45(DBL(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbl(cons(z0, z1))) → c45(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbl(sel(z0, z1))) → c45(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbl(indx(z0, z1))) → c45(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbl(from(z0))) → c45(DBL(from(proper(z0))), PROPER(from(z0)))
PROPER(dbl(dbl1(z0))) → c45(DBL(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbl(s1(z0))) → c45(DBL(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbl(sel1(z0, z1))) → c45(DBL(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbl(quote(z0))) → c45(DBL(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbl(0)) → c45(DBL(ok(0)))
PROPER(dbl(nil)) → c45(DBL(ok(nil)))
PROPER(dbl(01)) → c45(DBL(ok(01)))
PROPER(s(dbl(z0))) → c47(S(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(s(s(z0))) → c47(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(dbls(z0))) → c47(S(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(s(cons(z0, z1))) → c47(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(sel(z0, z1))) → c47(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(s(indx(z0, z1))) → c47(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(s(from(z0))) → c47(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(dbl1(z0))) → c47(S(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(s(s1(z0))) → c47(S(s1(proper(z0))), PROPER(s1(z0)))
PROPER(s(sel1(z0, z1))) → c47(S(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(s(quote(z0))) → c47(S(quote(proper(z0))), PROPER(quote(z0)))
PROPER(s(0)) → c47(S(ok(0)))
PROPER(s(nil)) → c47(S(ok(nil)))
PROPER(s(01)) → c47(S(ok(01)))
PROPER(dbls(dbl(z0))) → c48(DBLS(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbls(s(z0))) → c48(DBLS(s(proper(z0))), PROPER(s(z0)))
PROPER(dbls(dbls(z0))) → c48(DBLS(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbls(cons(z0, z1))) → c48(DBLS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbls(sel(z0, z1))) → c48(DBLS(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbls(indx(z0, z1))) → c48(DBLS(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbls(from(z0))) → c48(DBLS(from(proper(z0))), PROPER(from(z0)))
PROPER(dbls(dbl1(z0))) → c48(DBLS(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbls(s1(z0))) → c48(DBLS(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbls(sel1(z0, z1))) → c48(DBLS(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbls(quote(z0))) → c48(DBLS(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbls(0)) → c48(DBLS(ok(0)))
PROPER(dbls(nil)) → c48(DBLS(ok(nil)))
PROPER(dbls(01)) → c48(DBLS(ok(01)))
PROPER(cons(x0, dbl(z0))) → c50(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(cons(x0, s(z0))) → c50(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, dbls(z0))) → c50(CONS(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(cons(x0, cons(z0, z1))) → c50(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, sel(z0, z1))) → c50(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(cons(x0, indx(z0, z1))) → c50(CONS(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(cons(x0, from(z0))) → c50(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, dbl1(z0))) → c50(CONS(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(cons(x0, s1(z0))) → c50(CONS(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(cons(x0, sel1(z0, z1))) → c50(CONS(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(cons(x0, quote(z0))) → c50(CONS(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(cons(dbl(z0), x1)) → c50(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(cons(s(z0), x1)) → c50(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(dbls(z0), x1)) → c50(CONS(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c50(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(sel(z0, z1), x1)) → c50(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(cons(indx(z0, z1), x1)) → c50(CONS(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c50(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(dbl1(z0), x1)) → c50(CONS(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(cons(s1(z0), x1)) → c50(CONS(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(cons(sel1(z0, z1), x1)) → c50(CONS(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(cons(quote(z0), x1)) → c50(CONS(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c50(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c50(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, 01)) → c50(CONS(proper(x0), ok(01)), PROPER(x0))
PROPER(cons(0, x1)) → c50(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c50(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(01, x1)) → c50(CONS(ok(01), proper(x1)), PROPER(x1))
PROPER(sel(x0, dbl(z0))) → c51(SEL(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(sel(x0, s(z0))) → c51(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(sel(x0, dbls(z0))) → c51(SEL(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(sel(x0, cons(z0, z1))) → c51(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(sel(x0, sel(z0, z1))) → c51(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(sel(x0, indx(z0, z1))) → c51(SEL(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(sel(x0, from(z0))) → c51(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(sel(x0, dbl1(z0))) → c51(SEL(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(sel(x0, s1(z0))) → c51(SEL(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(sel(x0, sel1(z0, z1))) → c51(SEL(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(sel(x0, quote(z0))) → c51(SEL(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(sel(dbl(z0), x1)) → c51(SEL(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(sel(s(z0), x1)) → c51(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(sel(dbls(z0), x1)) → c51(SEL(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(sel(cons(z0, z1), x1)) → c51(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(sel(sel(z0, z1), x1)) → c51(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(sel(indx(z0, z1), x1)) → c51(SEL(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(sel(from(z0), x1)) → c51(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(sel(dbl1(z0), x1)) → c51(SEL(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(sel(s1(z0), x1)) → c51(SEL(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(sel(sel1(z0, z1), x1)) → c51(SEL(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(sel(quote(z0), x1)) → c51(SEL(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(sel(x0, 0)) → c51(SEL(proper(x0), ok(0)), PROPER(x0))
PROPER(sel(x0, nil)) → c51(SEL(proper(x0), ok(nil)), PROPER(x0))
PROPER(sel(x0, 01)) → c51(SEL(proper(x0), ok(01)), PROPER(x0))
PROPER(sel(0, x1)) → c51(SEL(ok(0), proper(x1)), PROPER(x1))
PROPER(sel(nil, x1)) → c51(SEL(ok(nil), proper(x1)), PROPER(x1))
PROPER(sel(01, x1)) → c51(SEL(ok(01), proper(x1)), PROPER(x1))
PROPER(indx(x0, dbl(z0))) → c52(INDX(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(indx(x0, s(z0))) → c52(INDX(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(indx(x0, dbls(z0))) → c52(INDX(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(indx(x0, cons(z0, z1))) → c52(INDX(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(indx(x0, sel(z0, z1))) → c52(INDX(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(indx(x0, indx(z0, z1))) → c52(INDX(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(indx(x0, from(z0))) → c52(INDX(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(indx(x0, dbl1(z0))) → c52(INDX(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(indx(x0, s1(z0))) → c52(INDX(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(indx(x0, sel1(z0, z1))) → c52(INDX(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(indx(x0, quote(z0))) → c52(INDX(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(indx(dbl(z0), x1)) → c52(INDX(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(indx(s(z0), x1)) → c52(INDX(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(indx(dbls(z0), x1)) → c52(INDX(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(indx(cons(z0, z1), x1)) → c52(INDX(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(indx(sel(z0, z1), x1)) → c52(INDX(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(indx(indx(z0, z1), x1)) → c52(INDX(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(indx(from(z0), x1)) → c52(INDX(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(indx(dbl1(z0), x1)) → c52(INDX(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(indx(s1(z0), x1)) → c52(INDX(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(indx(sel1(z0, z1), x1)) → c52(INDX(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(indx(quote(z0), x1)) → c52(INDX(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(indx(x0, 0)) → c52(INDX(proper(x0), ok(0)), PROPER(x0))
PROPER(indx(x0, nil)) → c52(INDX(proper(x0), ok(nil)), PROPER(x0))
PROPER(indx(x0, 01)) → c52(INDX(proper(x0), ok(01)), PROPER(x0))
PROPER(indx(0, x1)) → c52(INDX(ok(0), proper(x1)), PROPER(x1))
PROPER(indx(nil, x1)) → c52(INDX(ok(nil), proper(x1)), PROPER(x1))
PROPER(indx(01, x1)) → c52(INDX(ok(01), proper(x1)), PROPER(x1))
PROPER(from(dbl(z0))) → c53(FROM(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(from(s(z0))) → c53(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(dbls(z0))) → c53(FROM(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(from(cons(z0, z1))) → c53(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(sel(z0, z1))) → c53(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(from(indx(z0, z1))) → c53(FROM(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(from(from(z0))) → c53(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(dbl1(z0))) → c53(FROM(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(from(s1(z0))) → c53(FROM(s1(proper(z0))), PROPER(s1(z0)))
PROPER(from(sel1(z0, z1))) → c53(FROM(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(from(quote(z0))) → c53(FROM(quote(proper(z0))), PROPER(quote(z0)))
PROPER(from(0)) → c53(FROM(ok(0)))
PROPER(from(nil)) → c53(FROM(ok(nil)))
PROPER(from(01)) → c53(FROM(ok(01)))
PROPER(dbl1(dbl(z0))) → c54(DBL1(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbl1(s(z0))) → c54(DBL1(s(proper(z0))), PROPER(s(z0)))
PROPER(dbl1(dbls(z0))) → c54(DBL1(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbl1(cons(z0, z1))) → c54(DBL1(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbl1(sel(z0, z1))) → c54(DBL1(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbl1(indx(z0, z1))) → c54(DBL1(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbl1(from(z0))) → c54(DBL1(from(proper(z0))), PROPER(from(z0)))
PROPER(dbl1(dbl1(z0))) → c54(DBL1(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbl1(s1(z0))) → c54(DBL1(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbl1(sel1(z0, z1))) → c54(DBL1(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbl1(quote(z0))) → c54(DBL1(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbl1(0)) → c54(DBL1(ok(0)))
PROPER(dbl1(nil)) → c54(DBL1(ok(nil)))
PROPER(dbl1(01)) → c54(DBL1(ok(01)))
PROPER(s1(dbl(z0))) → c56(S1(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(s1(s(z0))) → c56(S1(s(proper(z0))), PROPER(s(z0)))
PROPER(s1(dbls(z0))) → c56(S1(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(s1(cons(z0, z1))) → c56(S1(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s1(sel(z0, z1))) → c56(S1(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(s1(indx(z0, z1))) → c56(S1(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(s1(from(z0))) → c56(S1(from(proper(z0))), PROPER(from(z0)))
PROPER(s1(dbl1(z0))) → c56(S1(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(s1(s1(z0))) → c56(S1(s1(proper(z0))), PROPER(s1(z0)))
PROPER(s1(sel1(z0, z1))) → c56(S1(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(s1(quote(z0))) → c56(S1(quote(proper(z0))), PROPER(quote(z0)))
PROPER(s1(0)) → c56(S1(ok(0)))
PROPER(s1(nil)) → c56(S1(ok(nil)))
PROPER(s1(01)) → c56(S1(ok(01)))
PROPER(sel1(x0, dbl(z0))) → c57(SEL1(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(sel1(x0, s(z0))) → c57(SEL1(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(sel1(x0, dbls(z0))) → c57(SEL1(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(sel1(x0, cons(z0, z1))) → c57(SEL1(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(sel1(x0, sel(z0, z1))) → c57(SEL1(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(sel1(x0, indx(z0, z1))) → c57(SEL1(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(sel1(x0, from(z0))) → c57(SEL1(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(sel1(x0, dbl1(z0))) → c57(SEL1(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(sel1(x0, s1(z0))) → c57(SEL1(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(sel1(x0, sel1(z0, z1))) → c57(SEL1(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(sel1(x0, quote(z0))) → c57(SEL1(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(sel1(dbl(z0), x1)) → c57(SEL1(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(sel1(s(z0), x1)) → c57(SEL1(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(sel1(dbls(z0), x1)) → c57(SEL1(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(sel1(cons(z0, z1), x1)) → c57(SEL1(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(sel1(sel(z0, z1), x1)) → c57(SEL1(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(sel1(indx(z0, z1), x1)) → c57(SEL1(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(sel1(from(z0), x1)) → c57(SEL1(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(sel1(dbl1(z0), x1)) → c57(SEL1(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(sel1(s1(z0), x1)) → c57(SEL1(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(sel1(sel1(z0, z1), x1)) → c57(SEL1(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(sel1(quote(z0), x1)) → c57(SEL1(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(sel1(x0, 0)) → c57(SEL1(proper(x0), ok(0)), PROPER(x0))
PROPER(sel1(x0, nil)) → c57(SEL1(proper(x0), ok(nil)), PROPER(x0))
PROPER(sel1(x0, 01)) → c57(SEL1(proper(x0), ok(01)), PROPER(x0))
PROPER(sel1(0, x1)) → c57(SEL1(ok(0), proper(x1)), PROPER(x1))
PROPER(sel1(nil, x1)) → c57(SEL1(ok(nil), proper(x1)), PROPER(x1))
PROPER(sel1(01, x1)) → c57(SEL1(ok(01), proper(x1)), PROPER(x1))
PROPER(quote(dbl(z0))) → c58(QUOTE(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(quote(s(z0))) → c58(QUOTE(s(proper(z0))), PROPER(s(z0)))
PROPER(quote(dbls(z0))) → c58(QUOTE(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(quote(cons(z0, z1))) → c58(QUOTE(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(quote(sel(z0, z1))) → c58(QUOTE(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(quote(indx(z0, z1))) → c58(QUOTE(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(quote(from(z0))) → c58(QUOTE(from(proper(z0))), PROPER(from(z0)))
PROPER(quote(dbl1(z0))) → c58(QUOTE(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(quote(s1(z0))) → c58(QUOTE(s1(proper(z0))), PROPER(s1(z0)))
PROPER(quote(sel1(z0, z1))) → c58(QUOTE(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(quote(quote(z0))) → c58(QUOTE(quote(proper(z0))), PROPER(quote(z0)))
PROPER(quote(0)) → c58(QUOTE(ok(0)))
PROPER(quote(nil)) → c58(QUOTE(ok(nil)))
PROPER(quote(01)) → c58(QUOTE(ok(01)))
TOP(mark(dbl(z0))) → c62(TOP(dbl(proper(z0))), PROPER(dbl(z0)))
TOP(mark(0)) → c62(TOP(ok(0)), PROPER(0))
TOP(mark(s(z0))) → c62(TOP(s(proper(z0))), PROPER(s(z0)))
TOP(mark(dbls(z0))) → c62(TOP(dbls(proper(z0))), PROPER(dbls(z0)))
TOP(mark(nil)) → c62(TOP(ok(nil)), PROPER(nil))
TOP(mark(cons(z0, z1))) → c62(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
TOP(mark(sel(z0, z1))) → c62(TOP(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
TOP(mark(indx(z0, z1))) → c62(TOP(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
TOP(mark(from(z0))) → c62(TOP(from(proper(z0))), PROPER(from(z0)))
TOP(mark(dbl1(z0))) → c62(TOP(dbl1(proper(z0))), PROPER(dbl1(z0)))
TOP(mark(01)) → c62(TOP(ok(01)), PROPER(01))
TOP(mark(s1(z0))) → c62(TOP(s1(proper(z0))), PROPER(s1(z0)))
TOP(mark(sel1(z0, z1))) → c62(TOP(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
TOP(mark(quote(z0))) → c62(TOP(quote(proper(z0))), PROPER(quote(z0)))
S tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)))
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0))))))
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0))))))
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0)))
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(indx(sel1(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(indx(sel1(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel1(z0, z2)), x1), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(indx(quote(dbl(z0)), x1)) → c21(INDX(mark(dbl1(z0)), x1), ACTIVE(quote(dbl(z0))))
ACTIVE(indx(quote(sel(z0, z1)), x1)) → c21(INDX(mark(sel1(z0, z1)), x1), ACTIVE(quote(sel(z0, z1))))
ACTIVE(indx(dbl(z0), x1)) → c21(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
ACTIVE(indx(dbls(z0), x1)) → c21(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(indx(z0, z1), x1)) → c21(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1)))
ACTIVE(indx(dbl1(z0), x1)) → c21(INDX(dbl1(active(z0)), x1), ACTIVE(dbl1(z0)))
ACTIVE(indx(s1(z0), x1)) → c21(INDX(s1(active(z0)), x1), ACTIVE(s1(z0)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(active(z0), z1), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(z0, active(z1)), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(quote(z0), x1)) → c21(INDX(quote(active(z0)), x1), ACTIVE(quote(z0)))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)))
ACTIVE(indx(dbl(0), x1)) → c21(INDX(mark(0), x1))
ACTIVE(indx(dbls(nil), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(indx(indx(nil, z0), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0))))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1))
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0)))
ACTIVE(dbl1(sel(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl1(sel(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl1(sel1(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl1(sel1(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl1(quote(dbl(z0)))) → c22(DBL1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl1(quote(sel(z0, z1)))) → c22(DBL1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl1(dbl(z0))) → c22(DBL1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl1(dbls(z0))) → c22(DBL1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(indx(z0, z1))) → c22(DBL1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl1(dbl1(z0))) → c22(DBL1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl1(s1(z0))) → c22(DBL1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(quote(z0))) → c22(DBL1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(dbl1(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(dbl(0))) → c22(DBL1(mark(0)))
ACTIVE(dbl1(dbls(nil))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(indx(nil, z0))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(dbl1(0))) → c22(DBL1(mark(01)))
ACTIVE(dbl(dbl1(s(z0)))) → c4(DBL(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(DBLS(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(INDX(mark(s1(s1(dbl1(z0)))), x1))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(DBL1(mark(s(s(dbl(z0))))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(ACTIVE(dbl(s(z0))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(DBL1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(DBL1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl1(from(z0))) → c4(DBL1(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl1(from(z0))) → c4(ACTIVE(from(z0)))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(DBL1(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(s1(sel(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(s1(sel(s(z0), cons(z1, z2)))) → c23(S1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(s1(sel1(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(s1(sel1(s(z0), cons(z1, z2)))) → c23(S1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(s1(quote(dbl(z0)))) → c23(S1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(s1(quote(sel(z0, z1)))) → c23(S1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(s1(dbl(z0))) → c23(S1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(s1(dbls(z0))) → c23(S1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(s1(indx(z0, z1))) → c23(S1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(s1(dbl1(z0))) → c23(S1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(s1(s1(z0))) → c23(S1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(quote(z0))) → c23(S1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(s1(dbl(0))) → c23(S1(mark(0)))
ACTIVE(s1(dbls(nil))) → c23(S1(mark(nil)))
ACTIVE(s1(indx(nil, z0))) → c23(S1(mark(nil)))
ACTIVE(s1(dbl1(0))) → c23(S1(mark(01)))
ACTIVE(s1(dbl(s(z0)))) → c6(S1(mark(s(s(dbl(z0))))))
ACTIVE(s1(dbl(s(z0)))) → c6(ACTIVE(dbl(s(z0))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(S1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(S1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(s1(from(z0))) → c6(S1(mark(cons(z0, from(s(z0))))))
ACTIVE(s1(from(z0))) → c6(ACTIVE(from(z0)))
ACTIVE(s1(dbl1(s(z0)))) → c6(S1(mark(s1(s1(dbl1(z0))))))
ACTIVE(s1(dbl1(s(z0)))) → c6(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(sel(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(quote(sel(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(quote(sel1(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(quote(sel1(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(quote(quote(dbl(z0)))) → c26(QUOTE(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(quote(quote(sel(z0, z1)))) → c26(QUOTE(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(quote(dbl(z0))) → c26(QUOTE(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(quote(dbls(z0))) → c26(QUOTE(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(quote(indx(z0, z1))) → c26(QUOTE(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(quote(dbl1(z0))) → c26(QUOTE(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(quote(s1(z0))) → c26(QUOTE(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(quote(z0))) → c26(QUOTE(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(quote(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(quote(0))) → c22(DBL1(mark(01)))
ACTIVE(s1(quote(0))) → c23(S1(mark(01)))
ACTIVE(quote(dbl(0))) → c26(QUOTE(mark(0)))
ACTIVE(quote(dbls(nil))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(indx(nil, z0))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(dbl1(0))) → c26(QUOTE(mark(01)))
ACTIVE(quote(quote(0))) → c26(QUOTE(mark(01)))
ACTIVE(dbl(quote(s(z0)))) → c7(DBL(mark(s1(quote(z0)))))
ACTIVE(dbl(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(s(z0)))) → c7(DBLS(mark(s1(quote(z0)))))
ACTIVE(dbls(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(indx(quote(s(z0)), x1)) → c7(INDX(mark(s1(quote(z0))), x1))
ACTIVE(indx(quote(s(z0)), x1)) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbl1(quote(s(z0)))) → c7(DBL1(mark(s1(quote(z0)))))
ACTIVE(dbl1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(s1(quote(s(z0)))) → c7(S1(mark(s1(quote(z0)))))
ACTIVE(s1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(quote(dbl(s(z0)))) → c7(QUOTE(mark(s(s(dbl(z0))))))
ACTIVE(quote(dbl(s(z0)))) → c7(ACTIVE(dbl(s(z0))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(QUOTE(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(QUOTE(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(quote(from(z0))) → c7(QUOTE(mark(cons(z0, from(s(z0))))))
ACTIVE(quote(from(z0))) → c7(ACTIVE(from(z0)))
ACTIVE(quote(dbl1(s(z0)))) → c7(QUOTE(mark(s1(s1(dbl1(z0))))))
ACTIVE(quote(dbl1(s(z0)))) → c7(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(quote(s(z0)))) → c7(QUOTE(mark(s1(quote(z0)))))
ACTIVE(quote(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
PROPER(dbl(dbl(z0))) → c45(DBL(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbl(s(z0))) → c45(DBL(s(proper(z0))), PROPER(s(z0)))
PROPER(dbl(dbls(z0))) → c45(DBL(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbl(cons(z0, z1))) → c45(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbl(sel(z0, z1))) → c45(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbl(indx(z0, z1))) → c45(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbl(from(z0))) → c45(DBL(from(proper(z0))), PROPER(from(z0)))
PROPER(dbl(dbl1(z0))) → c45(DBL(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbl(s1(z0))) → c45(DBL(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbl(sel1(z0, z1))) → c45(DBL(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbl(quote(z0))) → c45(DBL(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbl(0)) → c45(DBL(ok(0)))
PROPER(dbl(nil)) → c45(DBL(ok(nil)))
PROPER(dbl(01)) → c45(DBL(ok(01)))
PROPER(s(dbl(z0))) → c47(S(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(s(s(z0))) → c47(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(dbls(z0))) → c47(S(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(s(cons(z0, z1))) → c47(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(sel(z0, z1))) → c47(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(s(indx(z0, z1))) → c47(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(s(from(z0))) → c47(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(dbl1(z0))) → c47(S(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(s(s1(z0))) → c47(S(s1(proper(z0))), PROPER(s1(z0)))
PROPER(s(sel1(z0, z1))) → c47(S(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(s(quote(z0))) → c47(S(quote(proper(z0))), PROPER(quote(z0)))
PROPER(s(0)) → c47(S(ok(0)))
PROPER(s(nil)) → c47(S(ok(nil)))
PROPER(s(01)) → c47(S(ok(01)))
PROPER(dbls(dbl(z0))) → c48(DBLS(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbls(s(z0))) → c48(DBLS(s(proper(z0))), PROPER(s(z0)))
PROPER(dbls(dbls(z0))) → c48(DBLS(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbls(cons(z0, z1))) → c48(DBLS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbls(sel(z0, z1))) → c48(DBLS(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbls(indx(z0, z1))) → c48(DBLS(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbls(from(z0))) → c48(DBLS(from(proper(z0))), PROPER(from(z0)))
PROPER(dbls(dbl1(z0))) → c48(DBLS(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbls(s1(z0))) → c48(DBLS(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbls(sel1(z0, z1))) → c48(DBLS(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbls(quote(z0))) → c48(DBLS(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbls(0)) → c48(DBLS(ok(0)))
PROPER(dbls(nil)) → c48(DBLS(ok(nil)))
PROPER(dbls(01)) → c48(DBLS(ok(01)))
PROPER(cons(x0, dbl(z0))) → c50(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(cons(x0, s(z0))) → c50(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, dbls(z0))) → c50(CONS(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(cons(x0, cons(z0, z1))) → c50(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, sel(z0, z1))) → c50(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(cons(x0, indx(z0, z1))) → c50(CONS(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(cons(x0, from(z0))) → c50(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, dbl1(z0))) → c50(CONS(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(cons(x0, s1(z0))) → c50(CONS(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(cons(x0, sel1(z0, z1))) → c50(CONS(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(cons(x0, quote(z0))) → c50(CONS(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(cons(dbl(z0), x1)) → c50(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(cons(s(z0), x1)) → c50(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(dbls(z0), x1)) → c50(CONS(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c50(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(sel(z0, z1), x1)) → c50(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(cons(indx(z0, z1), x1)) → c50(CONS(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c50(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(dbl1(z0), x1)) → c50(CONS(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(cons(s1(z0), x1)) → c50(CONS(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(cons(sel1(z0, z1), x1)) → c50(CONS(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(cons(quote(z0), x1)) → c50(CONS(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c50(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c50(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, 01)) → c50(CONS(proper(x0), ok(01)), PROPER(x0))
PROPER(cons(0, x1)) → c50(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c50(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(01, x1)) → c50(CONS(ok(01), proper(x1)), PROPER(x1))
PROPER(sel(x0, dbl(z0))) → c51(SEL(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(sel(x0, s(z0))) → c51(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(sel(x0, dbls(z0))) → c51(SEL(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(sel(x0, cons(z0, z1))) → c51(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(sel(x0, sel(z0, z1))) → c51(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(sel(x0, indx(z0, z1))) → c51(SEL(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(sel(x0, from(z0))) → c51(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(sel(x0, dbl1(z0))) → c51(SEL(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(sel(x0, s1(z0))) → c51(SEL(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(sel(x0, sel1(z0, z1))) → c51(SEL(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(sel(x0, quote(z0))) → c51(SEL(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(sel(dbl(z0), x1)) → c51(SEL(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(sel(s(z0), x1)) → c51(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(sel(dbls(z0), x1)) → c51(SEL(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(sel(cons(z0, z1), x1)) → c51(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(sel(sel(z0, z1), x1)) → c51(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(sel(indx(z0, z1), x1)) → c51(SEL(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(sel(from(z0), x1)) → c51(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(sel(dbl1(z0), x1)) → c51(SEL(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(sel(s1(z0), x1)) → c51(SEL(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(sel(sel1(z0, z1), x1)) → c51(SEL(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(sel(quote(z0), x1)) → c51(SEL(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(sel(x0, 0)) → c51(SEL(proper(x0), ok(0)), PROPER(x0))
PROPER(sel(x0, nil)) → c51(SEL(proper(x0), ok(nil)), PROPER(x0))
PROPER(sel(x0, 01)) → c51(SEL(proper(x0), ok(01)), PROPER(x0))
PROPER(sel(0, x1)) → c51(SEL(ok(0), proper(x1)), PROPER(x1))
PROPER(sel(nil, x1)) → c51(SEL(ok(nil), proper(x1)), PROPER(x1))
PROPER(sel(01, x1)) → c51(SEL(ok(01), proper(x1)), PROPER(x1))
PROPER(indx(x0, dbl(z0))) → c52(INDX(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(indx(x0, s(z0))) → c52(INDX(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(indx(x0, dbls(z0))) → c52(INDX(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(indx(x0, cons(z0, z1))) → c52(INDX(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(indx(x0, sel(z0, z1))) → c52(INDX(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(indx(x0, indx(z0, z1))) → c52(INDX(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(indx(x0, from(z0))) → c52(INDX(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(indx(x0, dbl1(z0))) → c52(INDX(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(indx(x0, s1(z0))) → c52(INDX(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(indx(x0, sel1(z0, z1))) → c52(INDX(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(indx(x0, quote(z0))) → c52(INDX(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(indx(dbl(z0), x1)) → c52(INDX(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(indx(s(z0), x1)) → c52(INDX(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(indx(dbls(z0), x1)) → c52(INDX(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(indx(cons(z0, z1), x1)) → c52(INDX(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(indx(sel(z0, z1), x1)) → c52(INDX(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(indx(indx(z0, z1), x1)) → c52(INDX(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(indx(from(z0), x1)) → c52(INDX(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(indx(dbl1(z0), x1)) → c52(INDX(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(indx(s1(z0), x1)) → c52(INDX(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(indx(sel1(z0, z1), x1)) → c52(INDX(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(indx(quote(z0), x1)) → c52(INDX(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(indx(x0, 0)) → c52(INDX(proper(x0), ok(0)), PROPER(x0))
PROPER(indx(x0, nil)) → c52(INDX(proper(x0), ok(nil)), PROPER(x0))
PROPER(indx(x0, 01)) → c52(INDX(proper(x0), ok(01)), PROPER(x0))
PROPER(indx(0, x1)) → c52(INDX(ok(0), proper(x1)), PROPER(x1))
PROPER(indx(nil, x1)) → c52(INDX(ok(nil), proper(x1)), PROPER(x1))
PROPER(indx(01, x1)) → c52(INDX(ok(01), proper(x1)), PROPER(x1))
PROPER(from(dbl(z0))) → c53(FROM(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(from(s(z0))) → c53(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(dbls(z0))) → c53(FROM(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(from(cons(z0, z1))) → c53(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(sel(z0, z1))) → c53(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(from(indx(z0, z1))) → c53(FROM(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(from(from(z0))) → c53(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(dbl1(z0))) → c53(FROM(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(from(s1(z0))) → c53(FROM(s1(proper(z0))), PROPER(s1(z0)))
PROPER(from(sel1(z0, z1))) → c53(FROM(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(from(quote(z0))) → c53(FROM(quote(proper(z0))), PROPER(quote(z0)))
PROPER(from(0)) → c53(FROM(ok(0)))
PROPER(from(nil)) → c53(FROM(ok(nil)))
PROPER(from(01)) → c53(FROM(ok(01)))
PROPER(dbl1(dbl(z0))) → c54(DBL1(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbl1(s(z0))) → c54(DBL1(s(proper(z0))), PROPER(s(z0)))
PROPER(dbl1(dbls(z0))) → c54(DBL1(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbl1(cons(z0, z1))) → c54(DBL1(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbl1(sel(z0, z1))) → c54(DBL1(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbl1(indx(z0, z1))) → c54(DBL1(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbl1(from(z0))) → c54(DBL1(from(proper(z0))), PROPER(from(z0)))
PROPER(dbl1(dbl1(z0))) → c54(DBL1(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbl1(s1(z0))) → c54(DBL1(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbl1(sel1(z0, z1))) → c54(DBL1(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbl1(quote(z0))) → c54(DBL1(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbl1(0)) → c54(DBL1(ok(0)))
PROPER(dbl1(nil)) → c54(DBL1(ok(nil)))
PROPER(dbl1(01)) → c54(DBL1(ok(01)))
PROPER(s1(dbl(z0))) → c56(S1(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(s1(s(z0))) → c56(S1(s(proper(z0))), PROPER(s(z0)))
PROPER(s1(dbls(z0))) → c56(S1(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(s1(cons(z0, z1))) → c56(S1(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s1(sel(z0, z1))) → c56(S1(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(s1(indx(z0, z1))) → c56(S1(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(s1(from(z0))) → c56(S1(from(proper(z0))), PROPER(from(z0)))
PROPER(s1(dbl1(z0))) → c56(S1(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(s1(s1(z0))) → c56(S1(s1(proper(z0))), PROPER(s1(z0)))
PROPER(s1(sel1(z0, z1))) → c56(S1(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(s1(quote(z0))) → c56(S1(quote(proper(z0))), PROPER(quote(z0)))
PROPER(s1(0)) → c56(S1(ok(0)))
PROPER(s1(nil)) → c56(S1(ok(nil)))
PROPER(s1(01)) → c56(S1(ok(01)))
PROPER(sel1(x0, dbl(z0))) → c57(SEL1(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(sel1(x0, s(z0))) → c57(SEL1(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(sel1(x0, dbls(z0))) → c57(SEL1(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(sel1(x0, cons(z0, z1))) → c57(SEL1(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(sel1(x0, sel(z0, z1))) → c57(SEL1(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(sel1(x0, indx(z0, z1))) → c57(SEL1(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(sel1(x0, from(z0))) → c57(SEL1(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(sel1(x0, dbl1(z0))) → c57(SEL1(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(sel1(x0, s1(z0))) → c57(SEL1(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(sel1(x0, sel1(z0, z1))) → c57(SEL1(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(sel1(x0, quote(z0))) → c57(SEL1(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(sel1(dbl(z0), x1)) → c57(SEL1(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(sel1(s(z0), x1)) → c57(SEL1(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(sel1(dbls(z0), x1)) → c57(SEL1(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(sel1(cons(z0, z1), x1)) → c57(SEL1(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(sel1(sel(z0, z1), x1)) → c57(SEL1(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(sel1(indx(z0, z1), x1)) → c57(SEL1(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(sel1(from(z0), x1)) → c57(SEL1(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(sel1(dbl1(z0), x1)) → c57(SEL1(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(sel1(s1(z0), x1)) → c57(SEL1(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(sel1(sel1(z0, z1), x1)) → c57(SEL1(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(sel1(quote(z0), x1)) → c57(SEL1(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(sel1(x0, 0)) → c57(SEL1(proper(x0), ok(0)), PROPER(x0))
PROPER(sel1(x0, nil)) → c57(SEL1(proper(x0), ok(nil)), PROPER(x0))
PROPER(sel1(x0, 01)) → c57(SEL1(proper(x0), ok(01)), PROPER(x0))
PROPER(sel1(0, x1)) → c57(SEL1(ok(0), proper(x1)), PROPER(x1))
PROPER(sel1(nil, x1)) → c57(SEL1(ok(nil), proper(x1)), PROPER(x1))
PROPER(sel1(01, x1)) → c57(SEL1(ok(01), proper(x1)), PROPER(x1))
PROPER(quote(dbl(z0))) → c58(QUOTE(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(quote(s(z0))) → c58(QUOTE(s(proper(z0))), PROPER(s(z0)))
PROPER(quote(dbls(z0))) → c58(QUOTE(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(quote(cons(z0, z1))) → c58(QUOTE(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(quote(sel(z0, z1))) → c58(QUOTE(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(quote(indx(z0, z1))) → c58(QUOTE(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(quote(from(z0))) → c58(QUOTE(from(proper(z0))), PROPER(from(z0)))
PROPER(quote(dbl1(z0))) → c58(QUOTE(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(quote(s1(z0))) → c58(QUOTE(s1(proper(z0))), PROPER(s1(z0)))
PROPER(quote(sel1(z0, z1))) → c58(QUOTE(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(quote(quote(z0))) → c58(QUOTE(quote(proper(z0))), PROPER(quote(z0)))
PROPER(quote(0)) → c58(QUOTE(ok(0)))
PROPER(quote(nil)) → c58(QUOTE(ok(nil)))
PROPER(quote(01)) → c58(QUOTE(ok(01)))
TOP(mark(dbl(z0))) → c62(TOP(dbl(proper(z0))), PROPER(dbl(z0)))
TOP(mark(0)) → c62(TOP(ok(0)), PROPER(0))
TOP(mark(s(z0))) → c62(TOP(s(proper(z0))), PROPER(s(z0)))
TOP(mark(dbls(z0))) → c62(TOP(dbls(proper(z0))), PROPER(dbls(z0)))
TOP(mark(nil)) → c62(TOP(ok(nil)), PROPER(nil))
TOP(mark(cons(z0, z1))) → c62(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
TOP(mark(sel(z0, z1))) → c62(TOP(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
TOP(mark(indx(z0, z1))) → c62(TOP(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
TOP(mark(from(z0))) → c62(TOP(from(proper(z0))), PROPER(from(z0)))
TOP(mark(dbl1(z0))) → c62(TOP(dbl1(proper(z0))), PROPER(dbl1(z0)))
TOP(mark(01)) → c62(TOP(ok(01)), PROPER(01))
TOP(mark(s1(z0))) → c62(TOP(s1(proper(z0))), PROPER(s1(z0)))
TOP(mark(sel1(z0, z1))) → c62(TOP(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
TOP(mark(quote(z0))) → c62(TOP(quote(proper(z0))), PROPER(quote(z0)))
K tuples:none
Defined Rule Symbols:
active, s, dbl, cons, dbls, sel, indx, s1, dbl1, sel1, quote, proper, from
Defined Pair Symbols:
ACTIVE, DBL, DBLS, SEL, INDX, DBL1, S1, SEL1, QUOTE, S, CONS, FROM, TOP, PROPER
Compound Symbols:
c5, c12, c15, c16, c19, c20, c24, c25, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c59, c60, c61, c63, c8, c, c17, c17, c1, c18, c18, c2, c21, c21, c3, c22, c22, c4, c23, c23, c6, c26, c26, c7, c45, c45, c47, c47, c48, c48, c50, c50, c51, c51, c52, c52, c53, c53, c54, c54, c56, c56, c57, c57, c58, c58, c62
(93) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 3 trailing tuple parts
(94) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(dbl(0)) → mark(0)
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
active(dbls(nil)) → mark(nil)
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1)))
active(sel(0, cons(z0, z1))) → mark(z0)
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
active(indx(nil, z0)) → mark(nil)
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2)))
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(dbl1(0)) → mark(01)
active(dbl1(s(z0))) → mark(s1(s1(dbl1(z0))))
active(sel1(0, cons(z0, z1))) → mark(z0)
active(sel1(s(z0), cons(z1, z2))) → mark(sel1(z0, z2))
active(quote(0)) → mark(01)
active(quote(s(z0))) → mark(s1(quote(z0)))
active(quote(dbl(z0))) → mark(dbl1(z0))
active(quote(sel(z0, z1))) → mark(sel1(z0, z1))
active(dbl(z0)) → dbl(active(z0))
active(dbls(z0)) → dbls(active(z0))
active(sel(z0, z1)) → sel(active(z0), z1)
active(sel(z0, z1)) → sel(z0, active(z1))
active(indx(z0, z1)) → indx(active(z0), z1)
active(dbl1(z0)) → dbl1(active(z0))
active(s1(z0)) → s1(active(z0))
active(sel1(z0, z1)) → sel1(active(z0), z1)
active(sel1(z0, z1)) → sel1(z0, active(z1))
active(quote(z0)) → quote(active(z0))
s(ok(z0)) → ok(s(z0))
dbl(mark(z0)) → mark(dbl(z0))
dbl(ok(z0)) → ok(dbl(z0))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
dbls(mark(z0)) → mark(dbls(z0))
dbls(ok(z0)) → ok(dbls(z0))
sel(mark(z0), z1) → mark(sel(z0, z1))
sel(z0, mark(z1)) → mark(sel(z0, z1))
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
indx(mark(z0), z1) → mark(indx(z0, z1))
indx(ok(z0), ok(z1)) → ok(indx(z0, z1))
s1(mark(z0)) → mark(s1(z0))
s1(ok(z0)) → ok(s1(z0))
dbl1(mark(z0)) → mark(dbl1(z0))
dbl1(ok(z0)) → ok(dbl1(z0))
sel1(mark(z0), z1) → mark(sel1(z0, z1))
sel1(z0, mark(z1)) → mark(sel1(z0, z1))
sel1(ok(z0), ok(z1)) → ok(sel1(z0, z1))
quote(mark(z0)) → mark(quote(z0))
quote(ok(z0)) → ok(quote(z0))
proper(dbl(z0)) → dbl(proper(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(dbls(z0)) → dbls(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
proper(indx(z0, z1)) → indx(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(dbl1(z0)) → dbl1(proper(z0))
proper(01) → ok(01)
proper(s1(z0)) → s1(proper(z0))
proper(sel1(z0, z1)) → sel1(proper(z0), proper(z1))
proper(quote(z0)) → quote(proper(z0))
from(ok(z0)) → ok(from(z0))
Tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)))
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0))))))
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0))))))
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0)))
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(indx(sel1(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(indx(sel1(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel1(z0, z2)), x1), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(indx(quote(dbl(z0)), x1)) → c21(INDX(mark(dbl1(z0)), x1), ACTIVE(quote(dbl(z0))))
ACTIVE(indx(quote(sel(z0, z1)), x1)) → c21(INDX(mark(sel1(z0, z1)), x1), ACTIVE(quote(sel(z0, z1))))
ACTIVE(indx(dbl(z0), x1)) → c21(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
ACTIVE(indx(dbls(z0), x1)) → c21(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(indx(z0, z1), x1)) → c21(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1)))
ACTIVE(indx(dbl1(z0), x1)) → c21(INDX(dbl1(active(z0)), x1), ACTIVE(dbl1(z0)))
ACTIVE(indx(s1(z0), x1)) → c21(INDX(s1(active(z0)), x1), ACTIVE(s1(z0)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(active(z0), z1), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(z0, active(z1)), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(quote(z0), x1)) → c21(INDX(quote(active(z0)), x1), ACTIVE(quote(z0)))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)))
ACTIVE(indx(dbl(0), x1)) → c21(INDX(mark(0), x1))
ACTIVE(indx(dbls(nil), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(indx(indx(nil, z0), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0))))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1))
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0)))
ACTIVE(dbl1(sel(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl1(sel(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl1(sel1(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl1(sel1(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl1(quote(dbl(z0)))) → c22(DBL1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl1(quote(sel(z0, z1)))) → c22(DBL1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl1(dbl(z0))) → c22(DBL1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl1(dbls(z0))) → c22(DBL1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(indx(z0, z1))) → c22(DBL1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl1(dbl1(z0))) → c22(DBL1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl1(s1(z0))) → c22(DBL1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(quote(z0))) → c22(DBL1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(dbl1(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(dbl(0))) → c22(DBL1(mark(0)))
ACTIVE(dbl1(dbls(nil))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(indx(nil, z0))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(dbl1(0))) → c22(DBL1(mark(01)))
ACTIVE(dbl(dbl1(s(z0)))) → c4(DBL(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(DBLS(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(INDX(mark(s1(s1(dbl1(z0)))), x1))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(DBL1(mark(s(s(dbl(z0))))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(ACTIVE(dbl(s(z0))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(DBL1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(DBL1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl1(from(z0))) → c4(DBL1(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl1(from(z0))) → c4(ACTIVE(from(z0)))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(DBL1(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(s1(sel(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(s1(sel(s(z0), cons(z1, z2)))) → c23(S1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(s1(sel1(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(s1(sel1(s(z0), cons(z1, z2)))) → c23(S1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(s1(quote(dbl(z0)))) → c23(S1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(s1(quote(sel(z0, z1)))) → c23(S1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(s1(dbl(z0))) → c23(S1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(s1(dbls(z0))) → c23(S1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(s1(indx(z0, z1))) → c23(S1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(s1(dbl1(z0))) → c23(S1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(s1(s1(z0))) → c23(S1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(quote(z0))) → c23(S1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(s1(dbl(0))) → c23(S1(mark(0)))
ACTIVE(s1(dbls(nil))) → c23(S1(mark(nil)))
ACTIVE(s1(indx(nil, z0))) → c23(S1(mark(nil)))
ACTIVE(s1(dbl1(0))) → c23(S1(mark(01)))
ACTIVE(s1(dbl(s(z0)))) → c6(S1(mark(s(s(dbl(z0))))))
ACTIVE(s1(dbl(s(z0)))) → c6(ACTIVE(dbl(s(z0))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(S1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(S1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(s1(from(z0))) → c6(S1(mark(cons(z0, from(s(z0))))))
ACTIVE(s1(from(z0))) → c6(ACTIVE(from(z0)))
ACTIVE(s1(dbl1(s(z0)))) → c6(S1(mark(s1(s1(dbl1(z0))))))
ACTIVE(s1(dbl1(s(z0)))) → c6(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(sel(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(quote(sel(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(quote(sel1(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(quote(sel1(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(quote(quote(dbl(z0)))) → c26(QUOTE(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(quote(quote(sel(z0, z1)))) → c26(QUOTE(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(quote(dbl(z0))) → c26(QUOTE(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(quote(dbls(z0))) → c26(QUOTE(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(quote(indx(z0, z1))) → c26(QUOTE(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(quote(dbl1(z0))) → c26(QUOTE(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(quote(s1(z0))) → c26(QUOTE(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(quote(z0))) → c26(QUOTE(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(quote(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(quote(0))) → c22(DBL1(mark(01)))
ACTIVE(s1(quote(0))) → c23(S1(mark(01)))
ACTIVE(quote(dbl(0))) → c26(QUOTE(mark(0)))
ACTIVE(quote(dbls(nil))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(indx(nil, z0))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(dbl1(0))) → c26(QUOTE(mark(01)))
ACTIVE(quote(quote(0))) → c26(QUOTE(mark(01)))
ACTIVE(dbl(quote(s(z0)))) → c7(DBL(mark(s1(quote(z0)))))
ACTIVE(dbl(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(s(z0)))) → c7(DBLS(mark(s1(quote(z0)))))
ACTIVE(dbls(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(indx(quote(s(z0)), x1)) → c7(INDX(mark(s1(quote(z0))), x1))
ACTIVE(indx(quote(s(z0)), x1)) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbl1(quote(s(z0)))) → c7(DBL1(mark(s1(quote(z0)))))
ACTIVE(dbl1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(s1(quote(s(z0)))) → c7(S1(mark(s1(quote(z0)))))
ACTIVE(s1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(quote(dbl(s(z0)))) → c7(QUOTE(mark(s(s(dbl(z0))))))
ACTIVE(quote(dbl(s(z0)))) → c7(ACTIVE(dbl(s(z0))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(QUOTE(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(QUOTE(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(quote(from(z0))) → c7(QUOTE(mark(cons(z0, from(s(z0))))))
ACTIVE(quote(from(z0))) → c7(ACTIVE(from(z0)))
ACTIVE(quote(dbl1(s(z0)))) → c7(QUOTE(mark(s1(s1(dbl1(z0))))))
ACTIVE(quote(dbl1(s(z0)))) → c7(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(quote(s(z0)))) → c7(QUOTE(mark(s1(quote(z0)))))
ACTIVE(quote(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
PROPER(dbl(dbl(z0))) → c45(DBL(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbl(s(z0))) → c45(DBL(s(proper(z0))), PROPER(s(z0)))
PROPER(dbl(dbls(z0))) → c45(DBL(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbl(cons(z0, z1))) → c45(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbl(sel(z0, z1))) → c45(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbl(indx(z0, z1))) → c45(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbl(from(z0))) → c45(DBL(from(proper(z0))), PROPER(from(z0)))
PROPER(dbl(dbl1(z0))) → c45(DBL(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbl(s1(z0))) → c45(DBL(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbl(sel1(z0, z1))) → c45(DBL(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbl(quote(z0))) → c45(DBL(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbl(0)) → c45(DBL(ok(0)))
PROPER(dbl(nil)) → c45(DBL(ok(nil)))
PROPER(dbl(01)) → c45(DBL(ok(01)))
PROPER(s(dbl(z0))) → c47(S(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(s(s(z0))) → c47(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(dbls(z0))) → c47(S(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(s(cons(z0, z1))) → c47(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(sel(z0, z1))) → c47(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(s(indx(z0, z1))) → c47(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(s(from(z0))) → c47(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(dbl1(z0))) → c47(S(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(s(s1(z0))) → c47(S(s1(proper(z0))), PROPER(s1(z0)))
PROPER(s(sel1(z0, z1))) → c47(S(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(s(quote(z0))) → c47(S(quote(proper(z0))), PROPER(quote(z0)))
PROPER(s(0)) → c47(S(ok(0)))
PROPER(s(nil)) → c47(S(ok(nil)))
PROPER(s(01)) → c47(S(ok(01)))
PROPER(dbls(dbl(z0))) → c48(DBLS(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbls(s(z0))) → c48(DBLS(s(proper(z0))), PROPER(s(z0)))
PROPER(dbls(dbls(z0))) → c48(DBLS(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbls(cons(z0, z1))) → c48(DBLS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbls(sel(z0, z1))) → c48(DBLS(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbls(indx(z0, z1))) → c48(DBLS(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbls(from(z0))) → c48(DBLS(from(proper(z0))), PROPER(from(z0)))
PROPER(dbls(dbl1(z0))) → c48(DBLS(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbls(s1(z0))) → c48(DBLS(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbls(sel1(z0, z1))) → c48(DBLS(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbls(quote(z0))) → c48(DBLS(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbls(0)) → c48(DBLS(ok(0)))
PROPER(dbls(nil)) → c48(DBLS(ok(nil)))
PROPER(dbls(01)) → c48(DBLS(ok(01)))
PROPER(cons(x0, dbl(z0))) → c50(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(cons(x0, s(z0))) → c50(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, dbls(z0))) → c50(CONS(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(cons(x0, cons(z0, z1))) → c50(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, sel(z0, z1))) → c50(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(cons(x0, indx(z0, z1))) → c50(CONS(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(cons(x0, from(z0))) → c50(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, dbl1(z0))) → c50(CONS(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(cons(x0, s1(z0))) → c50(CONS(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(cons(x0, sel1(z0, z1))) → c50(CONS(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(cons(x0, quote(z0))) → c50(CONS(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(cons(dbl(z0), x1)) → c50(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(cons(s(z0), x1)) → c50(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(dbls(z0), x1)) → c50(CONS(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c50(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(sel(z0, z1), x1)) → c50(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(cons(indx(z0, z1), x1)) → c50(CONS(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c50(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(dbl1(z0), x1)) → c50(CONS(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(cons(s1(z0), x1)) → c50(CONS(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(cons(sel1(z0, z1), x1)) → c50(CONS(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(cons(quote(z0), x1)) → c50(CONS(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c50(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c50(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, 01)) → c50(CONS(proper(x0), ok(01)), PROPER(x0))
PROPER(cons(0, x1)) → c50(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c50(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(01, x1)) → c50(CONS(ok(01), proper(x1)), PROPER(x1))
PROPER(sel(x0, dbl(z0))) → c51(SEL(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(sel(x0, s(z0))) → c51(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(sel(x0, dbls(z0))) → c51(SEL(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(sel(x0, cons(z0, z1))) → c51(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(sel(x0, sel(z0, z1))) → c51(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(sel(x0, indx(z0, z1))) → c51(SEL(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(sel(x0, from(z0))) → c51(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(sel(x0, dbl1(z0))) → c51(SEL(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(sel(x0, s1(z0))) → c51(SEL(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(sel(x0, sel1(z0, z1))) → c51(SEL(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(sel(x0, quote(z0))) → c51(SEL(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(sel(dbl(z0), x1)) → c51(SEL(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(sel(s(z0), x1)) → c51(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(sel(dbls(z0), x1)) → c51(SEL(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(sel(cons(z0, z1), x1)) → c51(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(sel(sel(z0, z1), x1)) → c51(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(sel(indx(z0, z1), x1)) → c51(SEL(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(sel(from(z0), x1)) → c51(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(sel(dbl1(z0), x1)) → c51(SEL(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(sel(s1(z0), x1)) → c51(SEL(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(sel(sel1(z0, z1), x1)) → c51(SEL(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(sel(quote(z0), x1)) → c51(SEL(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(sel(x0, 0)) → c51(SEL(proper(x0), ok(0)), PROPER(x0))
PROPER(sel(x0, nil)) → c51(SEL(proper(x0), ok(nil)), PROPER(x0))
PROPER(sel(x0, 01)) → c51(SEL(proper(x0), ok(01)), PROPER(x0))
PROPER(sel(0, x1)) → c51(SEL(ok(0), proper(x1)), PROPER(x1))
PROPER(sel(nil, x1)) → c51(SEL(ok(nil), proper(x1)), PROPER(x1))
PROPER(sel(01, x1)) → c51(SEL(ok(01), proper(x1)), PROPER(x1))
PROPER(indx(x0, dbl(z0))) → c52(INDX(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(indx(x0, s(z0))) → c52(INDX(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(indx(x0, dbls(z0))) → c52(INDX(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(indx(x0, cons(z0, z1))) → c52(INDX(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(indx(x0, sel(z0, z1))) → c52(INDX(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(indx(x0, indx(z0, z1))) → c52(INDX(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(indx(x0, from(z0))) → c52(INDX(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(indx(x0, dbl1(z0))) → c52(INDX(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(indx(x0, s1(z0))) → c52(INDX(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(indx(x0, sel1(z0, z1))) → c52(INDX(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(indx(x0, quote(z0))) → c52(INDX(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(indx(dbl(z0), x1)) → c52(INDX(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(indx(s(z0), x1)) → c52(INDX(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(indx(dbls(z0), x1)) → c52(INDX(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(indx(cons(z0, z1), x1)) → c52(INDX(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(indx(sel(z0, z1), x1)) → c52(INDX(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(indx(indx(z0, z1), x1)) → c52(INDX(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(indx(from(z0), x1)) → c52(INDX(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(indx(dbl1(z0), x1)) → c52(INDX(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(indx(s1(z0), x1)) → c52(INDX(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(indx(sel1(z0, z1), x1)) → c52(INDX(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(indx(quote(z0), x1)) → c52(INDX(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(indx(x0, 0)) → c52(INDX(proper(x0), ok(0)), PROPER(x0))
PROPER(indx(x0, nil)) → c52(INDX(proper(x0), ok(nil)), PROPER(x0))
PROPER(indx(x0, 01)) → c52(INDX(proper(x0), ok(01)), PROPER(x0))
PROPER(indx(0, x1)) → c52(INDX(ok(0), proper(x1)), PROPER(x1))
PROPER(indx(nil, x1)) → c52(INDX(ok(nil), proper(x1)), PROPER(x1))
PROPER(indx(01, x1)) → c52(INDX(ok(01), proper(x1)), PROPER(x1))
PROPER(from(dbl(z0))) → c53(FROM(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(from(s(z0))) → c53(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(dbls(z0))) → c53(FROM(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(from(cons(z0, z1))) → c53(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(sel(z0, z1))) → c53(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(from(indx(z0, z1))) → c53(FROM(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(from(from(z0))) → c53(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(dbl1(z0))) → c53(FROM(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(from(s1(z0))) → c53(FROM(s1(proper(z0))), PROPER(s1(z0)))
PROPER(from(sel1(z0, z1))) → c53(FROM(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(from(quote(z0))) → c53(FROM(quote(proper(z0))), PROPER(quote(z0)))
PROPER(from(0)) → c53(FROM(ok(0)))
PROPER(from(nil)) → c53(FROM(ok(nil)))
PROPER(from(01)) → c53(FROM(ok(01)))
PROPER(dbl1(dbl(z0))) → c54(DBL1(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbl1(s(z0))) → c54(DBL1(s(proper(z0))), PROPER(s(z0)))
PROPER(dbl1(dbls(z0))) → c54(DBL1(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbl1(cons(z0, z1))) → c54(DBL1(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbl1(sel(z0, z1))) → c54(DBL1(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbl1(indx(z0, z1))) → c54(DBL1(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbl1(from(z0))) → c54(DBL1(from(proper(z0))), PROPER(from(z0)))
PROPER(dbl1(dbl1(z0))) → c54(DBL1(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbl1(s1(z0))) → c54(DBL1(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbl1(sel1(z0, z1))) → c54(DBL1(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbl1(quote(z0))) → c54(DBL1(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbl1(0)) → c54(DBL1(ok(0)))
PROPER(dbl1(nil)) → c54(DBL1(ok(nil)))
PROPER(dbl1(01)) → c54(DBL1(ok(01)))
PROPER(s1(dbl(z0))) → c56(S1(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(s1(s(z0))) → c56(S1(s(proper(z0))), PROPER(s(z0)))
PROPER(s1(dbls(z0))) → c56(S1(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(s1(cons(z0, z1))) → c56(S1(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s1(sel(z0, z1))) → c56(S1(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(s1(indx(z0, z1))) → c56(S1(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(s1(from(z0))) → c56(S1(from(proper(z0))), PROPER(from(z0)))
PROPER(s1(dbl1(z0))) → c56(S1(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(s1(s1(z0))) → c56(S1(s1(proper(z0))), PROPER(s1(z0)))
PROPER(s1(sel1(z0, z1))) → c56(S1(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(s1(quote(z0))) → c56(S1(quote(proper(z0))), PROPER(quote(z0)))
PROPER(s1(0)) → c56(S1(ok(0)))
PROPER(s1(nil)) → c56(S1(ok(nil)))
PROPER(s1(01)) → c56(S1(ok(01)))
PROPER(sel1(x0, dbl(z0))) → c57(SEL1(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(sel1(x0, s(z0))) → c57(SEL1(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(sel1(x0, dbls(z0))) → c57(SEL1(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(sel1(x0, cons(z0, z1))) → c57(SEL1(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(sel1(x0, sel(z0, z1))) → c57(SEL1(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(sel1(x0, indx(z0, z1))) → c57(SEL1(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(sel1(x0, from(z0))) → c57(SEL1(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(sel1(x0, dbl1(z0))) → c57(SEL1(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(sel1(x0, s1(z0))) → c57(SEL1(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(sel1(x0, sel1(z0, z1))) → c57(SEL1(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(sel1(x0, quote(z0))) → c57(SEL1(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(sel1(dbl(z0), x1)) → c57(SEL1(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(sel1(s(z0), x1)) → c57(SEL1(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(sel1(dbls(z0), x1)) → c57(SEL1(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(sel1(cons(z0, z1), x1)) → c57(SEL1(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(sel1(sel(z0, z1), x1)) → c57(SEL1(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(sel1(indx(z0, z1), x1)) → c57(SEL1(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(sel1(from(z0), x1)) → c57(SEL1(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(sel1(dbl1(z0), x1)) → c57(SEL1(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(sel1(s1(z0), x1)) → c57(SEL1(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(sel1(sel1(z0, z1), x1)) → c57(SEL1(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(sel1(quote(z0), x1)) → c57(SEL1(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(sel1(x0, 0)) → c57(SEL1(proper(x0), ok(0)), PROPER(x0))
PROPER(sel1(x0, nil)) → c57(SEL1(proper(x0), ok(nil)), PROPER(x0))
PROPER(sel1(x0, 01)) → c57(SEL1(proper(x0), ok(01)), PROPER(x0))
PROPER(sel1(0, x1)) → c57(SEL1(ok(0), proper(x1)), PROPER(x1))
PROPER(sel1(nil, x1)) → c57(SEL1(ok(nil), proper(x1)), PROPER(x1))
PROPER(sel1(01, x1)) → c57(SEL1(ok(01), proper(x1)), PROPER(x1))
PROPER(quote(dbl(z0))) → c58(QUOTE(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(quote(s(z0))) → c58(QUOTE(s(proper(z0))), PROPER(s(z0)))
PROPER(quote(dbls(z0))) → c58(QUOTE(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(quote(cons(z0, z1))) → c58(QUOTE(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(quote(sel(z0, z1))) → c58(QUOTE(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(quote(indx(z0, z1))) → c58(QUOTE(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(quote(from(z0))) → c58(QUOTE(from(proper(z0))), PROPER(from(z0)))
PROPER(quote(dbl1(z0))) → c58(QUOTE(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(quote(s1(z0))) → c58(QUOTE(s1(proper(z0))), PROPER(s1(z0)))
PROPER(quote(sel1(z0, z1))) → c58(QUOTE(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(quote(quote(z0))) → c58(QUOTE(quote(proper(z0))), PROPER(quote(z0)))
PROPER(quote(0)) → c58(QUOTE(ok(0)))
PROPER(quote(nil)) → c58(QUOTE(ok(nil)))
PROPER(quote(01)) → c58(QUOTE(ok(01)))
TOP(mark(dbl(z0))) → c62(TOP(dbl(proper(z0))), PROPER(dbl(z0)))
TOP(mark(s(z0))) → c62(TOP(s(proper(z0))), PROPER(s(z0)))
TOP(mark(dbls(z0))) → c62(TOP(dbls(proper(z0))), PROPER(dbls(z0)))
TOP(mark(cons(z0, z1))) → c62(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
TOP(mark(sel(z0, z1))) → c62(TOP(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
TOP(mark(indx(z0, z1))) → c62(TOP(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
TOP(mark(from(z0))) → c62(TOP(from(proper(z0))), PROPER(from(z0)))
TOP(mark(dbl1(z0))) → c62(TOP(dbl1(proper(z0))), PROPER(dbl1(z0)))
TOP(mark(s1(z0))) → c62(TOP(s1(proper(z0))), PROPER(s1(z0)))
TOP(mark(sel1(z0, z1))) → c62(TOP(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
TOP(mark(quote(z0))) → c62(TOP(quote(proper(z0))), PROPER(quote(z0)))
TOP(mark(0)) → c62(TOP(ok(0)))
TOP(mark(nil)) → c62(TOP(ok(nil)))
TOP(mark(01)) → c62(TOP(ok(01)))
S tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
TOP(ok(z0)) → c63(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)))
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0))))))
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0))))))
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0)))
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(indx(sel1(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(indx(sel1(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel1(z0, z2)), x1), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(indx(quote(dbl(z0)), x1)) → c21(INDX(mark(dbl1(z0)), x1), ACTIVE(quote(dbl(z0))))
ACTIVE(indx(quote(sel(z0, z1)), x1)) → c21(INDX(mark(sel1(z0, z1)), x1), ACTIVE(quote(sel(z0, z1))))
ACTIVE(indx(dbl(z0), x1)) → c21(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
ACTIVE(indx(dbls(z0), x1)) → c21(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(indx(z0, z1), x1)) → c21(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1)))
ACTIVE(indx(dbl1(z0), x1)) → c21(INDX(dbl1(active(z0)), x1), ACTIVE(dbl1(z0)))
ACTIVE(indx(s1(z0), x1)) → c21(INDX(s1(active(z0)), x1), ACTIVE(s1(z0)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(active(z0), z1), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(z0, active(z1)), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(quote(z0), x1)) → c21(INDX(quote(active(z0)), x1), ACTIVE(quote(z0)))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)))
ACTIVE(indx(dbl(0), x1)) → c21(INDX(mark(0), x1))
ACTIVE(indx(dbls(nil), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(indx(indx(nil, z0), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0))))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1))
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0)))
ACTIVE(dbl1(sel(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl1(sel(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl1(sel1(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl1(sel1(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl1(quote(dbl(z0)))) → c22(DBL1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl1(quote(sel(z0, z1)))) → c22(DBL1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl1(dbl(z0))) → c22(DBL1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl1(dbls(z0))) → c22(DBL1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(indx(z0, z1))) → c22(DBL1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl1(dbl1(z0))) → c22(DBL1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl1(s1(z0))) → c22(DBL1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(quote(z0))) → c22(DBL1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(dbl1(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(dbl(0))) → c22(DBL1(mark(0)))
ACTIVE(dbl1(dbls(nil))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(indx(nil, z0))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(dbl1(0))) → c22(DBL1(mark(01)))
ACTIVE(dbl(dbl1(s(z0)))) → c4(DBL(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(DBLS(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(INDX(mark(s1(s1(dbl1(z0)))), x1))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(DBL1(mark(s(s(dbl(z0))))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(ACTIVE(dbl(s(z0))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(DBL1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(DBL1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl1(from(z0))) → c4(DBL1(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl1(from(z0))) → c4(ACTIVE(from(z0)))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(DBL1(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(s1(sel(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(s1(sel(s(z0), cons(z1, z2)))) → c23(S1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(s1(sel1(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(s1(sel1(s(z0), cons(z1, z2)))) → c23(S1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(s1(quote(dbl(z0)))) → c23(S1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(s1(quote(sel(z0, z1)))) → c23(S1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(s1(dbl(z0))) → c23(S1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(s1(dbls(z0))) → c23(S1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(s1(indx(z0, z1))) → c23(S1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(s1(dbl1(z0))) → c23(S1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(s1(s1(z0))) → c23(S1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(quote(z0))) → c23(S1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(s1(dbl(0))) → c23(S1(mark(0)))
ACTIVE(s1(dbls(nil))) → c23(S1(mark(nil)))
ACTIVE(s1(indx(nil, z0))) → c23(S1(mark(nil)))
ACTIVE(s1(dbl1(0))) → c23(S1(mark(01)))
ACTIVE(s1(dbl(s(z0)))) → c6(S1(mark(s(s(dbl(z0))))))
ACTIVE(s1(dbl(s(z0)))) → c6(ACTIVE(dbl(s(z0))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(S1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(S1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(s1(from(z0))) → c6(S1(mark(cons(z0, from(s(z0))))))
ACTIVE(s1(from(z0))) → c6(ACTIVE(from(z0)))
ACTIVE(s1(dbl1(s(z0)))) → c6(S1(mark(s1(s1(dbl1(z0))))))
ACTIVE(s1(dbl1(s(z0)))) → c6(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(sel(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(quote(sel(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(quote(sel1(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(quote(sel1(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(quote(quote(dbl(z0)))) → c26(QUOTE(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(quote(quote(sel(z0, z1)))) → c26(QUOTE(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(quote(dbl(z0))) → c26(QUOTE(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(quote(dbls(z0))) → c26(QUOTE(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(quote(indx(z0, z1))) → c26(QUOTE(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(quote(dbl1(z0))) → c26(QUOTE(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(quote(s1(z0))) → c26(QUOTE(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(quote(z0))) → c26(QUOTE(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(quote(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(quote(0))) → c22(DBL1(mark(01)))
ACTIVE(s1(quote(0))) → c23(S1(mark(01)))
ACTIVE(quote(dbl(0))) → c26(QUOTE(mark(0)))
ACTIVE(quote(dbls(nil))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(indx(nil, z0))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(dbl1(0))) → c26(QUOTE(mark(01)))
ACTIVE(quote(quote(0))) → c26(QUOTE(mark(01)))
ACTIVE(dbl(quote(s(z0)))) → c7(DBL(mark(s1(quote(z0)))))
ACTIVE(dbl(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(s(z0)))) → c7(DBLS(mark(s1(quote(z0)))))
ACTIVE(dbls(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(indx(quote(s(z0)), x1)) → c7(INDX(mark(s1(quote(z0))), x1))
ACTIVE(indx(quote(s(z0)), x1)) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbl1(quote(s(z0)))) → c7(DBL1(mark(s1(quote(z0)))))
ACTIVE(dbl1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(s1(quote(s(z0)))) → c7(S1(mark(s1(quote(z0)))))
ACTIVE(s1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(quote(dbl(s(z0)))) → c7(QUOTE(mark(s(s(dbl(z0))))))
ACTIVE(quote(dbl(s(z0)))) → c7(ACTIVE(dbl(s(z0))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(QUOTE(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(QUOTE(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(quote(from(z0))) → c7(QUOTE(mark(cons(z0, from(s(z0))))))
ACTIVE(quote(from(z0))) → c7(ACTIVE(from(z0)))
ACTIVE(quote(dbl1(s(z0)))) → c7(QUOTE(mark(s1(s1(dbl1(z0))))))
ACTIVE(quote(dbl1(s(z0)))) → c7(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(quote(s(z0)))) → c7(QUOTE(mark(s1(quote(z0)))))
ACTIVE(quote(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
PROPER(dbl(dbl(z0))) → c45(DBL(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbl(s(z0))) → c45(DBL(s(proper(z0))), PROPER(s(z0)))
PROPER(dbl(dbls(z0))) → c45(DBL(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbl(cons(z0, z1))) → c45(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbl(sel(z0, z1))) → c45(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbl(indx(z0, z1))) → c45(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbl(from(z0))) → c45(DBL(from(proper(z0))), PROPER(from(z0)))
PROPER(dbl(dbl1(z0))) → c45(DBL(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbl(s1(z0))) → c45(DBL(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbl(sel1(z0, z1))) → c45(DBL(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbl(quote(z0))) → c45(DBL(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbl(0)) → c45(DBL(ok(0)))
PROPER(dbl(nil)) → c45(DBL(ok(nil)))
PROPER(dbl(01)) → c45(DBL(ok(01)))
PROPER(s(dbl(z0))) → c47(S(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(s(s(z0))) → c47(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(dbls(z0))) → c47(S(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(s(cons(z0, z1))) → c47(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(sel(z0, z1))) → c47(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(s(indx(z0, z1))) → c47(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(s(from(z0))) → c47(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(dbl1(z0))) → c47(S(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(s(s1(z0))) → c47(S(s1(proper(z0))), PROPER(s1(z0)))
PROPER(s(sel1(z0, z1))) → c47(S(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(s(quote(z0))) → c47(S(quote(proper(z0))), PROPER(quote(z0)))
PROPER(s(0)) → c47(S(ok(0)))
PROPER(s(nil)) → c47(S(ok(nil)))
PROPER(s(01)) → c47(S(ok(01)))
PROPER(dbls(dbl(z0))) → c48(DBLS(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbls(s(z0))) → c48(DBLS(s(proper(z0))), PROPER(s(z0)))
PROPER(dbls(dbls(z0))) → c48(DBLS(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbls(cons(z0, z1))) → c48(DBLS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbls(sel(z0, z1))) → c48(DBLS(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbls(indx(z0, z1))) → c48(DBLS(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbls(from(z0))) → c48(DBLS(from(proper(z0))), PROPER(from(z0)))
PROPER(dbls(dbl1(z0))) → c48(DBLS(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbls(s1(z0))) → c48(DBLS(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbls(sel1(z0, z1))) → c48(DBLS(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbls(quote(z0))) → c48(DBLS(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbls(0)) → c48(DBLS(ok(0)))
PROPER(dbls(nil)) → c48(DBLS(ok(nil)))
PROPER(dbls(01)) → c48(DBLS(ok(01)))
PROPER(cons(x0, dbl(z0))) → c50(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(cons(x0, s(z0))) → c50(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, dbls(z0))) → c50(CONS(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(cons(x0, cons(z0, z1))) → c50(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, sel(z0, z1))) → c50(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(cons(x0, indx(z0, z1))) → c50(CONS(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(cons(x0, from(z0))) → c50(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, dbl1(z0))) → c50(CONS(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(cons(x0, s1(z0))) → c50(CONS(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(cons(x0, sel1(z0, z1))) → c50(CONS(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(cons(x0, quote(z0))) → c50(CONS(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(cons(dbl(z0), x1)) → c50(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(cons(s(z0), x1)) → c50(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(dbls(z0), x1)) → c50(CONS(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c50(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(sel(z0, z1), x1)) → c50(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(cons(indx(z0, z1), x1)) → c50(CONS(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c50(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(dbl1(z0), x1)) → c50(CONS(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(cons(s1(z0), x1)) → c50(CONS(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(cons(sel1(z0, z1), x1)) → c50(CONS(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(cons(quote(z0), x1)) → c50(CONS(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c50(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c50(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, 01)) → c50(CONS(proper(x0), ok(01)), PROPER(x0))
PROPER(cons(0, x1)) → c50(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c50(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(01, x1)) → c50(CONS(ok(01), proper(x1)), PROPER(x1))
PROPER(sel(x0, dbl(z0))) → c51(SEL(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(sel(x0, s(z0))) → c51(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(sel(x0, dbls(z0))) → c51(SEL(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(sel(x0, cons(z0, z1))) → c51(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(sel(x0, sel(z0, z1))) → c51(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(sel(x0, indx(z0, z1))) → c51(SEL(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(sel(x0, from(z0))) → c51(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(sel(x0, dbl1(z0))) → c51(SEL(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(sel(x0, s1(z0))) → c51(SEL(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(sel(x0, sel1(z0, z1))) → c51(SEL(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(sel(x0, quote(z0))) → c51(SEL(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(sel(dbl(z0), x1)) → c51(SEL(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(sel(s(z0), x1)) → c51(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(sel(dbls(z0), x1)) → c51(SEL(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(sel(cons(z0, z1), x1)) → c51(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(sel(sel(z0, z1), x1)) → c51(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(sel(indx(z0, z1), x1)) → c51(SEL(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(sel(from(z0), x1)) → c51(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(sel(dbl1(z0), x1)) → c51(SEL(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(sel(s1(z0), x1)) → c51(SEL(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(sel(sel1(z0, z1), x1)) → c51(SEL(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(sel(quote(z0), x1)) → c51(SEL(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(sel(x0, 0)) → c51(SEL(proper(x0), ok(0)), PROPER(x0))
PROPER(sel(x0, nil)) → c51(SEL(proper(x0), ok(nil)), PROPER(x0))
PROPER(sel(x0, 01)) → c51(SEL(proper(x0), ok(01)), PROPER(x0))
PROPER(sel(0, x1)) → c51(SEL(ok(0), proper(x1)), PROPER(x1))
PROPER(sel(nil, x1)) → c51(SEL(ok(nil), proper(x1)), PROPER(x1))
PROPER(sel(01, x1)) → c51(SEL(ok(01), proper(x1)), PROPER(x1))
PROPER(indx(x0, dbl(z0))) → c52(INDX(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(indx(x0, s(z0))) → c52(INDX(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(indx(x0, dbls(z0))) → c52(INDX(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(indx(x0, cons(z0, z1))) → c52(INDX(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(indx(x0, sel(z0, z1))) → c52(INDX(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(indx(x0, indx(z0, z1))) → c52(INDX(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(indx(x0, from(z0))) → c52(INDX(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(indx(x0, dbl1(z0))) → c52(INDX(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(indx(x0, s1(z0))) → c52(INDX(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(indx(x0, sel1(z0, z1))) → c52(INDX(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(indx(x0, quote(z0))) → c52(INDX(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(indx(dbl(z0), x1)) → c52(INDX(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(indx(s(z0), x1)) → c52(INDX(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(indx(dbls(z0), x1)) → c52(INDX(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(indx(cons(z0, z1), x1)) → c52(INDX(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(indx(sel(z0, z1), x1)) → c52(INDX(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(indx(indx(z0, z1), x1)) → c52(INDX(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(indx(from(z0), x1)) → c52(INDX(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(indx(dbl1(z0), x1)) → c52(INDX(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(indx(s1(z0), x1)) → c52(INDX(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(indx(sel1(z0, z1), x1)) → c52(INDX(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(indx(quote(z0), x1)) → c52(INDX(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(indx(x0, 0)) → c52(INDX(proper(x0), ok(0)), PROPER(x0))
PROPER(indx(x0, nil)) → c52(INDX(proper(x0), ok(nil)), PROPER(x0))
PROPER(indx(x0, 01)) → c52(INDX(proper(x0), ok(01)), PROPER(x0))
PROPER(indx(0, x1)) → c52(INDX(ok(0), proper(x1)), PROPER(x1))
PROPER(indx(nil, x1)) → c52(INDX(ok(nil), proper(x1)), PROPER(x1))
PROPER(indx(01, x1)) → c52(INDX(ok(01), proper(x1)), PROPER(x1))
PROPER(from(dbl(z0))) → c53(FROM(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(from(s(z0))) → c53(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(dbls(z0))) → c53(FROM(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(from(cons(z0, z1))) → c53(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(sel(z0, z1))) → c53(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(from(indx(z0, z1))) → c53(FROM(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(from(from(z0))) → c53(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(dbl1(z0))) → c53(FROM(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(from(s1(z0))) → c53(FROM(s1(proper(z0))), PROPER(s1(z0)))
PROPER(from(sel1(z0, z1))) → c53(FROM(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(from(quote(z0))) → c53(FROM(quote(proper(z0))), PROPER(quote(z0)))
PROPER(from(0)) → c53(FROM(ok(0)))
PROPER(from(nil)) → c53(FROM(ok(nil)))
PROPER(from(01)) → c53(FROM(ok(01)))
PROPER(dbl1(dbl(z0))) → c54(DBL1(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbl1(s(z0))) → c54(DBL1(s(proper(z0))), PROPER(s(z0)))
PROPER(dbl1(dbls(z0))) → c54(DBL1(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbl1(cons(z0, z1))) → c54(DBL1(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbl1(sel(z0, z1))) → c54(DBL1(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbl1(indx(z0, z1))) → c54(DBL1(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbl1(from(z0))) → c54(DBL1(from(proper(z0))), PROPER(from(z0)))
PROPER(dbl1(dbl1(z0))) → c54(DBL1(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbl1(s1(z0))) → c54(DBL1(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbl1(sel1(z0, z1))) → c54(DBL1(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbl1(quote(z0))) → c54(DBL1(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbl1(0)) → c54(DBL1(ok(0)))
PROPER(dbl1(nil)) → c54(DBL1(ok(nil)))
PROPER(dbl1(01)) → c54(DBL1(ok(01)))
PROPER(s1(dbl(z0))) → c56(S1(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(s1(s(z0))) → c56(S1(s(proper(z0))), PROPER(s(z0)))
PROPER(s1(dbls(z0))) → c56(S1(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(s1(cons(z0, z1))) → c56(S1(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s1(sel(z0, z1))) → c56(S1(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(s1(indx(z0, z1))) → c56(S1(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(s1(from(z0))) → c56(S1(from(proper(z0))), PROPER(from(z0)))
PROPER(s1(dbl1(z0))) → c56(S1(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(s1(s1(z0))) → c56(S1(s1(proper(z0))), PROPER(s1(z0)))
PROPER(s1(sel1(z0, z1))) → c56(S1(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(s1(quote(z0))) → c56(S1(quote(proper(z0))), PROPER(quote(z0)))
PROPER(s1(0)) → c56(S1(ok(0)))
PROPER(s1(nil)) → c56(S1(ok(nil)))
PROPER(s1(01)) → c56(S1(ok(01)))
PROPER(sel1(x0, dbl(z0))) → c57(SEL1(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(sel1(x0, s(z0))) → c57(SEL1(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(sel1(x0, dbls(z0))) → c57(SEL1(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(sel1(x0, cons(z0, z1))) → c57(SEL1(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(sel1(x0, sel(z0, z1))) → c57(SEL1(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(sel1(x0, indx(z0, z1))) → c57(SEL1(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(sel1(x0, from(z0))) → c57(SEL1(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(sel1(x0, dbl1(z0))) → c57(SEL1(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(sel1(x0, s1(z0))) → c57(SEL1(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(sel1(x0, sel1(z0, z1))) → c57(SEL1(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(sel1(x0, quote(z0))) → c57(SEL1(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(sel1(dbl(z0), x1)) → c57(SEL1(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(sel1(s(z0), x1)) → c57(SEL1(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(sel1(dbls(z0), x1)) → c57(SEL1(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(sel1(cons(z0, z1), x1)) → c57(SEL1(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(sel1(sel(z0, z1), x1)) → c57(SEL1(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(sel1(indx(z0, z1), x1)) → c57(SEL1(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(sel1(from(z0), x1)) → c57(SEL1(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(sel1(dbl1(z0), x1)) → c57(SEL1(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(sel1(s1(z0), x1)) → c57(SEL1(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(sel1(sel1(z0, z1), x1)) → c57(SEL1(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(sel1(quote(z0), x1)) → c57(SEL1(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(sel1(x0, 0)) → c57(SEL1(proper(x0), ok(0)), PROPER(x0))
PROPER(sel1(x0, nil)) → c57(SEL1(proper(x0), ok(nil)), PROPER(x0))
PROPER(sel1(x0, 01)) → c57(SEL1(proper(x0), ok(01)), PROPER(x0))
PROPER(sel1(0, x1)) → c57(SEL1(ok(0), proper(x1)), PROPER(x1))
PROPER(sel1(nil, x1)) → c57(SEL1(ok(nil), proper(x1)), PROPER(x1))
PROPER(sel1(01, x1)) → c57(SEL1(ok(01), proper(x1)), PROPER(x1))
PROPER(quote(dbl(z0))) → c58(QUOTE(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(quote(s(z0))) → c58(QUOTE(s(proper(z0))), PROPER(s(z0)))
PROPER(quote(dbls(z0))) → c58(QUOTE(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(quote(cons(z0, z1))) → c58(QUOTE(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(quote(sel(z0, z1))) → c58(QUOTE(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(quote(indx(z0, z1))) → c58(QUOTE(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(quote(from(z0))) → c58(QUOTE(from(proper(z0))), PROPER(from(z0)))
PROPER(quote(dbl1(z0))) → c58(QUOTE(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(quote(s1(z0))) → c58(QUOTE(s1(proper(z0))), PROPER(s1(z0)))
PROPER(quote(sel1(z0, z1))) → c58(QUOTE(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(quote(quote(z0))) → c58(QUOTE(quote(proper(z0))), PROPER(quote(z0)))
PROPER(quote(0)) → c58(QUOTE(ok(0)))
PROPER(quote(nil)) → c58(QUOTE(ok(nil)))
PROPER(quote(01)) → c58(QUOTE(ok(01)))
TOP(mark(dbl(z0))) → c62(TOP(dbl(proper(z0))), PROPER(dbl(z0)))
TOP(mark(s(z0))) → c62(TOP(s(proper(z0))), PROPER(s(z0)))
TOP(mark(dbls(z0))) → c62(TOP(dbls(proper(z0))), PROPER(dbls(z0)))
TOP(mark(cons(z0, z1))) → c62(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
TOP(mark(sel(z0, z1))) → c62(TOP(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
TOP(mark(indx(z0, z1))) → c62(TOP(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
TOP(mark(from(z0))) → c62(TOP(from(proper(z0))), PROPER(from(z0)))
TOP(mark(dbl1(z0))) → c62(TOP(dbl1(proper(z0))), PROPER(dbl1(z0)))
TOP(mark(s1(z0))) → c62(TOP(s1(proper(z0))), PROPER(s1(z0)))
TOP(mark(sel1(z0, z1))) → c62(TOP(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
TOP(mark(quote(z0))) → c62(TOP(quote(proper(z0))), PROPER(quote(z0)))
TOP(mark(0)) → c62(TOP(ok(0)))
TOP(mark(nil)) → c62(TOP(ok(nil)))
TOP(mark(01)) → c62(TOP(ok(01)))
K tuples:none
Defined Rule Symbols:
active, s, dbl, cons, dbls, sel, indx, s1, dbl1, sel1, quote, proper, from
Defined Pair Symbols:
ACTIVE, DBL, DBLS, SEL, INDX, DBL1, S1, SEL1, QUOTE, S, CONS, FROM, TOP, PROPER
Compound Symbols:
c5, c12, c15, c16, c19, c20, c24, c25, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c59, c60, c61, c63, c8, c, c17, c17, c1, c18, c18, c2, c21, c21, c3, c22, c22, c4, c23, c23, c6, c26, c26, c7, c45, c45, c47, c47, c48, c48, c50, c50, c51, c51, c52, c52, c53, c53, c54, c54, c56, c56, c57, c57, c58, c58, c62, c62
(95) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
TOP(
ok(
z0)) →
c63(
TOP(
active(
z0)),
ACTIVE(
z0)) by
TOP(ok(dbl(0))) → c63(TOP(mark(0)), ACTIVE(dbl(0)))
TOP(ok(dbl(s(z0)))) → c63(TOP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
TOP(ok(dbls(nil))) → c63(TOP(mark(nil)), ACTIVE(dbls(nil)))
TOP(ok(dbls(cons(z0, z1)))) → c63(TOP(mark(cons(dbl(z0), dbls(z1)))), ACTIVE(dbls(cons(z0, z1))))
TOP(ok(sel(0, cons(z0, z1)))) → c63(TOP(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
TOP(ok(sel(s(z0), cons(z1, z2)))) → c63(TOP(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
TOP(ok(indx(nil, z0))) → c63(TOP(mark(nil)), ACTIVE(indx(nil, z0)))
TOP(ok(indx(cons(z0, z1), z2))) → c63(TOP(mark(cons(sel(z0, z2), indx(z1, z2)))), ACTIVE(indx(cons(z0, z1), z2)))
TOP(ok(from(z0))) → c63(TOP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
TOP(ok(dbl1(0))) → c63(TOP(mark(01)), ACTIVE(dbl1(0)))
TOP(ok(dbl1(s(z0)))) → c63(TOP(mark(s1(s1(dbl1(z0))))), ACTIVE(dbl1(s(z0))))
TOP(ok(sel1(0, cons(z0, z1)))) → c63(TOP(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
TOP(ok(sel1(s(z0), cons(z1, z2)))) → c63(TOP(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
TOP(ok(quote(0))) → c63(TOP(mark(01)), ACTIVE(quote(0)))
TOP(ok(quote(s(z0)))) → c63(TOP(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
TOP(ok(quote(dbl(z0)))) → c63(TOP(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
TOP(ok(quote(sel(z0, z1)))) → c63(TOP(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
TOP(ok(dbl(z0))) → c63(TOP(dbl(active(z0))), ACTIVE(dbl(z0)))
TOP(ok(dbls(z0))) → c63(TOP(dbls(active(z0))), ACTIVE(dbls(z0)))
TOP(ok(sel(z0, z1))) → c63(TOP(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
TOP(ok(sel(z0, z1))) → c63(TOP(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
TOP(ok(indx(z0, z1))) → c63(TOP(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
TOP(ok(dbl1(z0))) → c63(TOP(dbl1(active(z0))), ACTIVE(dbl1(z0)))
TOP(ok(s1(z0))) → c63(TOP(s1(active(z0))), ACTIVE(s1(z0)))
TOP(ok(sel1(z0, z1))) → c63(TOP(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
TOP(ok(sel1(z0, z1))) → c63(TOP(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
TOP(ok(quote(z0))) → c63(TOP(quote(active(z0))), ACTIVE(quote(z0)))
(96) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(dbl(0)) → mark(0)
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
active(dbls(nil)) → mark(nil)
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1)))
active(sel(0, cons(z0, z1))) → mark(z0)
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
active(indx(nil, z0)) → mark(nil)
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2)))
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(dbl1(0)) → mark(01)
active(dbl1(s(z0))) → mark(s1(s1(dbl1(z0))))
active(sel1(0, cons(z0, z1))) → mark(z0)
active(sel1(s(z0), cons(z1, z2))) → mark(sel1(z0, z2))
active(quote(0)) → mark(01)
active(quote(s(z0))) → mark(s1(quote(z0)))
active(quote(dbl(z0))) → mark(dbl1(z0))
active(quote(sel(z0, z1))) → mark(sel1(z0, z1))
active(dbl(z0)) → dbl(active(z0))
active(dbls(z0)) → dbls(active(z0))
active(sel(z0, z1)) → sel(active(z0), z1)
active(sel(z0, z1)) → sel(z0, active(z1))
active(indx(z0, z1)) → indx(active(z0), z1)
active(dbl1(z0)) → dbl1(active(z0))
active(s1(z0)) → s1(active(z0))
active(sel1(z0, z1)) → sel1(active(z0), z1)
active(sel1(z0, z1)) → sel1(z0, active(z1))
active(quote(z0)) → quote(active(z0))
s(ok(z0)) → ok(s(z0))
dbl(mark(z0)) → mark(dbl(z0))
dbl(ok(z0)) → ok(dbl(z0))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
dbls(mark(z0)) → mark(dbls(z0))
dbls(ok(z0)) → ok(dbls(z0))
sel(mark(z0), z1) → mark(sel(z0, z1))
sel(z0, mark(z1)) → mark(sel(z0, z1))
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
indx(mark(z0), z1) → mark(indx(z0, z1))
indx(ok(z0), ok(z1)) → ok(indx(z0, z1))
s1(mark(z0)) → mark(s1(z0))
s1(ok(z0)) → ok(s1(z0))
dbl1(mark(z0)) → mark(dbl1(z0))
dbl1(ok(z0)) → ok(dbl1(z0))
sel1(mark(z0), z1) → mark(sel1(z0, z1))
sel1(z0, mark(z1)) → mark(sel1(z0, z1))
sel1(ok(z0), ok(z1)) → ok(sel1(z0, z1))
quote(mark(z0)) → mark(quote(z0))
quote(ok(z0)) → ok(quote(z0))
proper(dbl(z0)) → dbl(proper(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(dbls(z0)) → dbls(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
proper(indx(z0, z1)) → indx(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(dbl1(z0)) → dbl1(proper(z0))
proper(01) → ok(01)
proper(s1(z0)) → s1(proper(z0))
proper(sel1(z0, z1)) → sel1(proper(z0), proper(z1))
proper(quote(z0)) → quote(proper(z0))
from(ok(z0)) → ok(from(z0))
Tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)))
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0))))))
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0))))))
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0)))
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(indx(sel1(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(indx(sel1(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel1(z0, z2)), x1), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(indx(quote(dbl(z0)), x1)) → c21(INDX(mark(dbl1(z0)), x1), ACTIVE(quote(dbl(z0))))
ACTIVE(indx(quote(sel(z0, z1)), x1)) → c21(INDX(mark(sel1(z0, z1)), x1), ACTIVE(quote(sel(z0, z1))))
ACTIVE(indx(dbl(z0), x1)) → c21(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
ACTIVE(indx(dbls(z0), x1)) → c21(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(indx(z0, z1), x1)) → c21(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1)))
ACTIVE(indx(dbl1(z0), x1)) → c21(INDX(dbl1(active(z0)), x1), ACTIVE(dbl1(z0)))
ACTIVE(indx(s1(z0), x1)) → c21(INDX(s1(active(z0)), x1), ACTIVE(s1(z0)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(active(z0), z1), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(z0, active(z1)), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(quote(z0), x1)) → c21(INDX(quote(active(z0)), x1), ACTIVE(quote(z0)))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)))
ACTIVE(indx(dbl(0), x1)) → c21(INDX(mark(0), x1))
ACTIVE(indx(dbls(nil), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(indx(indx(nil, z0), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0))))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1))
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0)))
ACTIVE(dbl1(sel(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl1(sel(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl1(sel1(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl1(sel1(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl1(quote(dbl(z0)))) → c22(DBL1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl1(quote(sel(z0, z1)))) → c22(DBL1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl1(dbl(z0))) → c22(DBL1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl1(dbls(z0))) → c22(DBL1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(indx(z0, z1))) → c22(DBL1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl1(dbl1(z0))) → c22(DBL1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl1(s1(z0))) → c22(DBL1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(quote(z0))) → c22(DBL1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(dbl1(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(dbl(0))) → c22(DBL1(mark(0)))
ACTIVE(dbl1(dbls(nil))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(indx(nil, z0))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(dbl1(0))) → c22(DBL1(mark(01)))
ACTIVE(dbl(dbl1(s(z0)))) → c4(DBL(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(DBLS(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(INDX(mark(s1(s1(dbl1(z0)))), x1))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(DBL1(mark(s(s(dbl(z0))))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(ACTIVE(dbl(s(z0))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(DBL1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(DBL1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl1(from(z0))) → c4(DBL1(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl1(from(z0))) → c4(ACTIVE(from(z0)))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(DBL1(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(s1(sel(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(s1(sel(s(z0), cons(z1, z2)))) → c23(S1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(s1(sel1(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(s1(sel1(s(z0), cons(z1, z2)))) → c23(S1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(s1(quote(dbl(z0)))) → c23(S1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(s1(quote(sel(z0, z1)))) → c23(S1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(s1(dbl(z0))) → c23(S1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(s1(dbls(z0))) → c23(S1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(s1(indx(z0, z1))) → c23(S1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(s1(dbl1(z0))) → c23(S1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(s1(s1(z0))) → c23(S1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(quote(z0))) → c23(S1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(s1(dbl(0))) → c23(S1(mark(0)))
ACTIVE(s1(dbls(nil))) → c23(S1(mark(nil)))
ACTIVE(s1(indx(nil, z0))) → c23(S1(mark(nil)))
ACTIVE(s1(dbl1(0))) → c23(S1(mark(01)))
ACTIVE(s1(dbl(s(z0)))) → c6(S1(mark(s(s(dbl(z0))))))
ACTIVE(s1(dbl(s(z0)))) → c6(ACTIVE(dbl(s(z0))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(S1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(S1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(s1(from(z0))) → c6(S1(mark(cons(z0, from(s(z0))))))
ACTIVE(s1(from(z0))) → c6(ACTIVE(from(z0)))
ACTIVE(s1(dbl1(s(z0)))) → c6(S1(mark(s1(s1(dbl1(z0))))))
ACTIVE(s1(dbl1(s(z0)))) → c6(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(sel(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(quote(sel(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(quote(sel1(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(quote(sel1(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(quote(quote(dbl(z0)))) → c26(QUOTE(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(quote(quote(sel(z0, z1)))) → c26(QUOTE(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(quote(dbl(z0))) → c26(QUOTE(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(quote(dbls(z0))) → c26(QUOTE(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(quote(indx(z0, z1))) → c26(QUOTE(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(quote(dbl1(z0))) → c26(QUOTE(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(quote(s1(z0))) → c26(QUOTE(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(quote(z0))) → c26(QUOTE(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(quote(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(quote(0))) → c22(DBL1(mark(01)))
ACTIVE(s1(quote(0))) → c23(S1(mark(01)))
ACTIVE(quote(dbl(0))) → c26(QUOTE(mark(0)))
ACTIVE(quote(dbls(nil))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(indx(nil, z0))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(dbl1(0))) → c26(QUOTE(mark(01)))
ACTIVE(quote(quote(0))) → c26(QUOTE(mark(01)))
ACTIVE(dbl(quote(s(z0)))) → c7(DBL(mark(s1(quote(z0)))))
ACTIVE(dbl(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(s(z0)))) → c7(DBLS(mark(s1(quote(z0)))))
ACTIVE(dbls(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(indx(quote(s(z0)), x1)) → c7(INDX(mark(s1(quote(z0))), x1))
ACTIVE(indx(quote(s(z0)), x1)) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbl1(quote(s(z0)))) → c7(DBL1(mark(s1(quote(z0)))))
ACTIVE(dbl1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(s1(quote(s(z0)))) → c7(S1(mark(s1(quote(z0)))))
ACTIVE(s1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(quote(dbl(s(z0)))) → c7(QUOTE(mark(s(s(dbl(z0))))))
ACTIVE(quote(dbl(s(z0)))) → c7(ACTIVE(dbl(s(z0))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(QUOTE(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(QUOTE(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(quote(from(z0))) → c7(QUOTE(mark(cons(z0, from(s(z0))))))
ACTIVE(quote(from(z0))) → c7(ACTIVE(from(z0)))
ACTIVE(quote(dbl1(s(z0)))) → c7(QUOTE(mark(s1(s1(dbl1(z0))))))
ACTIVE(quote(dbl1(s(z0)))) → c7(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(quote(s(z0)))) → c7(QUOTE(mark(s1(quote(z0)))))
ACTIVE(quote(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
PROPER(dbl(dbl(z0))) → c45(DBL(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbl(s(z0))) → c45(DBL(s(proper(z0))), PROPER(s(z0)))
PROPER(dbl(dbls(z0))) → c45(DBL(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbl(cons(z0, z1))) → c45(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbl(sel(z0, z1))) → c45(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbl(indx(z0, z1))) → c45(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbl(from(z0))) → c45(DBL(from(proper(z0))), PROPER(from(z0)))
PROPER(dbl(dbl1(z0))) → c45(DBL(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbl(s1(z0))) → c45(DBL(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbl(sel1(z0, z1))) → c45(DBL(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbl(quote(z0))) → c45(DBL(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbl(0)) → c45(DBL(ok(0)))
PROPER(dbl(nil)) → c45(DBL(ok(nil)))
PROPER(dbl(01)) → c45(DBL(ok(01)))
PROPER(s(dbl(z0))) → c47(S(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(s(s(z0))) → c47(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(dbls(z0))) → c47(S(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(s(cons(z0, z1))) → c47(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(sel(z0, z1))) → c47(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(s(indx(z0, z1))) → c47(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(s(from(z0))) → c47(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(dbl1(z0))) → c47(S(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(s(s1(z0))) → c47(S(s1(proper(z0))), PROPER(s1(z0)))
PROPER(s(sel1(z0, z1))) → c47(S(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(s(quote(z0))) → c47(S(quote(proper(z0))), PROPER(quote(z0)))
PROPER(s(0)) → c47(S(ok(0)))
PROPER(s(nil)) → c47(S(ok(nil)))
PROPER(s(01)) → c47(S(ok(01)))
PROPER(dbls(dbl(z0))) → c48(DBLS(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbls(s(z0))) → c48(DBLS(s(proper(z0))), PROPER(s(z0)))
PROPER(dbls(dbls(z0))) → c48(DBLS(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbls(cons(z0, z1))) → c48(DBLS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbls(sel(z0, z1))) → c48(DBLS(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbls(indx(z0, z1))) → c48(DBLS(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbls(from(z0))) → c48(DBLS(from(proper(z0))), PROPER(from(z0)))
PROPER(dbls(dbl1(z0))) → c48(DBLS(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbls(s1(z0))) → c48(DBLS(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbls(sel1(z0, z1))) → c48(DBLS(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbls(quote(z0))) → c48(DBLS(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbls(0)) → c48(DBLS(ok(0)))
PROPER(dbls(nil)) → c48(DBLS(ok(nil)))
PROPER(dbls(01)) → c48(DBLS(ok(01)))
PROPER(cons(x0, dbl(z0))) → c50(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(cons(x0, s(z0))) → c50(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, dbls(z0))) → c50(CONS(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(cons(x0, cons(z0, z1))) → c50(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, sel(z0, z1))) → c50(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(cons(x0, indx(z0, z1))) → c50(CONS(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(cons(x0, from(z0))) → c50(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, dbl1(z0))) → c50(CONS(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(cons(x0, s1(z0))) → c50(CONS(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(cons(x0, sel1(z0, z1))) → c50(CONS(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(cons(x0, quote(z0))) → c50(CONS(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(cons(dbl(z0), x1)) → c50(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(cons(s(z0), x1)) → c50(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(dbls(z0), x1)) → c50(CONS(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c50(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(sel(z0, z1), x1)) → c50(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(cons(indx(z0, z1), x1)) → c50(CONS(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c50(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(dbl1(z0), x1)) → c50(CONS(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(cons(s1(z0), x1)) → c50(CONS(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(cons(sel1(z0, z1), x1)) → c50(CONS(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(cons(quote(z0), x1)) → c50(CONS(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c50(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c50(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, 01)) → c50(CONS(proper(x0), ok(01)), PROPER(x0))
PROPER(cons(0, x1)) → c50(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c50(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(01, x1)) → c50(CONS(ok(01), proper(x1)), PROPER(x1))
PROPER(sel(x0, dbl(z0))) → c51(SEL(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(sel(x0, s(z0))) → c51(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(sel(x0, dbls(z0))) → c51(SEL(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(sel(x0, cons(z0, z1))) → c51(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(sel(x0, sel(z0, z1))) → c51(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(sel(x0, indx(z0, z1))) → c51(SEL(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(sel(x0, from(z0))) → c51(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(sel(x0, dbl1(z0))) → c51(SEL(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(sel(x0, s1(z0))) → c51(SEL(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(sel(x0, sel1(z0, z1))) → c51(SEL(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(sel(x0, quote(z0))) → c51(SEL(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(sel(dbl(z0), x1)) → c51(SEL(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(sel(s(z0), x1)) → c51(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(sel(dbls(z0), x1)) → c51(SEL(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(sel(cons(z0, z1), x1)) → c51(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(sel(sel(z0, z1), x1)) → c51(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(sel(indx(z0, z1), x1)) → c51(SEL(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(sel(from(z0), x1)) → c51(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(sel(dbl1(z0), x1)) → c51(SEL(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(sel(s1(z0), x1)) → c51(SEL(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(sel(sel1(z0, z1), x1)) → c51(SEL(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(sel(quote(z0), x1)) → c51(SEL(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(sel(x0, 0)) → c51(SEL(proper(x0), ok(0)), PROPER(x0))
PROPER(sel(x0, nil)) → c51(SEL(proper(x0), ok(nil)), PROPER(x0))
PROPER(sel(x0, 01)) → c51(SEL(proper(x0), ok(01)), PROPER(x0))
PROPER(sel(0, x1)) → c51(SEL(ok(0), proper(x1)), PROPER(x1))
PROPER(sel(nil, x1)) → c51(SEL(ok(nil), proper(x1)), PROPER(x1))
PROPER(sel(01, x1)) → c51(SEL(ok(01), proper(x1)), PROPER(x1))
PROPER(indx(x0, dbl(z0))) → c52(INDX(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(indx(x0, s(z0))) → c52(INDX(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(indx(x0, dbls(z0))) → c52(INDX(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(indx(x0, cons(z0, z1))) → c52(INDX(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(indx(x0, sel(z0, z1))) → c52(INDX(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(indx(x0, indx(z0, z1))) → c52(INDX(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(indx(x0, from(z0))) → c52(INDX(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(indx(x0, dbl1(z0))) → c52(INDX(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(indx(x0, s1(z0))) → c52(INDX(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(indx(x0, sel1(z0, z1))) → c52(INDX(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(indx(x0, quote(z0))) → c52(INDX(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(indx(dbl(z0), x1)) → c52(INDX(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(indx(s(z0), x1)) → c52(INDX(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(indx(dbls(z0), x1)) → c52(INDX(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(indx(cons(z0, z1), x1)) → c52(INDX(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(indx(sel(z0, z1), x1)) → c52(INDX(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(indx(indx(z0, z1), x1)) → c52(INDX(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(indx(from(z0), x1)) → c52(INDX(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(indx(dbl1(z0), x1)) → c52(INDX(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(indx(s1(z0), x1)) → c52(INDX(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(indx(sel1(z0, z1), x1)) → c52(INDX(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(indx(quote(z0), x1)) → c52(INDX(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(indx(x0, 0)) → c52(INDX(proper(x0), ok(0)), PROPER(x0))
PROPER(indx(x0, nil)) → c52(INDX(proper(x0), ok(nil)), PROPER(x0))
PROPER(indx(x0, 01)) → c52(INDX(proper(x0), ok(01)), PROPER(x0))
PROPER(indx(0, x1)) → c52(INDX(ok(0), proper(x1)), PROPER(x1))
PROPER(indx(nil, x1)) → c52(INDX(ok(nil), proper(x1)), PROPER(x1))
PROPER(indx(01, x1)) → c52(INDX(ok(01), proper(x1)), PROPER(x1))
PROPER(from(dbl(z0))) → c53(FROM(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(from(s(z0))) → c53(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(dbls(z0))) → c53(FROM(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(from(cons(z0, z1))) → c53(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(sel(z0, z1))) → c53(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(from(indx(z0, z1))) → c53(FROM(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(from(from(z0))) → c53(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(dbl1(z0))) → c53(FROM(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(from(s1(z0))) → c53(FROM(s1(proper(z0))), PROPER(s1(z0)))
PROPER(from(sel1(z0, z1))) → c53(FROM(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(from(quote(z0))) → c53(FROM(quote(proper(z0))), PROPER(quote(z0)))
PROPER(from(0)) → c53(FROM(ok(0)))
PROPER(from(nil)) → c53(FROM(ok(nil)))
PROPER(from(01)) → c53(FROM(ok(01)))
PROPER(dbl1(dbl(z0))) → c54(DBL1(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbl1(s(z0))) → c54(DBL1(s(proper(z0))), PROPER(s(z0)))
PROPER(dbl1(dbls(z0))) → c54(DBL1(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbl1(cons(z0, z1))) → c54(DBL1(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbl1(sel(z0, z1))) → c54(DBL1(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbl1(indx(z0, z1))) → c54(DBL1(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbl1(from(z0))) → c54(DBL1(from(proper(z0))), PROPER(from(z0)))
PROPER(dbl1(dbl1(z0))) → c54(DBL1(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbl1(s1(z0))) → c54(DBL1(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbl1(sel1(z0, z1))) → c54(DBL1(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbl1(quote(z0))) → c54(DBL1(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbl1(0)) → c54(DBL1(ok(0)))
PROPER(dbl1(nil)) → c54(DBL1(ok(nil)))
PROPER(dbl1(01)) → c54(DBL1(ok(01)))
PROPER(s1(dbl(z0))) → c56(S1(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(s1(s(z0))) → c56(S1(s(proper(z0))), PROPER(s(z0)))
PROPER(s1(dbls(z0))) → c56(S1(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(s1(cons(z0, z1))) → c56(S1(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s1(sel(z0, z1))) → c56(S1(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(s1(indx(z0, z1))) → c56(S1(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(s1(from(z0))) → c56(S1(from(proper(z0))), PROPER(from(z0)))
PROPER(s1(dbl1(z0))) → c56(S1(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(s1(s1(z0))) → c56(S1(s1(proper(z0))), PROPER(s1(z0)))
PROPER(s1(sel1(z0, z1))) → c56(S1(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(s1(quote(z0))) → c56(S1(quote(proper(z0))), PROPER(quote(z0)))
PROPER(s1(0)) → c56(S1(ok(0)))
PROPER(s1(nil)) → c56(S1(ok(nil)))
PROPER(s1(01)) → c56(S1(ok(01)))
PROPER(sel1(x0, dbl(z0))) → c57(SEL1(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(sel1(x0, s(z0))) → c57(SEL1(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(sel1(x0, dbls(z0))) → c57(SEL1(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(sel1(x0, cons(z0, z1))) → c57(SEL1(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(sel1(x0, sel(z0, z1))) → c57(SEL1(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(sel1(x0, indx(z0, z1))) → c57(SEL1(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(sel1(x0, from(z0))) → c57(SEL1(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(sel1(x0, dbl1(z0))) → c57(SEL1(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(sel1(x0, s1(z0))) → c57(SEL1(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(sel1(x0, sel1(z0, z1))) → c57(SEL1(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(sel1(x0, quote(z0))) → c57(SEL1(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(sel1(dbl(z0), x1)) → c57(SEL1(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(sel1(s(z0), x1)) → c57(SEL1(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(sel1(dbls(z0), x1)) → c57(SEL1(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(sel1(cons(z0, z1), x1)) → c57(SEL1(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(sel1(sel(z0, z1), x1)) → c57(SEL1(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(sel1(indx(z0, z1), x1)) → c57(SEL1(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(sel1(from(z0), x1)) → c57(SEL1(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(sel1(dbl1(z0), x1)) → c57(SEL1(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(sel1(s1(z0), x1)) → c57(SEL1(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(sel1(sel1(z0, z1), x1)) → c57(SEL1(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(sel1(quote(z0), x1)) → c57(SEL1(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(sel1(x0, 0)) → c57(SEL1(proper(x0), ok(0)), PROPER(x0))
PROPER(sel1(x0, nil)) → c57(SEL1(proper(x0), ok(nil)), PROPER(x0))
PROPER(sel1(x0, 01)) → c57(SEL1(proper(x0), ok(01)), PROPER(x0))
PROPER(sel1(0, x1)) → c57(SEL1(ok(0), proper(x1)), PROPER(x1))
PROPER(sel1(nil, x1)) → c57(SEL1(ok(nil), proper(x1)), PROPER(x1))
PROPER(sel1(01, x1)) → c57(SEL1(ok(01), proper(x1)), PROPER(x1))
PROPER(quote(dbl(z0))) → c58(QUOTE(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(quote(s(z0))) → c58(QUOTE(s(proper(z0))), PROPER(s(z0)))
PROPER(quote(dbls(z0))) → c58(QUOTE(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(quote(cons(z0, z1))) → c58(QUOTE(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(quote(sel(z0, z1))) → c58(QUOTE(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(quote(indx(z0, z1))) → c58(QUOTE(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(quote(from(z0))) → c58(QUOTE(from(proper(z0))), PROPER(from(z0)))
PROPER(quote(dbl1(z0))) → c58(QUOTE(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(quote(s1(z0))) → c58(QUOTE(s1(proper(z0))), PROPER(s1(z0)))
PROPER(quote(sel1(z0, z1))) → c58(QUOTE(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(quote(quote(z0))) → c58(QUOTE(quote(proper(z0))), PROPER(quote(z0)))
PROPER(quote(0)) → c58(QUOTE(ok(0)))
PROPER(quote(nil)) → c58(QUOTE(ok(nil)))
PROPER(quote(01)) → c58(QUOTE(ok(01)))
TOP(mark(dbl(z0))) → c62(TOP(dbl(proper(z0))), PROPER(dbl(z0)))
TOP(mark(s(z0))) → c62(TOP(s(proper(z0))), PROPER(s(z0)))
TOP(mark(dbls(z0))) → c62(TOP(dbls(proper(z0))), PROPER(dbls(z0)))
TOP(mark(cons(z0, z1))) → c62(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
TOP(mark(sel(z0, z1))) → c62(TOP(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
TOP(mark(indx(z0, z1))) → c62(TOP(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
TOP(mark(from(z0))) → c62(TOP(from(proper(z0))), PROPER(from(z0)))
TOP(mark(dbl1(z0))) → c62(TOP(dbl1(proper(z0))), PROPER(dbl1(z0)))
TOP(mark(s1(z0))) → c62(TOP(s1(proper(z0))), PROPER(s1(z0)))
TOP(mark(sel1(z0, z1))) → c62(TOP(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
TOP(mark(quote(z0))) → c62(TOP(quote(proper(z0))), PROPER(quote(z0)))
TOP(mark(0)) → c62(TOP(ok(0)))
TOP(mark(nil)) → c62(TOP(ok(nil)))
TOP(mark(01)) → c62(TOP(ok(01)))
TOP(ok(dbl(0))) → c63(TOP(mark(0)), ACTIVE(dbl(0)))
TOP(ok(dbl(s(z0)))) → c63(TOP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
TOP(ok(dbls(nil))) → c63(TOP(mark(nil)), ACTIVE(dbls(nil)))
TOP(ok(dbls(cons(z0, z1)))) → c63(TOP(mark(cons(dbl(z0), dbls(z1)))), ACTIVE(dbls(cons(z0, z1))))
TOP(ok(sel(0, cons(z0, z1)))) → c63(TOP(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
TOP(ok(sel(s(z0), cons(z1, z2)))) → c63(TOP(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
TOP(ok(indx(nil, z0))) → c63(TOP(mark(nil)), ACTIVE(indx(nil, z0)))
TOP(ok(indx(cons(z0, z1), z2))) → c63(TOP(mark(cons(sel(z0, z2), indx(z1, z2)))), ACTIVE(indx(cons(z0, z1), z2)))
TOP(ok(from(z0))) → c63(TOP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
TOP(ok(dbl1(0))) → c63(TOP(mark(01)), ACTIVE(dbl1(0)))
TOP(ok(dbl1(s(z0)))) → c63(TOP(mark(s1(s1(dbl1(z0))))), ACTIVE(dbl1(s(z0))))
TOP(ok(sel1(0, cons(z0, z1)))) → c63(TOP(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
TOP(ok(sel1(s(z0), cons(z1, z2)))) → c63(TOP(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
TOP(ok(quote(0))) → c63(TOP(mark(01)), ACTIVE(quote(0)))
TOP(ok(quote(s(z0)))) → c63(TOP(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
TOP(ok(quote(dbl(z0)))) → c63(TOP(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
TOP(ok(quote(sel(z0, z1)))) → c63(TOP(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
TOP(ok(dbl(z0))) → c63(TOP(dbl(active(z0))), ACTIVE(dbl(z0)))
TOP(ok(dbls(z0))) → c63(TOP(dbls(active(z0))), ACTIVE(dbls(z0)))
TOP(ok(sel(z0, z1))) → c63(TOP(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
TOP(ok(sel(z0, z1))) → c63(TOP(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
TOP(ok(indx(z0, z1))) → c63(TOP(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
TOP(ok(dbl1(z0))) → c63(TOP(dbl1(active(z0))), ACTIVE(dbl1(z0)))
TOP(ok(s1(z0))) → c63(TOP(s1(active(z0))), ACTIVE(s1(z0)))
TOP(ok(sel1(z0, z1))) → c63(TOP(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
TOP(ok(sel1(z0, z1))) → c63(TOP(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
TOP(ok(quote(z0))) → c63(TOP(quote(active(z0))), ACTIVE(quote(z0)))
S tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)))
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0))))))
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0))))))
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0)))
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(indx(sel1(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(indx(sel1(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel1(z0, z2)), x1), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(indx(quote(dbl(z0)), x1)) → c21(INDX(mark(dbl1(z0)), x1), ACTIVE(quote(dbl(z0))))
ACTIVE(indx(quote(sel(z0, z1)), x1)) → c21(INDX(mark(sel1(z0, z1)), x1), ACTIVE(quote(sel(z0, z1))))
ACTIVE(indx(dbl(z0), x1)) → c21(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
ACTIVE(indx(dbls(z0), x1)) → c21(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(indx(z0, z1), x1)) → c21(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1)))
ACTIVE(indx(dbl1(z0), x1)) → c21(INDX(dbl1(active(z0)), x1), ACTIVE(dbl1(z0)))
ACTIVE(indx(s1(z0), x1)) → c21(INDX(s1(active(z0)), x1), ACTIVE(s1(z0)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(active(z0), z1), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(z0, active(z1)), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(quote(z0), x1)) → c21(INDX(quote(active(z0)), x1), ACTIVE(quote(z0)))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)))
ACTIVE(indx(dbl(0), x1)) → c21(INDX(mark(0), x1))
ACTIVE(indx(dbls(nil), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(indx(indx(nil, z0), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0))))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1))
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0)))
ACTIVE(dbl1(sel(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl1(sel(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl1(sel1(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl1(sel1(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl1(quote(dbl(z0)))) → c22(DBL1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl1(quote(sel(z0, z1)))) → c22(DBL1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl1(dbl(z0))) → c22(DBL1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl1(dbls(z0))) → c22(DBL1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(indx(z0, z1))) → c22(DBL1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl1(dbl1(z0))) → c22(DBL1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl1(s1(z0))) → c22(DBL1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(quote(z0))) → c22(DBL1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(dbl1(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(dbl(0))) → c22(DBL1(mark(0)))
ACTIVE(dbl1(dbls(nil))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(indx(nil, z0))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(dbl1(0))) → c22(DBL1(mark(01)))
ACTIVE(dbl(dbl1(s(z0)))) → c4(DBL(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(DBLS(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(INDX(mark(s1(s1(dbl1(z0)))), x1))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(DBL1(mark(s(s(dbl(z0))))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(ACTIVE(dbl(s(z0))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(DBL1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(DBL1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl1(from(z0))) → c4(DBL1(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl1(from(z0))) → c4(ACTIVE(from(z0)))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(DBL1(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(s1(sel(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(s1(sel(s(z0), cons(z1, z2)))) → c23(S1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(s1(sel1(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(s1(sel1(s(z0), cons(z1, z2)))) → c23(S1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(s1(quote(dbl(z0)))) → c23(S1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(s1(quote(sel(z0, z1)))) → c23(S1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(s1(dbl(z0))) → c23(S1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(s1(dbls(z0))) → c23(S1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(s1(indx(z0, z1))) → c23(S1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(s1(dbl1(z0))) → c23(S1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(s1(s1(z0))) → c23(S1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(quote(z0))) → c23(S1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(s1(dbl(0))) → c23(S1(mark(0)))
ACTIVE(s1(dbls(nil))) → c23(S1(mark(nil)))
ACTIVE(s1(indx(nil, z0))) → c23(S1(mark(nil)))
ACTIVE(s1(dbl1(0))) → c23(S1(mark(01)))
ACTIVE(s1(dbl(s(z0)))) → c6(S1(mark(s(s(dbl(z0))))))
ACTIVE(s1(dbl(s(z0)))) → c6(ACTIVE(dbl(s(z0))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(S1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(S1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(s1(from(z0))) → c6(S1(mark(cons(z0, from(s(z0))))))
ACTIVE(s1(from(z0))) → c6(ACTIVE(from(z0)))
ACTIVE(s1(dbl1(s(z0)))) → c6(S1(mark(s1(s1(dbl1(z0))))))
ACTIVE(s1(dbl1(s(z0)))) → c6(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(sel(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(quote(sel(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(quote(sel1(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(quote(sel1(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(quote(quote(dbl(z0)))) → c26(QUOTE(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(quote(quote(sel(z0, z1)))) → c26(QUOTE(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(quote(dbl(z0))) → c26(QUOTE(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(quote(dbls(z0))) → c26(QUOTE(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(quote(indx(z0, z1))) → c26(QUOTE(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(quote(dbl1(z0))) → c26(QUOTE(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(quote(s1(z0))) → c26(QUOTE(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(quote(z0))) → c26(QUOTE(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(quote(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(quote(0))) → c22(DBL1(mark(01)))
ACTIVE(s1(quote(0))) → c23(S1(mark(01)))
ACTIVE(quote(dbl(0))) → c26(QUOTE(mark(0)))
ACTIVE(quote(dbls(nil))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(indx(nil, z0))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(dbl1(0))) → c26(QUOTE(mark(01)))
ACTIVE(quote(quote(0))) → c26(QUOTE(mark(01)))
ACTIVE(dbl(quote(s(z0)))) → c7(DBL(mark(s1(quote(z0)))))
ACTIVE(dbl(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(s(z0)))) → c7(DBLS(mark(s1(quote(z0)))))
ACTIVE(dbls(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(indx(quote(s(z0)), x1)) → c7(INDX(mark(s1(quote(z0))), x1))
ACTIVE(indx(quote(s(z0)), x1)) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbl1(quote(s(z0)))) → c7(DBL1(mark(s1(quote(z0)))))
ACTIVE(dbl1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(s1(quote(s(z0)))) → c7(S1(mark(s1(quote(z0)))))
ACTIVE(s1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(quote(dbl(s(z0)))) → c7(QUOTE(mark(s(s(dbl(z0))))))
ACTIVE(quote(dbl(s(z0)))) → c7(ACTIVE(dbl(s(z0))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(QUOTE(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(QUOTE(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(quote(from(z0))) → c7(QUOTE(mark(cons(z0, from(s(z0))))))
ACTIVE(quote(from(z0))) → c7(ACTIVE(from(z0)))
ACTIVE(quote(dbl1(s(z0)))) → c7(QUOTE(mark(s1(s1(dbl1(z0))))))
ACTIVE(quote(dbl1(s(z0)))) → c7(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(quote(s(z0)))) → c7(QUOTE(mark(s1(quote(z0)))))
ACTIVE(quote(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
PROPER(dbl(dbl(z0))) → c45(DBL(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbl(s(z0))) → c45(DBL(s(proper(z0))), PROPER(s(z0)))
PROPER(dbl(dbls(z0))) → c45(DBL(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbl(cons(z0, z1))) → c45(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbl(sel(z0, z1))) → c45(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbl(indx(z0, z1))) → c45(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbl(from(z0))) → c45(DBL(from(proper(z0))), PROPER(from(z0)))
PROPER(dbl(dbl1(z0))) → c45(DBL(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbl(s1(z0))) → c45(DBL(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbl(sel1(z0, z1))) → c45(DBL(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbl(quote(z0))) → c45(DBL(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbl(0)) → c45(DBL(ok(0)))
PROPER(dbl(nil)) → c45(DBL(ok(nil)))
PROPER(dbl(01)) → c45(DBL(ok(01)))
PROPER(s(dbl(z0))) → c47(S(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(s(s(z0))) → c47(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(dbls(z0))) → c47(S(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(s(cons(z0, z1))) → c47(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(sel(z0, z1))) → c47(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(s(indx(z0, z1))) → c47(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(s(from(z0))) → c47(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(dbl1(z0))) → c47(S(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(s(s1(z0))) → c47(S(s1(proper(z0))), PROPER(s1(z0)))
PROPER(s(sel1(z0, z1))) → c47(S(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(s(quote(z0))) → c47(S(quote(proper(z0))), PROPER(quote(z0)))
PROPER(s(0)) → c47(S(ok(0)))
PROPER(s(nil)) → c47(S(ok(nil)))
PROPER(s(01)) → c47(S(ok(01)))
PROPER(dbls(dbl(z0))) → c48(DBLS(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbls(s(z0))) → c48(DBLS(s(proper(z0))), PROPER(s(z0)))
PROPER(dbls(dbls(z0))) → c48(DBLS(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbls(cons(z0, z1))) → c48(DBLS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbls(sel(z0, z1))) → c48(DBLS(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbls(indx(z0, z1))) → c48(DBLS(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbls(from(z0))) → c48(DBLS(from(proper(z0))), PROPER(from(z0)))
PROPER(dbls(dbl1(z0))) → c48(DBLS(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbls(s1(z0))) → c48(DBLS(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbls(sel1(z0, z1))) → c48(DBLS(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbls(quote(z0))) → c48(DBLS(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbls(0)) → c48(DBLS(ok(0)))
PROPER(dbls(nil)) → c48(DBLS(ok(nil)))
PROPER(dbls(01)) → c48(DBLS(ok(01)))
PROPER(cons(x0, dbl(z0))) → c50(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(cons(x0, s(z0))) → c50(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, dbls(z0))) → c50(CONS(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(cons(x0, cons(z0, z1))) → c50(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, sel(z0, z1))) → c50(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(cons(x0, indx(z0, z1))) → c50(CONS(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(cons(x0, from(z0))) → c50(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, dbl1(z0))) → c50(CONS(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(cons(x0, s1(z0))) → c50(CONS(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(cons(x0, sel1(z0, z1))) → c50(CONS(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(cons(x0, quote(z0))) → c50(CONS(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(cons(dbl(z0), x1)) → c50(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(cons(s(z0), x1)) → c50(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(dbls(z0), x1)) → c50(CONS(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c50(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(sel(z0, z1), x1)) → c50(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(cons(indx(z0, z1), x1)) → c50(CONS(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c50(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(dbl1(z0), x1)) → c50(CONS(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(cons(s1(z0), x1)) → c50(CONS(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(cons(sel1(z0, z1), x1)) → c50(CONS(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(cons(quote(z0), x1)) → c50(CONS(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c50(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c50(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, 01)) → c50(CONS(proper(x0), ok(01)), PROPER(x0))
PROPER(cons(0, x1)) → c50(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c50(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(01, x1)) → c50(CONS(ok(01), proper(x1)), PROPER(x1))
PROPER(sel(x0, dbl(z0))) → c51(SEL(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(sel(x0, s(z0))) → c51(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(sel(x0, dbls(z0))) → c51(SEL(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(sel(x0, cons(z0, z1))) → c51(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(sel(x0, sel(z0, z1))) → c51(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(sel(x0, indx(z0, z1))) → c51(SEL(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(sel(x0, from(z0))) → c51(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(sel(x0, dbl1(z0))) → c51(SEL(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(sel(x0, s1(z0))) → c51(SEL(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(sel(x0, sel1(z0, z1))) → c51(SEL(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(sel(x0, quote(z0))) → c51(SEL(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(sel(dbl(z0), x1)) → c51(SEL(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(sel(s(z0), x1)) → c51(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(sel(dbls(z0), x1)) → c51(SEL(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(sel(cons(z0, z1), x1)) → c51(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(sel(sel(z0, z1), x1)) → c51(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(sel(indx(z0, z1), x1)) → c51(SEL(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(sel(from(z0), x1)) → c51(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(sel(dbl1(z0), x1)) → c51(SEL(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(sel(s1(z0), x1)) → c51(SEL(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(sel(sel1(z0, z1), x1)) → c51(SEL(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(sel(quote(z0), x1)) → c51(SEL(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(sel(x0, 0)) → c51(SEL(proper(x0), ok(0)), PROPER(x0))
PROPER(sel(x0, nil)) → c51(SEL(proper(x0), ok(nil)), PROPER(x0))
PROPER(sel(x0, 01)) → c51(SEL(proper(x0), ok(01)), PROPER(x0))
PROPER(sel(0, x1)) → c51(SEL(ok(0), proper(x1)), PROPER(x1))
PROPER(sel(nil, x1)) → c51(SEL(ok(nil), proper(x1)), PROPER(x1))
PROPER(sel(01, x1)) → c51(SEL(ok(01), proper(x1)), PROPER(x1))
PROPER(indx(x0, dbl(z0))) → c52(INDX(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(indx(x0, s(z0))) → c52(INDX(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(indx(x0, dbls(z0))) → c52(INDX(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(indx(x0, cons(z0, z1))) → c52(INDX(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(indx(x0, sel(z0, z1))) → c52(INDX(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(indx(x0, indx(z0, z1))) → c52(INDX(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(indx(x0, from(z0))) → c52(INDX(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(indx(x0, dbl1(z0))) → c52(INDX(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(indx(x0, s1(z0))) → c52(INDX(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(indx(x0, sel1(z0, z1))) → c52(INDX(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(indx(x0, quote(z0))) → c52(INDX(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(indx(dbl(z0), x1)) → c52(INDX(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(indx(s(z0), x1)) → c52(INDX(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(indx(dbls(z0), x1)) → c52(INDX(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(indx(cons(z0, z1), x1)) → c52(INDX(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(indx(sel(z0, z1), x1)) → c52(INDX(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(indx(indx(z0, z1), x1)) → c52(INDX(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(indx(from(z0), x1)) → c52(INDX(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(indx(dbl1(z0), x1)) → c52(INDX(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(indx(s1(z0), x1)) → c52(INDX(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(indx(sel1(z0, z1), x1)) → c52(INDX(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(indx(quote(z0), x1)) → c52(INDX(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(indx(x0, 0)) → c52(INDX(proper(x0), ok(0)), PROPER(x0))
PROPER(indx(x0, nil)) → c52(INDX(proper(x0), ok(nil)), PROPER(x0))
PROPER(indx(x0, 01)) → c52(INDX(proper(x0), ok(01)), PROPER(x0))
PROPER(indx(0, x1)) → c52(INDX(ok(0), proper(x1)), PROPER(x1))
PROPER(indx(nil, x1)) → c52(INDX(ok(nil), proper(x1)), PROPER(x1))
PROPER(indx(01, x1)) → c52(INDX(ok(01), proper(x1)), PROPER(x1))
PROPER(from(dbl(z0))) → c53(FROM(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(from(s(z0))) → c53(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(dbls(z0))) → c53(FROM(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(from(cons(z0, z1))) → c53(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(sel(z0, z1))) → c53(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(from(indx(z0, z1))) → c53(FROM(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(from(from(z0))) → c53(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(dbl1(z0))) → c53(FROM(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(from(s1(z0))) → c53(FROM(s1(proper(z0))), PROPER(s1(z0)))
PROPER(from(sel1(z0, z1))) → c53(FROM(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(from(quote(z0))) → c53(FROM(quote(proper(z0))), PROPER(quote(z0)))
PROPER(from(0)) → c53(FROM(ok(0)))
PROPER(from(nil)) → c53(FROM(ok(nil)))
PROPER(from(01)) → c53(FROM(ok(01)))
PROPER(dbl1(dbl(z0))) → c54(DBL1(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbl1(s(z0))) → c54(DBL1(s(proper(z0))), PROPER(s(z0)))
PROPER(dbl1(dbls(z0))) → c54(DBL1(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbl1(cons(z0, z1))) → c54(DBL1(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbl1(sel(z0, z1))) → c54(DBL1(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbl1(indx(z0, z1))) → c54(DBL1(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbl1(from(z0))) → c54(DBL1(from(proper(z0))), PROPER(from(z0)))
PROPER(dbl1(dbl1(z0))) → c54(DBL1(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbl1(s1(z0))) → c54(DBL1(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbl1(sel1(z0, z1))) → c54(DBL1(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbl1(quote(z0))) → c54(DBL1(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbl1(0)) → c54(DBL1(ok(0)))
PROPER(dbl1(nil)) → c54(DBL1(ok(nil)))
PROPER(dbl1(01)) → c54(DBL1(ok(01)))
PROPER(s1(dbl(z0))) → c56(S1(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(s1(s(z0))) → c56(S1(s(proper(z0))), PROPER(s(z0)))
PROPER(s1(dbls(z0))) → c56(S1(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(s1(cons(z0, z1))) → c56(S1(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s1(sel(z0, z1))) → c56(S1(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(s1(indx(z0, z1))) → c56(S1(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(s1(from(z0))) → c56(S1(from(proper(z0))), PROPER(from(z0)))
PROPER(s1(dbl1(z0))) → c56(S1(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(s1(s1(z0))) → c56(S1(s1(proper(z0))), PROPER(s1(z0)))
PROPER(s1(sel1(z0, z1))) → c56(S1(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(s1(quote(z0))) → c56(S1(quote(proper(z0))), PROPER(quote(z0)))
PROPER(s1(0)) → c56(S1(ok(0)))
PROPER(s1(nil)) → c56(S1(ok(nil)))
PROPER(s1(01)) → c56(S1(ok(01)))
PROPER(sel1(x0, dbl(z0))) → c57(SEL1(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(sel1(x0, s(z0))) → c57(SEL1(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(sel1(x0, dbls(z0))) → c57(SEL1(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(sel1(x0, cons(z0, z1))) → c57(SEL1(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(sel1(x0, sel(z0, z1))) → c57(SEL1(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(sel1(x0, indx(z0, z1))) → c57(SEL1(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(sel1(x0, from(z0))) → c57(SEL1(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(sel1(x0, dbl1(z0))) → c57(SEL1(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(sel1(x0, s1(z0))) → c57(SEL1(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(sel1(x0, sel1(z0, z1))) → c57(SEL1(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(sel1(x0, quote(z0))) → c57(SEL1(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(sel1(dbl(z0), x1)) → c57(SEL1(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(sel1(s(z0), x1)) → c57(SEL1(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(sel1(dbls(z0), x1)) → c57(SEL1(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(sel1(cons(z0, z1), x1)) → c57(SEL1(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(sel1(sel(z0, z1), x1)) → c57(SEL1(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(sel1(indx(z0, z1), x1)) → c57(SEL1(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(sel1(from(z0), x1)) → c57(SEL1(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(sel1(dbl1(z0), x1)) → c57(SEL1(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(sel1(s1(z0), x1)) → c57(SEL1(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(sel1(sel1(z0, z1), x1)) → c57(SEL1(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(sel1(quote(z0), x1)) → c57(SEL1(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(sel1(x0, 0)) → c57(SEL1(proper(x0), ok(0)), PROPER(x0))
PROPER(sel1(x0, nil)) → c57(SEL1(proper(x0), ok(nil)), PROPER(x0))
PROPER(sel1(x0, 01)) → c57(SEL1(proper(x0), ok(01)), PROPER(x0))
PROPER(sel1(0, x1)) → c57(SEL1(ok(0), proper(x1)), PROPER(x1))
PROPER(sel1(nil, x1)) → c57(SEL1(ok(nil), proper(x1)), PROPER(x1))
PROPER(sel1(01, x1)) → c57(SEL1(ok(01), proper(x1)), PROPER(x1))
PROPER(quote(dbl(z0))) → c58(QUOTE(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(quote(s(z0))) → c58(QUOTE(s(proper(z0))), PROPER(s(z0)))
PROPER(quote(dbls(z0))) → c58(QUOTE(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(quote(cons(z0, z1))) → c58(QUOTE(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(quote(sel(z0, z1))) → c58(QUOTE(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(quote(indx(z0, z1))) → c58(QUOTE(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(quote(from(z0))) → c58(QUOTE(from(proper(z0))), PROPER(from(z0)))
PROPER(quote(dbl1(z0))) → c58(QUOTE(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(quote(s1(z0))) → c58(QUOTE(s1(proper(z0))), PROPER(s1(z0)))
PROPER(quote(sel1(z0, z1))) → c58(QUOTE(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(quote(quote(z0))) → c58(QUOTE(quote(proper(z0))), PROPER(quote(z0)))
PROPER(quote(0)) → c58(QUOTE(ok(0)))
PROPER(quote(nil)) → c58(QUOTE(ok(nil)))
PROPER(quote(01)) → c58(QUOTE(ok(01)))
TOP(mark(dbl(z0))) → c62(TOP(dbl(proper(z0))), PROPER(dbl(z0)))
TOP(mark(s(z0))) → c62(TOP(s(proper(z0))), PROPER(s(z0)))
TOP(mark(dbls(z0))) → c62(TOP(dbls(proper(z0))), PROPER(dbls(z0)))
TOP(mark(cons(z0, z1))) → c62(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
TOP(mark(sel(z0, z1))) → c62(TOP(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
TOP(mark(indx(z0, z1))) → c62(TOP(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
TOP(mark(from(z0))) → c62(TOP(from(proper(z0))), PROPER(from(z0)))
TOP(mark(dbl1(z0))) → c62(TOP(dbl1(proper(z0))), PROPER(dbl1(z0)))
TOP(mark(s1(z0))) → c62(TOP(s1(proper(z0))), PROPER(s1(z0)))
TOP(mark(sel1(z0, z1))) → c62(TOP(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
TOP(mark(quote(z0))) → c62(TOP(quote(proper(z0))), PROPER(quote(z0)))
TOP(mark(0)) → c62(TOP(ok(0)))
TOP(mark(nil)) → c62(TOP(ok(nil)))
TOP(mark(01)) → c62(TOP(ok(01)))
TOP(ok(dbl(0))) → c63(TOP(mark(0)), ACTIVE(dbl(0)))
TOP(ok(dbl(s(z0)))) → c63(TOP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
TOP(ok(dbls(nil))) → c63(TOP(mark(nil)), ACTIVE(dbls(nil)))
TOP(ok(dbls(cons(z0, z1)))) → c63(TOP(mark(cons(dbl(z0), dbls(z1)))), ACTIVE(dbls(cons(z0, z1))))
TOP(ok(sel(0, cons(z0, z1)))) → c63(TOP(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
TOP(ok(sel(s(z0), cons(z1, z2)))) → c63(TOP(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
TOP(ok(indx(nil, z0))) → c63(TOP(mark(nil)), ACTIVE(indx(nil, z0)))
TOP(ok(indx(cons(z0, z1), z2))) → c63(TOP(mark(cons(sel(z0, z2), indx(z1, z2)))), ACTIVE(indx(cons(z0, z1), z2)))
TOP(ok(from(z0))) → c63(TOP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
TOP(ok(dbl1(0))) → c63(TOP(mark(01)), ACTIVE(dbl1(0)))
TOP(ok(dbl1(s(z0)))) → c63(TOP(mark(s1(s1(dbl1(z0))))), ACTIVE(dbl1(s(z0))))
TOP(ok(sel1(0, cons(z0, z1)))) → c63(TOP(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
TOP(ok(sel1(s(z0), cons(z1, z2)))) → c63(TOP(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
TOP(ok(quote(0))) → c63(TOP(mark(01)), ACTIVE(quote(0)))
TOP(ok(quote(s(z0)))) → c63(TOP(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
TOP(ok(quote(dbl(z0)))) → c63(TOP(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
TOP(ok(quote(sel(z0, z1)))) → c63(TOP(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
TOP(ok(dbl(z0))) → c63(TOP(dbl(active(z0))), ACTIVE(dbl(z0)))
TOP(ok(dbls(z0))) → c63(TOP(dbls(active(z0))), ACTIVE(dbls(z0)))
TOP(ok(sel(z0, z1))) → c63(TOP(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
TOP(ok(sel(z0, z1))) → c63(TOP(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
TOP(ok(indx(z0, z1))) → c63(TOP(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
TOP(ok(dbl1(z0))) → c63(TOP(dbl1(active(z0))), ACTIVE(dbl1(z0)))
TOP(ok(s1(z0))) → c63(TOP(s1(active(z0))), ACTIVE(s1(z0)))
TOP(ok(sel1(z0, z1))) → c63(TOP(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
TOP(ok(sel1(z0, z1))) → c63(TOP(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
TOP(ok(quote(z0))) → c63(TOP(quote(active(z0))), ACTIVE(quote(z0)))
K tuples:none
Defined Rule Symbols:
active, s, dbl, cons, dbls, sel, indx, s1, dbl1, sel1, quote, proper, from
Defined Pair Symbols:
ACTIVE, DBL, DBLS, SEL, INDX, DBL1, S1, SEL1, QUOTE, S, CONS, FROM, PROPER, TOP
Compound Symbols:
c5, c12, c15, c16, c19, c20, c24, c25, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c59, c60, c61, c8, c, c17, c17, c1, c18, c18, c2, c21, c21, c3, c22, c22, c4, c23, c23, c6, c26, c26, c7, c45, c45, c47, c47, c48, c48, c50, c50, c51, c51, c52, c52, c53, c53, c54, c54, c56, c56, c57, c57, c58, c58, c62, c62, c63
(97) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID) transformation)
Removed 8 trailing nodes:
TOP(mark(0)) → c62(TOP(ok(0)))
TOP(ok(dbl(0))) → c63(TOP(mark(0)), ACTIVE(dbl(0)))
TOP(mark(nil)) → c62(TOP(ok(nil)))
TOP(mark(01)) → c62(TOP(ok(01)))
TOP(ok(indx(nil, z0))) → c63(TOP(mark(nil)), ACTIVE(indx(nil, z0)))
TOP(ok(dbl1(0))) → c63(TOP(mark(01)), ACTIVE(dbl1(0)))
TOP(ok(quote(0))) → c63(TOP(mark(01)), ACTIVE(quote(0)))
TOP(ok(dbls(nil))) → c63(TOP(mark(nil)), ACTIVE(dbls(nil)))
(98) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(dbl(0)) → mark(0)
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
active(dbls(nil)) → mark(nil)
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1)))
active(sel(0, cons(z0, z1))) → mark(z0)
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
active(indx(nil, z0)) → mark(nil)
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2)))
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(dbl1(0)) → mark(01)
active(dbl1(s(z0))) → mark(s1(s1(dbl1(z0))))
active(sel1(0, cons(z0, z1))) → mark(z0)
active(sel1(s(z0), cons(z1, z2))) → mark(sel1(z0, z2))
active(quote(0)) → mark(01)
active(quote(s(z0))) → mark(s1(quote(z0)))
active(quote(dbl(z0))) → mark(dbl1(z0))
active(quote(sel(z0, z1))) → mark(sel1(z0, z1))
active(dbl(z0)) → dbl(active(z0))
active(dbls(z0)) → dbls(active(z0))
active(sel(z0, z1)) → sel(active(z0), z1)
active(sel(z0, z1)) → sel(z0, active(z1))
active(indx(z0, z1)) → indx(active(z0), z1)
active(dbl1(z0)) → dbl1(active(z0))
active(s1(z0)) → s1(active(z0))
active(sel1(z0, z1)) → sel1(active(z0), z1)
active(sel1(z0, z1)) → sel1(z0, active(z1))
active(quote(z0)) → quote(active(z0))
s(ok(z0)) → ok(s(z0))
dbl(mark(z0)) → mark(dbl(z0))
dbl(ok(z0)) → ok(dbl(z0))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
dbls(mark(z0)) → mark(dbls(z0))
dbls(ok(z0)) → ok(dbls(z0))
sel(mark(z0), z1) → mark(sel(z0, z1))
sel(z0, mark(z1)) → mark(sel(z0, z1))
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
indx(mark(z0), z1) → mark(indx(z0, z1))
indx(ok(z0), ok(z1)) → ok(indx(z0, z1))
s1(mark(z0)) → mark(s1(z0))
s1(ok(z0)) → ok(s1(z0))
dbl1(mark(z0)) → mark(dbl1(z0))
dbl1(ok(z0)) → ok(dbl1(z0))
sel1(mark(z0), z1) → mark(sel1(z0, z1))
sel1(z0, mark(z1)) → mark(sel1(z0, z1))
sel1(ok(z0), ok(z1)) → ok(sel1(z0, z1))
quote(mark(z0)) → mark(quote(z0))
quote(ok(z0)) → ok(quote(z0))
proper(dbl(z0)) → dbl(proper(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(dbls(z0)) → dbls(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
proper(indx(z0, z1)) → indx(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(dbl1(z0)) → dbl1(proper(z0))
proper(01) → ok(01)
proper(s1(z0)) → s1(proper(z0))
proper(sel1(z0, z1)) → sel1(proper(z0), proper(z1))
proper(quote(z0)) → quote(proper(z0))
from(ok(z0)) → ok(from(z0))
Tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)))
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0))))))
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0))))))
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0)))
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(indx(sel1(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(indx(sel1(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel1(z0, z2)), x1), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(indx(quote(dbl(z0)), x1)) → c21(INDX(mark(dbl1(z0)), x1), ACTIVE(quote(dbl(z0))))
ACTIVE(indx(quote(sel(z0, z1)), x1)) → c21(INDX(mark(sel1(z0, z1)), x1), ACTIVE(quote(sel(z0, z1))))
ACTIVE(indx(dbl(z0), x1)) → c21(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
ACTIVE(indx(dbls(z0), x1)) → c21(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(indx(z0, z1), x1)) → c21(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1)))
ACTIVE(indx(dbl1(z0), x1)) → c21(INDX(dbl1(active(z0)), x1), ACTIVE(dbl1(z0)))
ACTIVE(indx(s1(z0), x1)) → c21(INDX(s1(active(z0)), x1), ACTIVE(s1(z0)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(active(z0), z1), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(z0, active(z1)), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(quote(z0), x1)) → c21(INDX(quote(active(z0)), x1), ACTIVE(quote(z0)))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)))
ACTIVE(indx(dbl(0), x1)) → c21(INDX(mark(0), x1))
ACTIVE(indx(dbls(nil), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(indx(indx(nil, z0), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0))))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1))
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0)))
ACTIVE(dbl1(sel(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl1(sel(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl1(sel1(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl1(sel1(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl1(quote(dbl(z0)))) → c22(DBL1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl1(quote(sel(z0, z1)))) → c22(DBL1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl1(dbl(z0))) → c22(DBL1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl1(dbls(z0))) → c22(DBL1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(indx(z0, z1))) → c22(DBL1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl1(dbl1(z0))) → c22(DBL1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl1(s1(z0))) → c22(DBL1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(quote(z0))) → c22(DBL1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(dbl1(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(dbl(0))) → c22(DBL1(mark(0)))
ACTIVE(dbl1(dbls(nil))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(indx(nil, z0))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(dbl1(0))) → c22(DBL1(mark(01)))
ACTIVE(dbl(dbl1(s(z0)))) → c4(DBL(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(DBLS(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(INDX(mark(s1(s1(dbl1(z0)))), x1))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(DBL1(mark(s(s(dbl(z0))))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(ACTIVE(dbl(s(z0))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(DBL1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(DBL1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl1(from(z0))) → c4(DBL1(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl1(from(z0))) → c4(ACTIVE(from(z0)))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(DBL1(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(s1(sel(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(s1(sel(s(z0), cons(z1, z2)))) → c23(S1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(s1(sel1(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(s1(sel1(s(z0), cons(z1, z2)))) → c23(S1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(s1(quote(dbl(z0)))) → c23(S1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(s1(quote(sel(z0, z1)))) → c23(S1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(s1(dbl(z0))) → c23(S1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(s1(dbls(z0))) → c23(S1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(s1(indx(z0, z1))) → c23(S1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(s1(dbl1(z0))) → c23(S1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(s1(s1(z0))) → c23(S1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(quote(z0))) → c23(S1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(s1(dbl(0))) → c23(S1(mark(0)))
ACTIVE(s1(dbls(nil))) → c23(S1(mark(nil)))
ACTIVE(s1(indx(nil, z0))) → c23(S1(mark(nil)))
ACTIVE(s1(dbl1(0))) → c23(S1(mark(01)))
ACTIVE(s1(dbl(s(z0)))) → c6(S1(mark(s(s(dbl(z0))))))
ACTIVE(s1(dbl(s(z0)))) → c6(ACTIVE(dbl(s(z0))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(S1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(S1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(s1(from(z0))) → c6(S1(mark(cons(z0, from(s(z0))))))
ACTIVE(s1(from(z0))) → c6(ACTIVE(from(z0)))
ACTIVE(s1(dbl1(s(z0)))) → c6(S1(mark(s1(s1(dbl1(z0))))))
ACTIVE(s1(dbl1(s(z0)))) → c6(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(sel(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(quote(sel(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(quote(sel1(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(quote(sel1(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(quote(quote(dbl(z0)))) → c26(QUOTE(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(quote(quote(sel(z0, z1)))) → c26(QUOTE(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(quote(dbl(z0))) → c26(QUOTE(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(quote(dbls(z0))) → c26(QUOTE(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(quote(indx(z0, z1))) → c26(QUOTE(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(quote(dbl1(z0))) → c26(QUOTE(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(quote(s1(z0))) → c26(QUOTE(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(quote(z0))) → c26(QUOTE(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(quote(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(quote(0))) → c22(DBL1(mark(01)))
ACTIVE(s1(quote(0))) → c23(S1(mark(01)))
ACTIVE(quote(dbl(0))) → c26(QUOTE(mark(0)))
ACTIVE(quote(dbls(nil))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(indx(nil, z0))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(dbl1(0))) → c26(QUOTE(mark(01)))
ACTIVE(quote(quote(0))) → c26(QUOTE(mark(01)))
ACTIVE(dbl(quote(s(z0)))) → c7(DBL(mark(s1(quote(z0)))))
ACTIVE(dbl(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(s(z0)))) → c7(DBLS(mark(s1(quote(z0)))))
ACTIVE(dbls(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(indx(quote(s(z0)), x1)) → c7(INDX(mark(s1(quote(z0))), x1))
ACTIVE(indx(quote(s(z0)), x1)) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbl1(quote(s(z0)))) → c7(DBL1(mark(s1(quote(z0)))))
ACTIVE(dbl1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(s1(quote(s(z0)))) → c7(S1(mark(s1(quote(z0)))))
ACTIVE(s1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(quote(dbl(s(z0)))) → c7(QUOTE(mark(s(s(dbl(z0))))))
ACTIVE(quote(dbl(s(z0)))) → c7(ACTIVE(dbl(s(z0))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(QUOTE(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(QUOTE(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(quote(from(z0))) → c7(QUOTE(mark(cons(z0, from(s(z0))))))
ACTIVE(quote(from(z0))) → c7(ACTIVE(from(z0)))
ACTIVE(quote(dbl1(s(z0)))) → c7(QUOTE(mark(s1(s1(dbl1(z0))))))
ACTIVE(quote(dbl1(s(z0)))) → c7(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(quote(s(z0)))) → c7(QUOTE(mark(s1(quote(z0)))))
ACTIVE(quote(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
PROPER(dbl(dbl(z0))) → c45(DBL(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbl(s(z0))) → c45(DBL(s(proper(z0))), PROPER(s(z0)))
PROPER(dbl(dbls(z0))) → c45(DBL(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbl(cons(z0, z1))) → c45(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbl(sel(z0, z1))) → c45(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbl(indx(z0, z1))) → c45(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbl(from(z0))) → c45(DBL(from(proper(z0))), PROPER(from(z0)))
PROPER(dbl(dbl1(z0))) → c45(DBL(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbl(s1(z0))) → c45(DBL(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbl(sel1(z0, z1))) → c45(DBL(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbl(quote(z0))) → c45(DBL(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbl(0)) → c45(DBL(ok(0)))
PROPER(dbl(nil)) → c45(DBL(ok(nil)))
PROPER(dbl(01)) → c45(DBL(ok(01)))
PROPER(s(dbl(z0))) → c47(S(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(s(s(z0))) → c47(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(dbls(z0))) → c47(S(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(s(cons(z0, z1))) → c47(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(sel(z0, z1))) → c47(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(s(indx(z0, z1))) → c47(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(s(from(z0))) → c47(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(dbl1(z0))) → c47(S(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(s(s1(z0))) → c47(S(s1(proper(z0))), PROPER(s1(z0)))
PROPER(s(sel1(z0, z1))) → c47(S(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(s(quote(z0))) → c47(S(quote(proper(z0))), PROPER(quote(z0)))
PROPER(s(0)) → c47(S(ok(0)))
PROPER(s(nil)) → c47(S(ok(nil)))
PROPER(s(01)) → c47(S(ok(01)))
PROPER(dbls(dbl(z0))) → c48(DBLS(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbls(s(z0))) → c48(DBLS(s(proper(z0))), PROPER(s(z0)))
PROPER(dbls(dbls(z0))) → c48(DBLS(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbls(cons(z0, z1))) → c48(DBLS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbls(sel(z0, z1))) → c48(DBLS(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbls(indx(z0, z1))) → c48(DBLS(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbls(from(z0))) → c48(DBLS(from(proper(z0))), PROPER(from(z0)))
PROPER(dbls(dbl1(z0))) → c48(DBLS(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbls(s1(z0))) → c48(DBLS(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbls(sel1(z0, z1))) → c48(DBLS(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbls(quote(z0))) → c48(DBLS(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbls(0)) → c48(DBLS(ok(0)))
PROPER(dbls(nil)) → c48(DBLS(ok(nil)))
PROPER(dbls(01)) → c48(DBLS(ok(01)))
PROPER(cons(x0, dbl(z0))) → c50(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(cons(x0, s(z0))) → c50(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, dbls(z0))) → c50(CONS(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(cons(x0, cons(z0, z1))) → c50(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, sel(z0, z1))) → c50(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(cons(x0, indx(z0, z1))) → c50(CONS(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(cons(x0, from(z0))) → c50(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, dbl1(z0))) → c50(CONS(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(cons(x0, s1(z0))) → c50(CONS(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(cons(x0, sel1(z0, z1))) → c50(CONS(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(cons(x0, quote(z0))) → c50(CONS(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(cons(dbl(z0), x1)) → c50(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(cons(s(z0), x1)) → c50(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(dbls(z0), x1)) → c50(CONS(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c50(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(sel(z0, z1), x1)) → c50(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(cons(indx(z0, z1), x1)) → c50(CONS(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c50(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(dbl1(z0), x1)) → c50(CONS(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(cons(s1(z0), x1)) → c50(CONS(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(cons(sel1(z0, z1), x1)) → c50(CONS(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(cons(quote(z0), x1)) → c50(CONS(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c50(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c50(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, 01)) → c50(CONS(proper(x0), ok(01)), PROPER(x0))
PROPER(cons(0, x1)) → c50(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c50(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(01, x1)) → c50(CONS(ok(01), proper(x1)), PROPER(x1))
PROPER(sel(x0, dbl(z0))) → c51(SEL(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(sel(x0, s(z0))) → c51(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(sel(x0, dbls(z0))) → c51(SEL(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(sel(x0, cons(z0, z1))) → c51(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(sel(x0, sel(z0, z1))) → c51(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(sel(x0, indx(z0, z1))) → c51(SEL(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(sel(x0, from(z0))) → c51(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(sel(x0, dbl1(z0))) → c51(SEL(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(sel(x0, s1(z0))) → c51(SEL(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(sel(x0, sel1(z0, z1))) → c51(SEL(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(sel(x0, quote(z0))) → c51(SEL(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(sel(dbl(z0), x1)) → c51(SEL(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(sel(s(z0), x1)) → c51(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(sel(dbls(z0), x1)) → c51(SEL(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(sel(cons(z0, z1), x1)) → c51(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(sel(sel(z0, z1), x1)) → c51(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(sel(indx(z0, z1), x1)) → c51(SEL(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(sel(from(z0), x1)) → c51(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(sel(dbl1(z0), x1)) → c51(SEL(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(sel(s1(z0), x1)) → c51(SEL(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(sel(sel1(z0, z1), x1)) → c51(SEL(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(sel(quote(z0), x1)) → c51(SEL(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(sel(x0, 0)) → c51(SEL(proper(x0), ok(0)), PROPER(x0))
PROPER(sel(x0, nil)) → c51(SEL(proper(x0), ok(nil)), PROPER(x0))
PROPER(sel(x0, 01)) → c51(SEL(proper(x0), ok(01)), PROPER(x0))
PROPER(sel(0, x1)) → c51(SEL(ok(0), proper(x1)), PROPER(x1))
PROPER(sel(nil, x1)) → c51(SEL(ok(nil), proper(x1)), PROPER(x1))
PROPER(sel(01, x1)) → c51(SEL(ok(01), proper(x1)), PROPER(x1))
PROPER(indx(x0, dbl(z0))) → c52(INDX(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(indx(x0, s(z0))) → c52(INDX(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(indx(x0, dbls(z0))) → c52(INDX(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(indx(x0, cons(z0, z1))) → c52(INDX(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(indx(x0, sel(z0, z1))) → c52(INDX(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(indx(x0, indx(z0, z1))) → c52(INDX(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(indx(x0, from(z0))) → c52(INDX(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(indx(x0, dbl1(z0))) → c52(INDX(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(indx(x0, s1(z0))) → c52(INDX(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(indx(x0, sel1(z0, z1))) → c52(INDX(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(indx(x0, quote(z0))) → c52(INDX(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(indx(dbl(z0), x1)) → c52(INDX(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(indx(s(z0), x1)) → c52(INDX(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(indx(dbls(z0), x1)) → c52(INDX(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(indx(cons(z0, z1), x1)) → c52(INDX(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(indx(sel(z0, z1), x1)) → c52(INDX(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(indx(indx(z0, z1), x1)) → c52(INDX(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(indx(from(z0), x1)) → c52(INDX(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(indx(dbl1(z0), x1)) → c52(INDX(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(indx(s1(z0), x1)) → c52(INDX(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(indx(sel1(z0, z1), x1)) → c52(INDX(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(indx(quote(z0), x1)) → c52(INDX(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(indx(x0, 0)) → c52(INDX(proper(x0), ok(0)), PROPER(x0))
PROPER(indx(x0, nil)) → c52(INDX(proper(x0), ok(nil)), PROPER(x0))
PROPER(indx(x0, 01)) → c52(INDX(proper(x0), ok(01)), PROPER(x0))
PROPER(indx(0, x1)) → c52(INDX(ok(0), proper(x1)), PROPER(x1))
PROPER(indx(nil, x1)) → c52(INDX(ok(nil), proper(x1)), PROPER(x1))
PROPER(indx(01, x1)) → c52(INDX(ok(01), proper(x1)), PROPER(x1))
PROPER(from(dbl(z0))) → c53(FROM(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(from(s(z0))) → c53(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(dbls(z0))) → c53(FROM(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(from(cons(z0, z1))) → c53(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(sel(z0, z1))) → c53(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(from(indx(z0, z1))) → c53(FROM(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(from(from(z0))) → c53(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(dbl1(z0))) → c53(FROM(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(from(s1(z0))) → c53(FROM(s1(proper(z0))), PROPER(s1(z0)))
PROPER(from(sel1(z0, z1))) → c53(FROM(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(from(quote(z0))) → c53(FROM(quote(proper(z0))), PROPER(quote(z0)))
PROPER(from(0)) → c53(FROM(ok(0)))
PROPER(from(nil)) → c53(FROM(ok(nil)))
PROPER(from(01)) → c53(FROM(ok(01)))
PROPER(dbl1(dbl(z0))) → c54(DBL1(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbl1(s(z0))) → c54(DBL1(s(proper(z0))), PROPER(s(z0)))
PROPER(dbl1(dbls(z0))) → c54(DBL1(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbl1(cons(z0, z1))) → c54(DBL1(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbl1(sel(z0, z1))) → c54(DBL1(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbl1(indx(z0, z1))) → c54(DBL1(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbl1(from(z0))) → c54(DBL1(from(proper(z0))), PROPER(from(z0)))
PROPER(dbl1(dbl1(z0))) → c54(DBL1(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbl1(s1(z0))) → c54(DBL1(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbl1(sel1(z0, z1))) → c54(DBL1(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbl1(quote(z0))) → c54(DBL1(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbl1(0)) → c54(DBL1(ok(0)))
PROPER(dbl1(nil)) → c54(DBL1(ok(nil)))
PROPER(dbl1(01)) → c54(DBL1(ok(01)))
PROPER(s1(dbl(z0))) → c56(S1(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(s1(s(z0))) → c56(S1(s(proper(z0))), PROPER(s(z0)))
PROPER(s1(dbls(z0))) → c56(S1(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(s1(cons(z0, z1))) → c56(S1(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s1(sel(z0, z1))) → c56(S1(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(s1(indx(z0, z1))) → c56(S1(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(s1(from(z0))) → c56(S1(from(proper(z0))), PROPER(from(z0)))
PROPER(s1(dbl1(z0))) → c56(S1(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(s1(s1(z0))) → c56(S1(s1(proper(z0))), PROPER(s1(z0)))
PROPER(s1(sel1(z0, z1))) → c56(S1(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(s1(quote(z0))) → c56(S1(quote(proper(z0))), PROPER(quote(z0)))
PROPER(s1(0)) → c56(S1(ok(0)))
PROPER(s1(nil)) → c56(S1(ok(nil)))
PROPER(s1(01)) → c56(S1(ok(01)))
PROPER(sel1(x0, dbl(z0))) → c57(SEL1(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(sel1(x0, s(z0))) → c57(SEL1(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(sel1(x0, dbls(z0))) → c57(SEL1(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(sel1(x0, cons(z0, z1))) → c57(SEL1(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(sel1(x0, sel(z0, z1))) → c57(SEL1(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(sel1(x0, indx(z0, z1))) → c57(SEL1(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(sel1(x0, from(z0))) → c57(SEL1(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(sel1(x0, dbl1(z0))) → c57(SEL1(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(sel1(x0, s1(z0))) → c57(SEL1(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(sel1(x0, sel1(z0, z1))) → c57(SEL1(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(sel1(x0, quote(z0))) → c57(SEL1(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(sel1(dbl(z0), x1)) → c57(SEL1(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(sel1(s(z0), x1)) → c57(SEL1(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(sel1(dbls(z0), x1)) → c57(SEL1(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(sel1(cons(z0, z1), x1)) → c57(SEL1(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(sel1(sel(z0, z1), x1)) → c57(SEL1(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(sel1(indx(z0, z1), x1)) → c57(SEL1(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(sel1(from(z0), x1)) → c57(SEL1(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(sel1(dbl1(z0), x1)) → c57(SEL1(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(sel1(s1(z0), x1)) → c57(SEL1(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(sel1(sel1(z0, z1), x1)) → c57(SEL1(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(sel1(quote(z0), x1)) → c57(SEL1(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(sel1(x0, 0)) → c57(SEL1(proper(x0), ok(0)), PROPER(x0))
PROPER(sel1(x0, nil)) → c57(SEL1(proper(x0), ok(nil)), PROPER(x0))
PROPER(sel1(x0, 01)) → c57(SEL1(proper(x0), ok(01)), PROPER(x0))
PROPER(sel1(0, x1)) → c57(SEL1(ok(0), proper(x1)), PROPER(x1))
PROPER(sel1(nil, x1)) → c57(SEL1(ok(nil), proper(x1)), PROPER(x1))
PROPER(sel1(01, x1)) → c57(SEL1(ok(01), proper(x1)), PROPER(x1))
PROPER(quote(dbl(z0))) → c58(QUOTE(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(quote(s(z0))) → c58(QUOTE(s(proper(z0))), PROPER(s(z0)))
PROPER(quote(dbls(z0))) → c58(QUOTE(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(quote(cons(z0, z1))) → c58(QUOTE(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(quote(sel(z0, z1))) → c58(QUOTE(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(quote(indx(z0, z1))) → c58(QUOTE(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(quote(from(z0))) → c58(QUOTE(from(proper(z0))), PROPER(from(z0)))
PROPER(quote(dbl1(z0))) → c58(QUOTE(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(quote(s1(z0))) → c58(QUOTE(s1(proper(z0))), PROPER(s1(z0)))
PROPER(quote(sel1(z0, z1))) → c58(QUOTE(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(quote(quote(z0))) → c58(QUOTE(quote(proper(z0))), PROPER(quote(z0)))
PROPER(quote(0)) → c58(QUOTE(ok(0)))
PROPER(quote(nil)) → c58(QUOTE(ok(nil)))
PROPER(quote(01)) → c58(QUOTE(ok(01)))
TOP(mark(dbl(z0))) → c62(TOP(dbl(proper(z0))), PROPER(dbl(z0)))
TOP(mark(s(z0))) → c62(TOP(s(proper(z0))), PROPER(s(z0)))
TOP(mark(dbls(z0))) → c62(TOP(dbls(proper(z0))), PROPER(dbls(z0)))
TOP(mark(cons(z0, z1))) → c62(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
TOP(mark(sel(z0, z1))) → c62(TOP(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
TOP(mark(indx(z0, z1))) → c62(TOP(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
TOP(mark(from(z0))) → c62(TOP(from(proper(z0))), PROPER(from(z0)))
TOP(mark(dbl1(z0))) → c62(TOP(dbl1(proper(z0))), PROPER(dbl1(z0)))
TOP(mark(s1(z0))) → c62(TOP(s1(proper(z0))), PROPER(s1(z0)))
TOP(mark(sel1(z0, z1))) → c62(TOP(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
TOP(mark(quote(z0))) → c62(TOP(quote(proper(z0))), PROPER(quote(z0)))
TOP(ok(dbl(s(z0)))) → c63(TOP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
TOP(ok(dbls(cons(z0, z1)))) → c63(TOP(mark(cons(dbl(z0), dbls(z1)))), ACTIVE(dbls(cons(z0, z1))))
TOP(ok(sel(0, cons(z0, z1)))) → c63(TOP(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
TOP(ok(sel(s(z0), cons(z1, z2)))) → c63(TOP(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
TOP(ok(indx(cons(z0, z1), z2))) → c63(TOP(mark(cons(sel(z0, z2), indx(z1, z2)))), ACTIVE(indx(cons(z0, z1), z2)))
TOP(ok(from(z0))) → c63(TOP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
TOP(ok(dbl1(s(z0)))) → c63(TOP(mark(s1(s1(dbl1(z0))))), ACTIVE(dbl1(s(z0))))
TOP(ok(sel1(0, cons(z0, z1)))) → c63(TOP(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
TOP(ok(sel1(s(z0), cons(z1, z2)))) → c63(TOP(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
TOP(ok(quote(s(z0)))) → c63(TOP(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
TOP(ok(quote(dbl(z0)))) → c63(TOP(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
TOP(ok(quote(sel(z0, z1)))) → c63(TOP(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
TOP(ok(dbl(z0))) → c63(TOP(dbl(active(z0))), ACTIVE(dbl(z0)))
TOP(ok(dbls(z0))) → c63(TOP(dbls(active(z0))), ACTIVE(dbls(z0)))
TOP(ok(sel(z0, z1))) → c63(TOP(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
TOP(ok(sel(z0, z1))) → c63(TOP(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
TOP(ok(indx(z0, z1))) → c63(TOP(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
TOP(ok(dbl1(z0))) → c63(TOP(dbl1(active(z0))), ACTIVE(dbl1(z0)))
TOP(ok(s1(z0))) → c63(TOP(s1(active(z0))), ACTIVE(s1(z0)))
TOP(ok(sel1(z0, z1))) → c63(TOP(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
TOP(ok(sel1(z0, z1))) → c63(TOP(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
TOP(ok(quote(z0))) → c63(TOP(quote(active(z0))), ACTIVE(quote(z0)))
S tuples:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)))
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0))))))
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0))))))
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0)))
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(indx(sel1(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(indx(sel1(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel1(z0, z2)), x1), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(indx(quote(dbl(z0)), x1)) → c21(INDX(mark(dbl1(z0)), x1), ACTIVE(quote(dbl(z0))))
ACTIVE(indx(quote(sel(z0, z1)), x1)) → c21(INDX(mark(sel1(z0, z1)), x1), ACTIVE(quote(sel(z0, z1))))
ACTIVE(indx(dbl(z0), x1)) → c21(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
ACTIVE(indx(dbls(z0), x1)) → c21(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(indx(z0, z1), x1)) → c21(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1)))
ACTIVE(indx(dbl1(z0), x1)) → c21(INDX(dbl1(active(z0)), x1), ACTIVE(dbl1(z0)))
ACTIVE(indx(s1(z0), x1)) → c21(INDX(s1(active(z0)), x1), ACTIVE(s1(z0)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(active(z0), z1), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(z0, active(z1)), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(quote(z0), x1)) → c21(INDX(quote(active(z0)), x1), ACTIVE(quote(z0)))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)))
ACTIVE(indx(dbl(0), x1)) → c21(INDX(mark(0), x1))
ACTIVE(indx(dbls(nil), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(indx(indx(nil, z0), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0))))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1))
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0)))
ACTIVE(dbl1(sel(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl1(sel(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl1(sel1(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl1(sel1(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl1(quote(dbl(z0)))) → c22(DBL1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl1(quote(sel(z0, z1)))) → c22(DBL1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl1(dbl(z0))) → c22(DBL1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl1(dbls(z0))) → c22(DBL1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(indx(z0, z1))) → c22(DBL1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl1(dbl1(z0))) → c22(DBL1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl1(s1(z0))) → c22(DBL1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(quote(z0))) → c22(DBL1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(dbl1(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(dbl(0))) → c22(DBL1(mark(0)))
ACTIVE(dbl1(dbls(nil))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(indx(nil, z0))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(dbl1(0))) → c22(DBL1(mark(01)))
ACTIVE(dbl(dbl1(s(z0)))) → c4(DBL(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(DBLS(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(INDX(mark(s1(s1(dbl1(z0)))), x1))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(DBL1(mark(s(s(dbl(z0))))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(ACTIVE(dbl(s(z0))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(DBL1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(DBL1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl1(from(z0))) → c4(DBL1(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl1(from(z0))) → c4(ACTIVE(from(z0)))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(DBL1(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(s1(sel(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(s1(sel(s(z0), cons(z1, z2)))) → c23(S1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(s1(sel1(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(s1(sel1(s(z0), cons(z1, z2)))) → c23(S1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(s1(quote(dbl(z0)))) → c23(S1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(s1(quote(sel(z0, z1)))) → c23(S1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(s1(dbl(z0))) → c23(S1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(s1(dbls(z0))) → c23(S1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(s1(indx(z0, z1))) → c23(S1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(s1(dbl1(z0))) → c23(S1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(s1(s1(z0))) → c23(S1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(quote(z0))) → c23(S1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(s1(dbl(0))) → c23(S1(mark(0)))
ACTIVE(s1(dbls(nil))) → c23(S1(mark(nil)))
ACTIVE(s1(indx(nil, z0))) → c23(S1(mark(nil)))
ACTIVE(s1(dbl1(0))) → c23(S1(mark(01)))
ACTIVE(s1(dbl(s(z0)))) → c6(S1(mark(s(s(dbl(z0))))))
ACTIVE(s1(dbl(s(z0)))) → c6(ACTIVE(dbl(s(z0))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(S1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(S1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(s1(from(z0))) → c6(S1(mark(cons(z0, from(s(z0))))))
ACTIVE(s1(from(z0))) → c6(ACTIVE(from(z0)))
ACTIVE(s1(dbl1(s(z0)))) → c6(S1(mark(s1(s1(dbl1(z0))))))
ACTIVE(s1(dbl1(s(z0)))) → c6(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(sel(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(quote(sel(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(quote(sel1(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(quote(sel1(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(quote(quote(dbl(z0)))) → c26(QUOTE(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(quote(quote(sel(z0, z1)))) → c26(QUOTE(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(quote(dbl(z0))) → c26(QUOTE(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(quote(dbls(z0))) → c26(QUOTE(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(quote(indx(z0, z1))) → c26(QUOTE(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(quote(dbl1(z0))) → c26(QUOTE(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(quote(s1(z0))) → c26(QUOTE(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(quote(z0))) → c26(QUOTE(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(quote(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(quote(0))) → c22(DBL1(mark(01)))
ACTIVE(s1(quote(0))) → c23(S1(mark(01)))
ACTIVE(quote(dbl(0))) → c26(QUOTE(mark(0)))
ACTIVE(quote(dbls(nil))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(indx(nil, z0))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(dbl1(0))) → c26(QUOTE(mark(01)))
ACTIVE(quote(quote(0))) → c26(QUOTE(mark(01)))
ACTIVE(dbl(quote(s(z0)))) → c7(DBL(mark(s1(quote(z0)))))
ACTIVE(dbl(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(s(z0)))) → c7(DBLS(mark(s1(quote(z0)))))
ACTIVE(dbls(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(indx(quote(s(z0)), x1)) → c7(INDX(mark(s1(quote(z0))), x1))
ACTIVE(indx(quote(s(z0)), x1)) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbl1(quote(s(z0)))) → c7(DBL1(mark(s1(quote(z0)))))
ACTIVE(dbl1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(s1(quote(s(z0)))) → c7(S1(mark(s1(quote(z0)))))
ACTIVE(s1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(quote(dbl(s(z0)))) → c7(QUOTE(mark(s(s(dbl(z0))))))
ACTIVE(quote(dbl(s(z0)))) → c7(ACTIVE(dbl(s(z0))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(QUOTE(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(QUOTE(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(quote(from(z0))) → c7(QUOTE(mark(cons(z0, from(s(z0))))))
ACTIVE(quote(from(z0))) → c7(ACTIVE(from(z0)))
ACTIVE(quote(dbl1(s(z0)))) → c7(QUOTE(mark(s1(s1(dbl1(z0))))))
ACTIVE(quote(dbl1(s(z0)))) → c7(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(quote(s(z0)))) → c7(QUOTE(mark(s1(quote(z0)))))
ACTIVE(quote(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
PROPER(dbl(dbl(z0))) → c45(DBL(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbl(s(z0))) → c45(DBL(s(proper(z0))), PROPER(s(z0)))
PROPER(dbl(dbls(z0))) → c45(DBL(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbl(cons(z0, z1))) → c45(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbl(sel(z0, z1))) → c45(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbl(indx(z0, z1))) → c45(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbl(from(z0))) → c45(DBL(from(proper(z0))), PROPER(from(z0)))
PROPER(dbl(dbl1(z0))) → c45(DBL(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbl(s1(z0))) → c45(DBL(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbl(sel1(z0, z1))) → c45(DBL(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbl(quote(z0))) → c45(DBL(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbl(0)) → c45(DBL(ok(0)))
PROPER(dbl(nil)) → c45(DBL(ok(nil)))
PROPER(dbl(01)) → c45(DBL(ok(01)))
PROPER(s(dbl(z0))) → c47(S(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(s(s(z0))) → c47(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(dbls(z0))) → c47(S(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(s(cons(z0, z1))) → c47(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(sel(z0, z1))) → c47(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(s(indx(z0, z1))) → c47(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(s(from(z0))) → c47(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(dbl1(z0))) → c47(S(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(s(s1(z0))) → c47(S(s1(proper(z0))), PROPER(s1(z0)))
PROPER(s(sel1(z0, z1))) → c47(S(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(s(quote(z0))) → c47(S(quote(proper(z0))), PROPER(quote(z0)))
PROPER(s(0)) → c47(S(ok(0)))
PROPER(s(nil)) → c47(S(ok(nil)))
PROPER(s(01)) → c47(S(ok(01)))
PROPER(dbls(dbl(z0))) → c48(DBLS(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbls(s(z0))) → c48(DBLS(s(proper(z0))), PROPER(s(z0)))
PROPER(dbls(dbls(z0))) → c48(DBLS(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbls(cons(z0, z1))) → c48(DBLS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbls(sel(z0, z1))) → c48(DBLS(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbls(indx(z0, z1))) → c48(DBLS(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbls(from(z0))) → c48(DBLS(from(proper(z0))), PROPER(from(z0)))
PROPER(dbls(dbl1(z0))) → c48(DBLS(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbls(s1(z0))) → c48(DBLS(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbls(sel1(z0, z1))) → c48(DBLS(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbls(quote(z0))) → c48(DBLS(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbls(0)) → c48(DBLS(ok(0)))
PROPER(dbls(nil)) → c48(DBLS(ok(nil)))
PROPER(dbls(01)) → c48(DBLS(ok(01)))
PROPER(cons(x0, dbl(z0))) → c50(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(cons(x0, s(z0))) → c50(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, dbls(z0))) → c50(CONS(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(cons(x0, cons(z0, z1))) → c50(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, sel(z0, z1))) → c50(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(cons(x0, indx(z0, z1))) → c50(CONS(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(cons(x0, from(z0))) → c50(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, dbl1(z0))) → c50(CONS(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(cons(x0, s1(z0))) → c50(CONS(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(cons(x0, sel1(z0, z1))) → c50(CONS(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(cons(x0, quote(z0))) → c50(CONS(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(cons(dbl(z0), x1)) → c50(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(cons(s(z0), x1)) → c50(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(dbls(z0), x1)) → c50(CONS(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c50(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(sel(z0, z1), x1)) → c50(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(cons(indx(z0, z1), x1)) → c50(CONS(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c50(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(dbl1(z0), x1)) → c50(CONS(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(cons(s1(z0), x1)) → c50(CONS(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(cons(sel1(z0, z1), x1)) → c50(CONS(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(cons(quote(z0), x1)) → c50(CONS(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c50(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c50(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, 01)) → c50(CONS(proper(x0), ok(01)), PROPER(x0))
PROPER(cons(0, x1)) → c50(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c50(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(01, x1)) → c50(CONS(ok(01), proper(x1)), PROPER(x1))
PROPER(sel(x0, dbl(z0))) → c51(SEL(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(sel(x0, s(z0))) → c51(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(sel(x0, dbls(z0))) → c51(SEL(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(sel(x0, cons(z0, z1))) → c51(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(sel(x0, sel(z0, z1))) → c51(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(sel(x0, indx(z0, z1))) → c51(SEL(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(sel(x0, from(z0))) → c51(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(sel(x0, dbl1(z0))) → c51(SEL(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(sel(x0, s1(z0))) → c51(SEL(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(sel(x0, sel1(z0, z1))) → c51(SEL(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(sel(x0, quote(z0))) → c51(SEL(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(sel(dbl(z0), x1)) → c51(SEL(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(sel(s(z0), x1)) → c51(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(sel(dbls(z0), x1)) → c51(SEL(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(sel(cons(z0, z1), x1)) → c51(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(sel(sel(z0, z1), x1)) → c51(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(sel(indx(z0, z1), x1)) → c51(SEL(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(sel(from(z0), x1)) → c51(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(sel(dbl1(z0), x1)) → c51(SEL(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(sel(s1(z0), x1)) → c51(SEL(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(sel(sel1(z0, z1), x1)) → c51(SEL(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(sel(quote(z0), x1)) → c51(SEL(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(sel(x0, 0)) → c51(SEL(proper(x0), ok(0)), PROPER(x0))
PROPER(sel(x0, nil)) → c51(SEL(proper(x0), ok(nil)), PROPER(x0))
PROPER(sel(x0, 01)) → c51(SEL(proper(x0), ok(01)), PROPER(x0))
PROPER(sel(0, x1)) → c51(SEL(ok(0), proper(x1)), PROPER(x1))
PROPER(sel(nil, x1)) → c51(SEL(ok(nil), proper(x1)), PROPER(x1))
PROPER(sel(01, x1)) → c51(SEL(ok(01), proper(x1)), PROPER(x1))
PROPER(indx(x0, dbl(z0))) → c52(INDX(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(indx(x0, s(z0))) → c52(INDX(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(indx(x0, dbls(z0))) → c52(INDX(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(indx(x0, cons(z0, z1))) → c52(INDX(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(indx(x0, sel(z0, z1))) → c52(INDX(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(indx(x0, indx(z0, z1))) → c52(INDX(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(indx(x0, from(z0))) → c52(INDX(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(indx(x0, dbl1(z0))) → c52(INDX(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(indx(x0, s1(z0))) → c52(INDX(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(indx(x0, sel1(z0, z1))) → c52(INDX(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(indx(x0, quote(z0))) → c52(INDX(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(indx(dbl(z0), x1)) → c52(INDX(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(indx(s(z0), x1)) → c52(INDX(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(indx(dbls(z0), x1)) → c52(INDX(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(indx(cons(z0, z1), x1)) → c52(INDX(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(indx(sel(z0, z1), x1)) → c52(INDX(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(indx(indx(z0, z1), x1)) → c52(INDX(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(indx(from(z0), x1)) → c52(INDX(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(indx(dbl1(z0), x1)) → c52(INDX(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(indx(s1(z0), x1)) → c52(INDX(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(indx(sel1(z0, z1), x1)) → c52(INDX(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(indx(quote(z0), x1)) → c52(INDX(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(indx(x0, 0)) → c52(INDX(proper(x0), ok(0)), PROPER(x0))
PROPER(indx(x0, nil)) → c52(INDX(proper(x0), ok(nil)), PROPER(x0))
PROPER(indx(x0, 01)) → c52(INDX(proper(x0), ok(01)), PROPER(x0))
PROPER(indx(0, x1)) → c52(INDX(ok(0), proper(x1)), PROPER(x1))
PROPER(indx(nil, x1)) → c52(INDX(ok(nil), proper(x1)), PROPER(x1))
PROPER(indx(01, x1)) → c52(INDX(ok(01), proper(x1)), PROPER(x1))
PROPER(from(dbl(z0))) → c53(FROM(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(from(s(z0))) → c53(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(dbls(z0))) → c53(FROM(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(from(cons(z0, z1))) → c53(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(sel(z0, z1))) → c53(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(from(indx(z0, z1))) → c53(FROM(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(from(from(z0))) → c53(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(dbl1(z0))) → c53(FROM(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(from(s1(z0))) → c53(FROM(s1(proper(z0))), PROPER(s1(z0)))
PROPER(from(sel1(z0, z1))) → c53(FROM(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(from(quote(z0))) → c53(FROM(quote(proper(z0))), PROPER(quote(z0)))
PROPER(from(0)) → c53(FROM(ok(0)))
PROPER(from(nil)) → c53(FROM(ok(nil)))
PROPER(from(01)) → c53(FROM(ok(01)))
PROPER(dbl1(dbl(z0))) → c54(DBL1(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbl1(s(z0))) → c54(DBL1(s(proper(z0))), PROPER(s(z0)))
PROPER(dbl1(dbls(z0))) → c54(DBL1(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbl1(cons(z0, z1))) → c54(DBL1(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbl1(sel(z0, z1))) → c54(DBL1(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbl1(indx(z0, z1))) → c54(DBL1(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbl1(from(z0))) → c54(DBL1(from(proper(z0))), PROPER(from(z0)))
PROPER(dbl1(dbl1(z0))) → c54(DBL1(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbl1(s1(z0))) → c54(DBL1(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbl1(sel1(z0, z1))) → c54(DBL1(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbl1(quote(z0))) → c54(DBL1(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbl1(0)) → c54(DBL1(ok(0)))
PROPER(dbl1(nil)) → c54(DBL1(ok(nil)))
PROPER(dbl1(01)) → c54(DBL1(ok(01)))
PROPER(s1(dbl(z0))) → c56(S1(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(s1(s(z0))) → c56(S1(s(proper(z0))), PROPER(s(z0)))
PROPER(s1(dbls(z0))) → c56(S1(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(s1(cons(z0, z1))) → c56(S1(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s1(sel(z0, z1))) → c56(S1(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(s1(indx(z0, z1))) → c56(S1(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(s1(from(z0))) → c56(S1(from(proper(z0))), PROPER(from(z0)))
PROPER(s1(dbl1(z0))) → c56(S1(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(s1(s1(z0))) → c56(S1(s1(proper(z0))), PROPER(s1(z0)))
PROPER(s1(sel1(z0, z1))) → c56(S1(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(s1(quote(z0))) → c56(S1(quote(proper(z0))), PROPER(quote(z0)))
PROPER(s1(0)) → c56(S1(ok(0)))
PROPER(s1(nil)) → c56(S1(ok(nil)))
PROPER(s1(01)) → c56(S1(ok(01)))
PROPER(sel1(x0, dbl(z0))) → c57(SEL1(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(sel1(x0, s(z0))) → c57(SEL1(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(sel1(x0, dbls(z0))) → c57(SEL1(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(sel1(x0, cons(z0, z1))) → c57(SEL1(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(sel1(x0, sel(z0, z1))) → c57(SEL1(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(sel1(x0, indx(z0, z1))) → c57(SEL1(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(sel1(x0, from(z0))) → c57(SEL1(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(sel1(x0, dbl1(z0))) → c57(SEL1(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(sel1(x0, s1(z0))) → c57(SEL1(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(sel1(x0, sel1(z0, z1))) → c57(SEL1(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(sel1(x0, quote(z0))) → c57(SEL1(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(sel1(dbl(z0), x1)) → c57(SEL1(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(sel1(s(z0), x1)) → c57(SEL1(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(sel1(dbls(z0), x1)) → c57(SEL1(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(sel1(cons(z0, z1), x1)) → c57(SEL1(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(sel1(sel(z0, z1), x1)) → c57(SEL1(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(sel1(indx(z0, z1), x1)) → c57(SEL1(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(sel1(from(z0), x1)) → c57(SEL1(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(sel1(dbl1(z0), x1)) → c57(SEL1(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(sel1(s1(z0), x1)) → c57(SEL1(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(sel1(sel1(z0, z1), x1)) → c57(SEL1(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(sel1(quote(z0), x1)) → c57(SEL1(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(sel1(x0, 0)) → c57(SEL1(proper(x0), ok(0)), PROPER(x0))
PROPER(sel1(x0, nil)) → c57(SEL1(proper(x0), ok(nil)), PROPER(x0))
PROPER(sel1(x0, 01)) → c57(SEL1(proper(x0), ok(01)), PROPER(x0))
PROPER(sel1(0, x1)) → c57(SEL1(ok(0), proper(x1)), PROPER(x1))
PROPER(sel1(nil, x1)) → c57(SEL1(ok(nil), proper(x1)), PROPER(x1))
PROPER(sel1(01, x1)) → c57(SEL1(ok(01), proper(x1)), PROPER(x1))
PROPER(quote(dbl(z0))) → c58(QUOTE(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(quote(s(z0))) → c58(QUOTE(s(proper(z0))), PROPER(s(z0)))
PROPER(quote(dbls(z0))) → c58(QUOTE(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(quote(cons(z0, z1))) → c58(QUOTE(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(quote(sel(z0, z1))) → c58(QUOTE(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(quote(indx(z0, z1))) → c58(QUOTE(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(quote(from(z0))) → c58(QUOTE(from(proper(z0))), PROPER(from(z0)))
PROPER(quote(dbl1(z0))) → c58(QUOTE(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(quote(s1(z0))) → c58(QUOTE(s1(proper(z0))), PROPER(s1(z0)))
PROPER(quote(sel1(z0, z1))) → c58(QUOTE(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(quote(quote(z0))) → c58(QUOTE(quote(proper(z0))), PROPER(quote(z0)))
PROPER(quote(0)) → c58(QUOTE(ok(0)))
PROPER(quote(nil)) → c58(QUOTE(ok(nil)))
PROPER(quote(01)) → c58(QUOTE(ok(01)))
TOP(mark(dbl(z0))) → c62(TOP(dbl(proper(z0))), PROPER(dbl(z0)))
TOP(mark(s(z0))) → c62(TOP(s(proper(z0))), PROPER(s(z0)))
TOP(mark(dbls(z0))) → c62(TOP(dbls(proper(z0))), PROPER(dbls(z0)))
TOP(mark(cons(z0, z1))) → c62(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
TOP(mark(sel(z0, z1))) → c62(TOP(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
TOP(mark(indx(z0, z1))) → c62(TOP(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
TOP(mark(from(z0))) → c62(TOP(from(proper(z0))), PROPER(from(z0)))
TOP(mark(dbl1(z0))) → c62(TOP(dbl1(proper(z0))), PROPER(dbl1(z0)))
TOP(mark(s1(z0))) → c62(TOP(s1(proper(z0))), PROPER(s1(z0)))
TOP(mark(sel1(z0, z1))) → c62(TOP(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
TOP(mark(quote(z0))) → c62(TOP(quote(proper(z0))), PROPER(quote(z0)))
TOP(ok(dbl(s(z0)))) → c63(TOP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
TOP(ok(dbls(cons(z0, z1)))) → c63(TOP(mark(cons(dbl(z0), dbls(z1)))), ACTIVE(dbls(cons(z0, z1))))
TOP(ok(sel(0, cons(z0, z1)))) → c63(TOP(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
TOP(ok(sel(s(z0), cons(z1, z2)))) → c63(TOP(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
TOP(ok(indx(cons(z0, z1), z2))) → c63(TOP(mark(cons(sel(z0, z2), indx(z1, z2)))), ACTIVE(indx(cons(z0, z1), z2)))
TOP(ok(from(z0))) → c63(TOP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
TOP(ok(dbl1(s(z0)))) → c63(TOP(mark(s1(s1(dbl1(z0))))), ACTIVE(dbl1(s(z0))))
TOP(ok(sel1(0, cons(z0, z1)))) → c63(TOP(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
TOP(ok(sel1(s(z0), cons(z1, z2)))) → c63(TOP(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
TOP(ok(quote(s(z0)))) → c63(TOP(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
TOP(ok(quote(dbl(z0)))) → c63(TOP(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
TOP(ok(quote(sel(z0, z1)))) → c63(TOP(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
TOP(ok(dbl(z0))) → c63(TOP(dbl(active(z0))), ACTIVE(dbl(z0)))
TOP(ok(dbls(z0))) → c63(TOP(dbls(active(z0))), ACTIVE(dbls(z0)))
TOP(ok(sel(z0, z1))) → c63(TOP(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
TOP(ok(sel(z0, z1))) → c63(TOP(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
TOP(ok(indx(z0, z1))) → c63(TOP(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
TOP(ok(dbl1(z0))) → c63(TOP(dbl1(active(z0))), ACTIVE(dbl1(z0)))
TOP(ok(s1(z0))) → c63(TOP(s1(active(z0))), ACTIVE(s1(z0)))
TOP(ok(sel1(z0, z1))) → c63(TOP(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
TOP(ok(sel1(z0, z1))) → c63(TOP(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
TOP(ok(quote(z0))) → c63(TOP(quote(active(z0))), ACTIVE(quote(z0)))
K tuples:none
Defined Rule Symbols:
active, s, dbl, cons, dbls, sel, indx, s1, dbl1, sel1, quote, proper, from
Defined Pair Symbols:
ACTIVE, DBL, DBLS, SEL, INDX, DBL1, S1, SEL1, QUOTE, S, CONS, FROM, PROPER, TOP
Compound Symbols:
c5, c12, c15, c16, c19, c20, c24, c25, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c59, c60, c61, c8, c, c17, c17, c1, c18, c18, c2, c21, c21, c3, c22, c22, c4, c23, c23, c6, c26, c26, c7, c45, c45, c47, c47, c48, c48, c50, c50, c51, c51, c52, c52, c53, c53, c54, c54, c56, c56, c57, c57, c58, c58, c62, c63
(99) CdtUnreachableProof (EQUIVALENT transformation)
The following tuples could be removed as they are not reachable from basic start terms:
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c12(SEL1(z0, z2))
ACTIVE(quote(dbl(z0))) → c15(DBL1(z0))
ACTIVE(quote(sel(z0, z1))) → c16(SEL1(z0, z1))
ACTIVE(sel(z0, z1)) → c19(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c20(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(sel1(z0, z1)) → c24(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c25(SEL1(z0, active(z1)), ACTIVE(z1))
ACTIVE(from(z0)) → c8(S(z0))
ACTIVE(dbl(s(z0))) → c(S(s(dbl(z0))))
ACTIVE(dbl(s(z0))) → c(S(dbl(z0)))
ACTIVE(dbl(s(z0))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(CONS(dbl(z0), dbls(z1)))
ACTIVE(dbls(cons(z0, z1))) → c(DBL(z0))
ACTIVE(dbls(cons(z0, z1))) → c(DBLS(z1))
ACTIVE(indx(cons(z0, z1), z2)) → c(CONS(sel(z0, z2), indx(z1, z2)))
ACTIVE(indx(cons(z0, z1), z2)) → c(SEL(z0, z2))
ACTIVE(indx(cons(z0, z1), z2)) → c(INDX(z1, z2))
ACTIVE(dbl1(s(z0))) → c(S1(s1(dbl1(z0))))
ACTIVE(dbl1(s(z0))) → c(S1(dbl1(z0)))
ACTIVE(dbl1(s(z0))) → c(DBL1(z0))
ACTIVE(quote(s(z0))) → c(S1(quote(z0)))
ACTIVE(quote(s(z0))) → c(QUOTE(z0))
ACTIVE(dbl(sel(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl(sel(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl(sel1(0, cons(z0, z1)))) → c17(DBL(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl(sel1(s(z0), cons(z1, z2)))) → c17(DBL(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl(quote(dbl(z0)))) → c17(DBL(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl(quote(sel(z0, z1)))) → c17(DBL(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl(dbl(z0))) → c17(DBL(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl(dbls(z0))) → c17(DBL(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(sel(z0, z1))) → c17(DBL(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl(indx(z0, z1))) → c17(DBL(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl(dbl1(z0))) → c17(DBL(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl(s1(z0))) → c17(DBL(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(sel1(z0, z1))) → c17(DBL(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl(quote(z0))) → c17(DBL(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl(0))) → c17(DBL(mark(0)))
ACTIVE(dbl(dbl(s(z0)))) → c1(DBL(mark(s(s(dbl(z0))))))
ACTIVE(dbl(dbl(s(z0)))) → c1(ACTIVE(dbl(s(z0))))
ACTIVE(dbl(from(z0))) → c1(DBL(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl(from(z0))) → c1(ACTIVE(from(z0)))
ACTIVE(dbls(sel(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbls(sel(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbls(sel1(0, cons(z0, z1)))) → c18(DBLS(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbls(sel1(s(z0), cons(z1, z2)))) → c18(DBLS(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbls(quote(dbl(z0)))) → c18(DBLS(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbls(quote(sel(z0, z1)))) → c18(DBLS(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbls(dbl(z0))) → c18(DBLS(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbls(dbls(z0))) → c18(DBLS(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(sel(z0, z1))) → c18(DBLS(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbls(indx(z0, z1))) → c18(DBLS(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbls(dbl1(z0))) → c18(DBLS(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbls(s1(z0))) → c18(DBLS(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(sel1(z0, z1))) → c18(DBLS(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbls(quote(z0))) → c18(DBLS(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbls(nil))) → c17(DBL(mark(nil)))
ACTIVE(dbls(dbl(0))) → c18(DBLS(mark(0)))
ACTIVE(dbls(dbls(nil))) → c18(DBLS(mark(nil)))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(DBL(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(dbl(s(z0)))) → c2(DBLS(mark(s(s(dbl(z0))))))
ACTIVE(dbls(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(DBLS(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbls(dbls(cons(z0, z1)))) → c2(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbls(from(z0))) → c2(DBLS(mark(cons(z0, from(s(z0))))))
ACTIVE(dbls(from(z0))) → c2(ACTIVE(from(z0)))
ACTIVE(indx(sel(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(indx(sel(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(indx(sel1(0, cons(z0, z1)), x1)) → c21(INDX(mark(z0), x1), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(indx(sel1(s(z0), cons(z1, z2)), x1)) → c21(INDX(mark(sel1(z0, z2)), x1), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(indx(quote(dbl(z0)), x1)) → c21(INDX(mark(dbl1(z0)), x1), ACTIVE(quote(dbl(z0))))
ACTIVE(indx(quote(sel(z0, z1)), x1)) → c21(INDX(mark(sel1(z0, z1)), x1), ACTIVE(quote(sel(z0, z1))))
ACTIVE(indx(dbl(z0), x1)) → c21(INDX(dbl(active(z0)), x1), ACTIVE(dbl(z0)))
ACTIVE(indx(dbls(z0), x1)) → c21(INDX(dbls(active(z0)), x1), ACTIVE(dbls(z0)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(sel(z0, z1), x1)) → c21(INDX(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
ACTIVE(indx(indx(z0, z1), x1)) → c21(INDX(indx(active(z0), z1), x1), ACTIVE(indx(z0, z1)))
ACTIVE(indx(dbl1(z0), x1)) → c21(INDX(dbl1(active(z0)), x1), ACTIVE(dbl1(z0)))
ACTIVE(indx(s1(z0), x1)) → c21(INDX(s1(active(z0)), x1), ACTIVE(s1(z0)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(active(z0), z1), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(sel1(z0, z1), x1)) → c21(INDX(sel1(z0, active(z1)), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(indx(quote(z0), x1)) → c21(INDX(quote(active(z0)), x1), ACTIVE(quote(z0)))
ACTIVE(dbl(indx(nil, z0))) → c17(DBL(mark(nil)))
ACTIVE(dbls(indx(nil, z0))) → c18(DBLS(mark(nil)))
ACTIVE(indx(dbl(0), x1)) → c21(INDX(mark(0), x1))
ACTIVE(indx(dbls(nil), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(indx(indx(nil, z0), x1)) → c21(INDX(mark(nil), x1))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(DBL(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(DBLS(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbls(indx(cons(z0, z1), z2))) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(INDX(mark(s(s(dbl(z0)))), x1))
ACTIVE(indx(dbl(s(z0)), x1)) → c3(ACTIVE(dbl(s(z0))))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(INDX(mark(cons(dbl(z0), dbls(z1))), x1))
ACTIVE(indx(dbls(cons(z0, z1)), x1)) → c3(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(INDX(mark(cons(sel(z0, z2), indx(z1, z2))), x1))
ACTIVE(indx(indx(cons(z0, z1), z2), x1)) → c3(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(indx(from(z0), x1)) → c3(INDX(mark(cons(z0, from(s(z0)))), x1))
ACTIVE(indx(from(z0), x1)) → c3(ACTIVE(from(z0)))
ACTIVE(dbl1(sel(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(dbl1(sel(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(dbl1(sel1(0, cons(z0, z1)))) → c22(DBL1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(dbl1(sel1(s(z0), cons(z1, z2)))) → c22(DBL1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(dbl1(quote(dbl(z0)))) → c22(DBL1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(dbl1(quote(sel(z0, z1)))) → c22(DBL1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(dbl1(dbl(z0))) → c22(DBL1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(dbl1(dbls(z0))) → c22(DBL1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(sel(z0, z1))) → c22(DBL1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(dbl1(indx(z0, z1))) → c22(DBL1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(dbl1(dbl1(z0))) → c22(DBL1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(dbl1(s1(z0))) → c22(DBL1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(sel1(z0, z1))) → c22(DBL1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(dbl1(quote(z0))) → c22(DBL1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(dbl1(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(dbl1(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(dbl1(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(dbl(0))) → c22(DBL1(mark(0)))
ACTIVE(dbl1(dbls(nil))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(indx(nil, z0))) → c22(DBL1(mark(nil)))
ACTIVE(dbl1(dbl1(0))) → c22(DBL1(mark(01)))
ACTIVE(dbl(dbl1(s(z0)))) → c4(DBL(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(DBLS(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbls(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(INDX(mark(s1(s1(dbl1(z0)))), x1))
ACTIVE(indx(dbl1(s(z0)), x1)) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(DBL1(mark(s(s(dbl(z0))))))
ACTIVE(dbl1(dbl(s(z0)))) → c4(ACTIVE(dbl(s(z0))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(DBL1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(dbl1(dbls(cons(z0, z1)))) → c4(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(DBL1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(dbl1(indx(cons(z0, z1), z2))) → c4(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(dbl1(from(z0))) → c4(DBL1(mark(cons(z0, from(s(z0))))))
ACTIVE(dbl1(from(z0))) → c4(ACTIVE(from(z0)))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(DBL1(mark(s1(s1(dbl1(z0))))))
ACTIVE(dbl1(dbl1(s(z0)))) → c4(ACTIVE(dbl1(s(z0))))
ACTIVE(s1(sel(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(s1(sel(s(z0), cons(z1, z2)))) → c23(S1(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(s1(sel1(0, cons(z0, z1)))) → c23(S1(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(s1(sel1(s(z0), cons(z1, z2)))) → c23(S1(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(s1(quote(dbl(z0)))) → c23(S1(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(s1(quote(sel(z0, z1)))) → c23(S1(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(s1(dbl(z0))) → c23(S1(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(s1(dbls(z0))) → c23(S1(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(s1(sel(z0, z1))) → c23(S1(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(s1(indx(z0, z1))) → c23(S1(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(s1(dbl1(z0))) → c23(S1(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(s1(s1(z0))) → c23(S1(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(sel1(z0, z1))) → c23(S1(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(s1(quote(z0))) → c23(S1(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(s1(dbl(0))) → c23(S1(mark(0)))
ACTIVE(s1(dbls(nil))) → c23(S1(mark(nil)))
ACTIVE(s1(indx(nil, z0))) → c23(S1(mark(nil)))
ACTIVE(s1(dbl1(0))) → c23(S1(mark(01)))
ACTIVE(s1(dbl(s(z0)))) → c6(S1(mark(s(s(dbl(z0))))))
ACTIVE(s1(dbl(s(z0)))) → c6(ACTIVE(dbl(s(z0))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(S1(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(s1(dbls(cons(z0, z1)))) → c6(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(S1(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(s1(indx(cons(z0, z1), z2))) → c6(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(s1(from(z0))) → c6(S1(mark(cons(z0, from(s(z0))))))
ACTIVE(s1(from(z0))) → c6(ACTIVE(from(z0)))
ACTIVE(s1(dbl1(s(z0)))) → c6(S1(mark(s1(s1(dbl1(z0))))))
ACTIVE(s1(dbl1(s(z0)))) → c6(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(sel(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(quote(sel(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(quote(sel1(0, cons(z0, z1)))) → c26(QUOTE(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(quote(sel1(s(z0), cons(z1, z2)))) → c26(QUOTE(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(quote(quote(dbl(z0)))) → c26(QUOTE(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
ACTIVE(quote(quote(sel(z0, z1)))) → c26(QUOTE(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(quote(dbl(z0))) → c26(QUOTE(dbl(active(z0))), ACTIVE(dbl(z0)))
ACTIVE(quote(dbls(z0))) → c26(QUOTE(dbls(active(z0))), ACTIVE(dbls(z0)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(quote(sel(z0, z1))) → c26(QUOTE(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(quote(indx(z0, z1))) → c26(QUOTE(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
ACTIVE(quote(dbl1(z0))) → c26(QUOTE(dbl1(active(z0))), ACTIVE(dbl1(z0)))
ACTIVE(quote(s1(z0))) → c26(QUOTE(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(sel1(z0, z1))) → c26(QUOTE(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(quote(quote(z0))) → c26(QUOTE(quote(active(z0))), ACTIVE(quote(z0)))
ACTIVE(dbl(quote(0))) → c17(DBL(mark(01)))
ACTIVE(dbls(quote(0))) → c18(DBLS(mark(01)))
ACTIVE(indx(quote(0), x1)) → c21(INDX(mark(01), x1))
ACTIVE(dbl1(quote(0))) → c22(DBL1(mark(01)))
ACTIVE(s1(quote(0))) → c23(S1(mark(01)))
ACTIVE(quote(dbl(0))) → c26(QUOTE(mark(0)))
ACTIVE(quote(dbls(nil))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(indx(nil, z0))) → c26(QUOTE(mark(nil)))
ACTIVE(quote(dbl1(0))) → c26(QUOTE(mark(01)))
ACTIVE(quote(quote(0))) → c26(QUOTE(mark(01)))
ACTIVE(dbl(quote(s(z0)))) → c7(DBL(mark(s1(quote(z0)))))
ACTIVE(dbl(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbls(quote(s(z0)))) → c7(DBLS(mark(s1(quote(z0)))))
ACTIVE(dbls(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(indx(quote(s(z0)), x1)) → c7(INDX(mark(s1(quote(z0))), x1))
ACTIVE(indx(quote(s(z0)), x1)) → c7(ACTIVE(quote(s(z0))))
ACTIVE(dbl1(quote(s(z0)))) → c7(DBL1(mark(s1(quote(z0)))))
ACTIVE(dbl1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(s1(quote(s(z0)))) → c7(S1(mark(s1(quote(z0)))))
ACTIVE(s1(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
ACTIVE(quote(dbl(s(z0)))) → c7(QUOTE(mark(s(s(dbl(z0))))))
ACTIVE(quote(dbl(s(z0)))) → c7(ACTIVE(dbl(s(z0))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(QUOTE(mark(cons(dbl(z0), dbls(z1)))))
ACTIVE(quote(dbls(cons(z0, z1)))) → c7(ACTIVE(dbls(cons(z0, z1))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(QUOTE(mark(cons(sel(z0, z2), indx(z1, z2)))))
ACTIVE(quote(indx(cons(z0, z1), z2))) → c7(ACTIVE(indx(cons(z0, z1), z2)))
ACTIVE(quote(from(z0))) → c7(QUOTE(mark(cons(z0, from(s(z0))))))
ACTIVE(quote(from(z0))) → c7(ACTIVE(from(z0)))
ACTIVE(quote(dbl1(s(z0)))) → c7(QUOTE(mark(s1(s1(dbl1(z0))))))
ACTIVE(quote(dbl1(s(z0)))) → c7(ACTIVE(dbl1(s(z0))))
ACTIVE(quote(quote(s(z0)))) → c7(QUOTE(mark(s1(quote(z0)))))
ACTIVE(quote(quote(s(z0)))) → c7(ACTIVE(quote(s(z0))))
PROPER(dbl(dbl(z0))) → c45(DBL(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbl(s(z0))) → c45(DBL(s(proper(z0))), PROPER(s(z0)))
PROPER(dbl(dbls(z0))) → c45(DBL(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbl(cons(z0, z1))) → c45(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbl(sel(z0, z1))) → c45(DBL(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbl(indx(z0, z1))) → c45(DBL(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbl(from(z0))) → c45(DBL(from(proper(z0))), PROPER(from(z0)))
PROPER(dbl(dbl1(z0))) → c45(DBL(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbl(s1(z0))) → c45(DBL(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbl(sel1(z0, z1))) → c45(DBL(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbl(quote(z0))) → c45(DBL(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbl(0)) → c45(DBL(ok(0)))
PROPER(dbl(nil)) → c45(DBL(ok(nil)))
PROPER(dbl(01)) → c45(DBL(ok(01)))
PROPER(s(dbl(z0))) → c47(S(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(s(s(z0))) → c47(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(dbls(z0))) → c47(S(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(s(cons(z0, z1))) → c47(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s(sel(z0, z1))) → c47(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(s(indx(z0, z1))) → c47(S(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(s(from(z0))) → c47(S(from(proper(z0))), PROPER(from(z0)))
PROPER(s(dbl1(z0))) → c47(S(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(s(s1(z0))) → c47(S(s1(proper(z0))), PROPER(s1(z0)))
PROPER(s(sel1(z0, z1))) → c47(S(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(s(quote(z0))) → c47(S(quote(proper(z0))), PROPER(quote(z0)))
PROPER(s(0)) → c47(S(ok(0)))
PROPER(s(nil)) → c47(S(ok(nil)))
PROPER(s(01)) → c47(S(ok(01)))
PROPER(dbls(dbl(z0))) → c48(DBLS(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbls(s(z0))) → c48(DBLS(s(proper(z0))), PROPER(s(z0)))
PROPER(dbls(dbls(z0))) → c48(DBLS(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbls(cons(z0, z1))) → c48(DBLS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbls(sel(z0, z1))) → c48(DBLS(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbls(indx(z0, z1))) → c48(DBLS(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbls(from(z0))) → c48(DBLS(from(proper(z0))), PROPER(from(z0)))
PROPER(dbls(dbl1(z0))) → c48(DBLS(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbls(s1(z0))) → c48(DBLS(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbls(sel1(z0, z1))) → c48(DBLS(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbls(quote(z0))) → c48(DBLS(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbls(0)) → c48(DBLS(ok(0)))
PROPER(dbls(nil)) → c48(DBLS(ok(nil)))
PROPER(dbls(01)) → c48(DBLS(ok(01)))
PROPER(cons(x0, dbl(z0))) → c50(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(cons(x0, s(z0))) → c50(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(cons(x0, dbls(z0))) → c50(CONS(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(cons(x0, cons(z0, z1))) → c50(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(cons(x0, sel(z0, z1))) → c50(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(cons(x0, indx(z0, z1))) → c50(CONS(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(cons(x0, from(z0))) → c50(CONS(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(cons(x0, dbl1(z0))) → c50(CONS(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(cons(x0, s1(z0))) → c50(CONS(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(cons(x0, sel1(z0, z1))) → c50(CONS(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(cons(x0, quote(z0))) → c50(CONS(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(cons(dbl(z0), x1)) → c50(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(cons(s(z0), x1)) → c50(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(cons(dbls(z0), x1)) → c50(CONS(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(cons(cons(z0, z1), x1)) → c50(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(cons(sel(z0, z1), x1)) → c50(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(cons(indx(z0, z1), x1)) → c50(CONS(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(cons(from(z0), x1)) → c50(CONS(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(cons(dbl1(z0), x1)) → c50(CONS(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(cons(s1(z0), x1)) → c50(CONS(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(cons(sel1(z0, z1), x1)) → c50(CONS(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(cons(quote(z0), x1)) → c50(CONS(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(cons(x0, 0)) → c50(CONS(proper(x0), ok(0)), PROPER(x0))
PROPER(cons(x0, nil)) → c50(CONS(proper(x0), ok(nil)), PROPER(x0))
PROPER(cons(x0, 01)) → c50(CONS(proper(x0), ok(01)), PROPER(x0))
PROPER(cons(0, x1)) → c50(CONS(ok(0), proper(x1)), PROPER(x1))
PROPER(cons(nil, x1)) → c50(CONS(ok(nil), proper(x1)), PROPER(x1))
PROPER(cons(01, x1)) → c50(CONS(ok(01), proper(x1)), PROPER(x1))
PROPER(sel(x0, dbl(z0))) → c51(SEL(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(sel(x0, s(z0))) → c51(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(sel(x0, dbls(z0))) → c51(SEL(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(sel(x0, cons(z0, z1))) → c51(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(sel(x0, sel(z0, z1))) → c51(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(sel(x0, indx(z0, z1))) → c51(SEL(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(sel(x0, from(z0))) → c51(SEL(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(sel(x0, dbl1(z0))) → c51(SEL(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(sel(x0, s1(z0))) → c51(SEL(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(sel(x0, sel1(z0, z1))) → c51(SEL(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(sel(x0, quote(z0))) → c51(SEL(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(sel(dbl(z0), x1)) → c51(SEL(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(sel(s(z0), x1)) → c51(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(sel(dbls(z0), x1)) → c51(SEL(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(sel(cons(z0, z1), x1)) → c51(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(sel(sel(z0, z1), x1)) → c51(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(sel(indx(z0, z1), x1)) → c51(SEL(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(sel(from(z0), x1)) → c51(SEL(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(sel(dbl1(z0), x1)) → c51(SEL(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(sel(s1(z0), x1)) → c51(SEL(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(sel(sel1(z0, z1), x1)) → c51(SEL(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(sel(quote(z0), x1)) → c51(SEL(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(sel(x0, 0)) → c51(SEL(proper(x0), ok(0)), PROPER(x0))
PROPER(sel(x0, nil)) → c51(SEL(proper(x0), ok(nil)), PROPER(x0))
PROPER(sel(x0, 01)) → c51(SEL(proper(x0), ok(01)), PROPER(x0))
PROPER(sel(0, x1)) → c51(SEL(ok(0), proper(x1)), PROPER(x1))
PROPER(sel(nil, x1)) → c51(SEL(ok(nil), proper(x1)), PROPER(x1))
PROPER(sel(01, x1)) → c51(SEL(ok(01), proper(x1)), PROPER(x1))
PROPER(indx(x0, dbl(z0))) → c52(INDX(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(indx(x0, s(z0))) → c52(INDX(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(indx(x0, dbls(z0))) → c52(INDX(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(indx(x0, cons(z0, z1))) → c52(INDX(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(indx(x0, sel(z0, z1))) → c52(INDX(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(indx(x0, indx(z0, z1))) → c52(INDX(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(indx(x0, from(z0))) → c52(INDX(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(indx(x0, dbl1(z0))) → c52(INDX(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(indx(x0, s1(z0))) → c52(INDX(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(indx(x0, sel1(z0, z1))) → c52(INDX(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(indx(x0, quote(z0))) → c52(INDX(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(indx(dbl(z0), x1)) → c52(INDX(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(indx(s(z0), x1)) → c52(INDX(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(indx(dbls(z0), x1)) → c52(INDX(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(indx(cons(z0, z1), x1)) → c52(INDX(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(indx(sel(z0, z1), x1)) → c52(INDX(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(indx(indx(z0, z1), x1)) → c52(INDX(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(indx(from(z0), x1)) → c52(INDX(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(indx(dbl1(z0), x1)) → c52(INDX(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(indx(s1(z0), x1)) → c52(INDX(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(indx(sel1(z0, z1), x1)) → c52(INDX(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(indx(quote(z0), x1)) → c52(INDX(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(indx(x0, 0)) → c52(INDX(proper(x0), ok(0)), PROPER(x0))
PROPER(indx(x0, nil)) → c52(INDX(proper(x0), ok(nil)), PROPER(x0))
PROPER(indx(x0, 01)) → c52(INDX(proper(x0), ok(01)), PROPER(x0))
PROPER(indx(0, x1)) → c52(INDX(ok(0), proper(x1)), PROPER(x1))
PROPER(indx(nil, x1)) → c52(INDX(ok(nil), proper(x1)), PROPER(x1))
PROPER(indx(01, x1)) → c52(INDX(ok(01), proper(x1)), PROPER(x1))
PROPER(from(dbl(z0))) → c53(FROM(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(from(s(z0))) → c53(FROM(s(proper(z0))), PROPER(s(z0)))
PROPER(from(dbls(z0))) → c53(FROM(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(from(cons(z0, z1))) → c53(FROM(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(from(sel(z0, z1))) → c53(FROM(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(from(indx(z0, z1))) → c53(FROM(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(from(from(z0))) → c53(FROM(from(proper(z0))), PROPER(from(z0)))
PROPER(from(dbl1(z0))) → c53(FROM(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(from(s1(z0))) → c53(FROM(s1(proper(z0))), PROPER(s1(z0)))
PROPER(from(sel1(z0, z1))) → c53(FROM(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(from(quote(z0))) → c53(FROM(quote(proper(z0))), PROPER(quote(z0)))
PROPER(from(0)) → c53(FROM(ok(0)))
PROPER(from(nil)) → c53(FROM(ok(nil)))
PROPER(from(01)) → c53(FROM(ok(01)))
PROPER(dbl1(dbl(z0))) → c54(DBL1(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(dbl1(s(z0))) → c54(DBL1(s(proper(z0))), PROPER(s(z0)))
PROPER(dbl1(dbls(z0))) → c54(DBL1(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(dbl1(cons(z0, z1))) → c54(DBL1(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(dbl1(sel(z0, z1))) → c54(DBL1(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(dbl1(indx(z0, z1))) → c54(DBL1(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(dbl1(from(z0))) → c54(DBL1(from(proper(z0))), PROPER(from(z0)))
PROPER(dbl1(dbl1(z0))) → c54(DBL1(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(dbl1(s1(z0))) → c54(DBL1(s1(proper(z0))), PROPER(s1(z0)))
PROPER(dbl1(sel1(z0, z1))) → c54(DBL1(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(dbl1(quote(z0))) → c54(DBL1(quote(proper(z0))), PROPER(quote(z0)))
PROPER(dbl1(0)) → c54(DBL1(ok(0)))
PROPER(dbl1(nil)) → c54(DBL1(ok(nil)))
PROPER(dbl1(01)) → c54(DBL1(ok(01)))
PROPER(s1(dbl(z0))) → c56(S1(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(s1(s(z0))) → c56(S1(s(proper(z0))), PROPER(s(z0)))
PROPER(s1(dbls(z0))) → c56(S1(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(s1(cons(z0, z1))) → c56(S1(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(s1(sel(z0, z1))) → c56(S1(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(s1(indx(z0, z1))) → c56(S1(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(s1(from(z0))) → c56(S1(from(proper(z0))), PROPER(from(z0)))
PROPER(s1(dbl1(z0))) → c56(S1(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(s1(s1(z0))) → c56(S1(s1(proper(z0))), PROPER(s1(z0)))
PROPER(s1(sel1(z0, z1))) → c56(S1(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(s1(quote(z0))) → c56(S1(quote(proper(z0))), PROPER(quote(z0)))
PROPER(s1(0)) → c56(S1(ok(0)))
PROPER(s1(nil)) → c56(S1(ok(nil)))
PROPER(s1(01)) → c56(S1(ok(01)))
PROPER(sel1(x0, dbl(z0))) → c57(SEL1(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0)))
PROPER(sel1(x0, s(z0))) → c57(SEL1(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(sel1(x0, dbls(z0))) → c57(SEL1(proper(x0), dbls(proper(z0))), PROPER(x0), PROPER(dbls(z0)))
PROPER(sel1(x0, cons(z0, z1))) → c57(SEL1(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1)))
PROPER(sel1(x0, sel(z0, z1))) → c57(SEL1(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1)))
PROPER(sel1(x0, indx(z0, z1))) → c57(SEL1(proper(x0), indx(proper(z0), proper(z1))), PROPER(x0), PROPER(indx(z0, z1)))
PROPER(sel1(x0, from(z0))) → c57(SEL1(proper(x0), from(proper(z0))), PROPER(x0), PROPER(from(z0)))
PROPER(sel1(x0, dbl1(z0))) → c57(SEL1(proper(x0), dbl1(proper(z0))), PROPER(x0), PROPER(dbl1(z0)))
PROPER(sel1(x0, s1(z0))) → c57(SEL1(proper(x0), s1(proper(z0))), PROPER(x0), PROPER(s1(z0)))
PROPER(sel1(x0, sel1(z0, z1))) → c57(SEL1(proper(x0), sel1(proper(z0), proper(z1))), PROPER(x0), PROPER(sel1(z0, z1)))
PROPER(sel1(x0, quote(z0))) → c57(SEL1(proper(x0), quote(proper(z0))), PROPER(x0), PROPER(quote(z0)))
PROPER(sel1(dbl(z0), x1)) → c57(SEL1(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1))
PROPER(sel1(s(z0), x1)) → c57(SEL1(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(sel1(dbls(z0), x1)) → c57(SEL1(dbls(proper(z0)), proper(x1)), PROPER(dbls(z0)), PROPER(x1))
PROPER(sel1(cons(z0, z1), x1)) → c57(SEL1(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1))
PROPER(sel1(sel(z0, z1), x1)) → c57(SEL1(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1))
PROPER(sel1(indx(z0, z1), x1)) → c57(SEL1(indx(proper(z0), proper(z1)), proper(x1)), PROPER(indx(z0, z1)), PROPER(x1))
PROPER(sel1(from(z0), x1)) → c57(SEL1(from(proper(z0)), proper(x1)), PROPER(from(z0)), PROPER(x1))
PROPER(sel1(dbl1(z0), x1)) → c57(SEL1(dbl1(proper(z0)), proper(x1)), PROPER(dbl1(z0)), PROPER(x1))
PROPER(sel1(s1(z0), x1)) → c57(SEL1(s1(proper(z0)), proper(x1)), PROPER(s1(z0)), PROPER(x1))
PROPER(sel1(sel1(z0, z1), x1)) → c57(SEL1(sel1(proper(z0), proper(z1)), proper(x1)), PROPER(sel1(z0, z1)), PROPER(x1))
PROPER(sel1(quote(z0), x1)) → c57(SEL1(quote(proper(z0)), proper(x1)), PROPER(quote(z0)), PROPER(x1))
PROPER(sel1(x0, 0)) → c57(SEL1(proper(x0), ok(0)), PROPER(x0))
PROPER(sel1(x0, nil)) → c57(SEL1(proper(x0), ok(nil)), PROPER(x0))
PROPER(sel1(x0, 01)) → c57(SEL1(proper(x0), ok(01)), PROPER(x0))
PROPER(sel1(0, x1)) → c57(SEL1(ok(0), proper(x1)), PROPER(x1))
PROPER(sel1(nil, x1)) → c57(SEL1(ok(nil), proper(x1)), PROPER(x1))
PROPER(sel1(01, x1)) → c57(SEL1(ok(01), proper(x1)), PROPER(x1))
PROPER(quote(dbl(z0))) → c58(QUOTE(dbl(proper(z0))), PROPER(dbl(z0)))
PROPER(quote(s(z0))) → c58(QUOTE(s(proper(z0))), PROPER(s(z0)))
PROPER(quote(dbls(z0))) → c58(QUOTE(dbls(proper(z0))), PROPER(dbls(z0)))
PROPER(quote(cons(z0, z1))) → c58(QUOTE(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
PROPER(quote(sel(z0, z1))) → c58(QUOTE(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
PROPER(quote(indx(z0, z1))) → c58(QUOTE(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
PROPER(quote(from(z0))) → c58(QUOTE(from(proper(z0))), PROPER(from(z0)))
PROPER(quote(dbl1(z0))) → c58(QUOTE(dbl1(proper(z0))), PROPER(dbl1(z0)))
PROPER(quote(s1(z0))) → c58(QUOTE(s1(proper(z0))), PROPER(s1(z0)))
PROPER(quote(sel1(z0, z1))) → c58(QUOTE(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
PROPER(quote(quote(z0))) → c58(QUOTE(quote(proper(z0))), PROPER(quote(z0)))
PROPER(quote(0)) → c58(QUOTE(ok(0)))
PROPER(quote(nil)) → c58(QUOTE(ok(nil)))
PROPER(quote(01)) → c58(QUOTE(ok(01)))
TOP(mark(dbl(z0))) → c62(TOP(dbl(proper(z0))), PROPER(dbl(z0)))
TOP(mark(s(z0))) → c62(TOP(s(proper(z0))), PROPER(s(z0)))
TOP(mark(dbls(z0))) → c62(TOP(dbls(proper(z0))), PROPER(dbls(z0)))
TOP(mark(cons(z0, z1))) → c62(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1)))
TOP(mark(sel(z0, z1))) → c62(TOP(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1)))
TOP(mark(indx(z0, z1))) → c62(TOP(indx(proper(z0), proper(z1))), PROPER(indx(z0, z1)))
TOP(mark(from(z0))) → c62(TOP(from(proper(z0))), PROPER(from(z0)))
TOP(mark(dbl1(z0))) → c62(TOP(dbl1(proper(z0))), PROPER(dbl1(z0)))
TOP(mark(s1(z0))) → c62(TOP(s1(proper(z0))), PROPER(s1(z0)))
TOP(mark(sel1(z0, z1))) → c62(TOP(sel1(proper(z0), proper(z1))), PROPER(sel1(z0, z1)))
TOP(mark(quote(z0))) → c62(TOP(quote(proper(z0))), PROPER(quote(z0)))
TOP(ok(dbl(s(z0)))) → c63(TOP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0))))
TOP(ok(dbls(cons(z0, z1)))) → c63(TOP(mark(cons(dbl(z0), dbls(z1)))), ACTIVE(dbls(cons(z0, z1))))
TOP(ok(sel(0, cons(z0, z1)))) → c63(TOP(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
TOP(ok(sel(s(z0), cons(z1, z2)))) → c63(TOP(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
TOP(ok(indx(cons(z0, z1), z2))) → c63(TOP(mark(cons(sel(z0, z2), indx(z1, z2)))), ACTIVE(indx(cons(z0, z1), z2)))
TOP(ok(from(z0))) → c63(TOP(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
TOP(ok(dbl1(s(z0)))) → c63(TOP(mark(s1(s1(dbl1(z0))))), ACTIVE(dbl1(s(z0))))
TOP(ok(sel1(0, cons(z0, z1)))) → c63(TOP(mark(z0)), ACTIVE(sel1(0, cons(z0, z1))))
TOP(ok(sel1(s(z0), cons(z1, z2)))) → c63(TOP(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
TOP(ok(quote(s(z0)))) → c63(TOP(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
TOP(ok(quote(dbl(z0)))) → c63(TOP(mark(dbl1(z0))), ACTIVE(quote(dbl(z0))))
TOP(ok(quote(sel(z0, z1)))) → c63(TOP(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
TOP(ok(dbl(z0))) → c63(TOP(dbl(active(z0))), ACTIVE(dbl(z0)))
TOP(ok(dbls(z0))) → c63(TOP(dbls(active(z0))), ACTIVE(dbls(z0)))
TOP(ok(sel(z0, z1))) → c63(TOP(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
TOP(ok(sel(z0, z1))) → c63(TOP(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
TOP(ok(indx(z0, z1))) → c63(TOP(indx(active(z0), z1)), ACTIVE(indx(z0, z1)))
TOP(ok(dbl1(z0))) → c63(TOP(dbl1(active(z0))), ACTIVE(dbl1(z0)))
TOP(ok(s1(z0))) → c63(TOP(s1(active(z0))), ACTIVE(s1(z0)))
TOP(ok(sel1(z0, z1))) → c63(TOP(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
TOP(ok(sel1(z0, z1))) → c63(TOP(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
TOP(ok(quote(z0))) → c63(TOP(quote(active(z0))), ACTIVE(quote(z0)))
(100) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(dbl(0)) → mark(0)
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
active(dbls(nil)) → mark(nil)
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1)))
active(sel(0, cons(z0, z1))) → mark(z0)
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
active(indx(nil, z0)) → mark(nil)
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2)))
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(dbl1(0)) → mark(01)
active(dbl1(s(z0))) → mark(s1(s1(dbl1(z0))))
active(sel1(0, cons(z0, z1))) → mark(z0)
active(sel1(s(z0), cons(z1, z2))) → mark(sel1(z0, z2))
active(quote(0)) → mark(01)
active(quote(s(z0))) → mark(s1(quote(z0)))
active(quote(dbl(z0))) → mark(dbl1(z0))
active(quote(sel(z0, z1))) → mark(sel1(z0, z1))
active(dbl(z0)) → dbl(active(z0))
active(dbls(z0)) → dbls(active(z0))
active(sel(z0, z1)) → sel(active(z0), z1)
active(sel(z0, z1)) → sel(z0, active(z1))
active(indx(z0, z1)) → indx(active(z0), z1)
active(dbl1(z0)) → dbl1(active(z0))
active(s1(z0)) → s1(active(z0))
active(sel1(z0, z1)) → sel1(active(z0), z1)
active(sel1(z0, z1)) → sel1(z0, active(z1))
active(quote(z0)) → quote(active(z0))
s(ok(z0)) → ok(s(z0))
dbl(mark(z0)) → mark(dbl(z0))
dbl(ok(z0)) → ok(dbl(z0))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
dbls(mark(z0)) → mark(dbls(z0))
dbls(ok(z0)) → ok(dbls(z0))
sel(mark(z0), z1) → mark(sel(z0, z1))
sel(z0, mark(z1)) → mark(sel(z0, z1))
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
indx(mark(z0), z1) → mark(indx(z0, z1))
indx(ok(z0), ok(z1)) → ok(indx(z0, z1))
s1(mark(z0)) → mark(s1(z0))
s1(ok(z0)) → ok(s1(z0))
dbl1(mark(z0)) → mark(dbl1(z0))
dbl1(ok(z0)) → ok(dbl1(z0))
sel1(mark(z0), z1) → mark(sel1(z0, z1))
sel1(z0, mark(z1)) → mark(sel1(z0, z1))
sel1(ok(z0), ok(z1)) → ok(sel1(z0, z1))
quote(mark(z0)) → mark(quote(z0))
quote(ok(z0)) → ok(quote(z0))
proper(dbl(z0)) → dbl(proper(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(dbls(z0)) → dbls(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
proper(indx(z0, z1)) → indx(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(dbl1(z0)) → dbl1(proper(z0))
proper(01) → ok(01)
proper(s1(z0)) → s1(proper(z0))
proper(sel1(z0, z1)) → sel1(proper(z0), proper(z1))
proper(quote(z0)) → quote(proper(z0))
from(ok(z0)) → ok(from(z0))
Tuples:
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
S tuples:
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
K tuples:none
Defined Rule Symbols:
active, s, dbl, cons, dbls, sel, indx, s1, dbl1, sel1, quote, proper, from
Defined Pair Symbols:
DBL, DBLS, SEL, INDX, DBL1, S1, SEL1, QUOTE, S, CONS, FROM
Compound Symbols:
c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c59, c60, c61
(101) CdtUsableRulesProof (EQUIVALENT transformation)
The following rules are not usable and were removed:
active(dbl(0)) → mark(0)
active(dbl(s(z0))) → mark(s(s(dbl(z0))))
active(dbls(nil)) → mark(nil)
active(dbls(cons(z0, z1))) → mark(cons(dbl(z0), dbls(z1)))
active(sel(0, cons(z0, z1))) → mark(z0)
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
active(indx(nil, z0)) → mark(nil)
active(indx(cons(z0, z1), z2)) → mark(cons(sel(z0, z2), indx(z1, z2)))
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(dbl1(0)) → mark(01)
active(dbl1(s(z0))) → mark(s1(s1(dbl1(z0))))
active(sel1(0, cons(z0, z1))) → mark(z0)
active(sel1(s(z0), cons(z1, z2))) → mark(sel1(z0, z2))
active(quote(0)) → mark(01)
active(quote(s(z0))) → mark(s1(quote(z0)))
active(quote(dbl(z0))) → mark(dbl1(z0))
active(quote(sel(z0, z1))) → mark(sel1(z0, z1))
active(dbl(z0)) → dbl(active(z0))
active(dbls(z0)) → dbls(active(z0))
active(sel(z0, z1)) → sel(active(z0), z1)
active(sel(z0, z1)) → sel(z0, active(z1))
active(indx(z0, z1)) → indx(active(z0), z1)
active(dbl1(z0)) → dbl1(active(z0))
active(s1(z0)) → s1(active(z0))
active(sel1(z0, z1)) → sel1(active(z0), z1)
active(sel1(z0, z1)) → sel1(z0, active(z1))
active(quote(z0)) → quote(active(z0))
s(ok(z0)) → ok(s(z0))
dbl(mark(z0)) → mark(dbl(z0))
dbl(ok(z0)) → ok(dbl(z0))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
dbls(mark(z0)) → mark(dbls(z0))
dbls(ok(z0)) → ok(dbls(z0))
sel(mark(z0), z1) → mark(sel(z0, z1))
sel(z0, mark(z1)) → mark(sel(z0, z1))
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
indx(mark(z0), z1) → mark(indx(z0, z1))
indx(ok(z0), ok(z1)) → ok(indx(z0, z1))
s1(mark(z0)) → mark(s1(z0))
s1(ok(z0)) → ok(s1(z0))
dbl1(mark(z0)) → mark(dbl1(z0))
dbl1(ok(z0)) → ok(dbl1(z0))
sel1(mark(z0), z1) → mark(sel1(z0, z1))
sel1(z0, mark(z1)) → mark(sel1(z0, z1))
sel1(ok(z0), ok(z1)) → ok(sel1(z0, z1))
quote(mark(z0)) → mark(quote(z0))
quote(ok(z0)) → ok(quote(z0))
proper(dbl(z0)) → dbl(proper(z0))
proper(0) → ok(0)
proper(s(z0)) → s(proper(z0))
proper(dbls(z0)) → dbls(proper(z0))
proper(nil) → ok(nil)
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
proper(indx(z0, z1)) → indx(proper(z0), proper(z1))
proper(from(z0)) → from(proper(z0))
proper(dbl1(z0)) → dbl1(proper(z0))
proper(01) → ok(01)
proper(s1(z0)) → s1(proper(z0))
proper(sel1(z0, z1)) → sel1(proper(z0), proper(z1))
proper(quote(z0)) → quote(proper(z0))
from(ok(z0)) → ok(from(z0))
(102) Obligation:
Complexity Dependency Tuples Problem
Rules:none
Tuples:
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
S tuples:
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
K tuples:none
Defined Rule Symbols:none
Defined Pair Symbols:
DBL, DBLS, SEL, INDX, DBL1, S1, SEL1, QUOTE, S, CONS, FROM
Compound Symbols:
c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c59, c60, c61
(103) CdtRuleRemovalProof (UPPER BOUND (ADD(O(n^1))) transformation)
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
DBLS(mark(z0)) → c29(DBLS(z0))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
We considered the (Usable) Rules:none
And the Tuples:
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
The order we found is given by the following interpretation:
Polynomial interpretation :
POL(CONS(x1, x2)) = [3]x1 + [2]x2
POL(DBL(x1)) = 0
POL(DBL1(x1)) = x1
POL(DBLS(x1)) = [2]x1
POL(FROM(x1)) = [2]x1
POL(INDX(x1, x2)) = x2
POL(QUOTE(x1)) = 0
POL(S(x1)) = [3]x1
POL(S1(x1)) = [2]x1
POL(SEL(x1, x2)) = [4]x2
POL(SEL1(x1, x2)) = 0
POL(c27(x1)) = 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(c59(x1)) = x1
POL(c60(x1)) = x1
POL(c61(x1)) = x1
POL(mark(x1)) = [2] + x1
POL(ok(x1)) = x1
(104) Obligation:
Complexity Dependency Tuples Problem
Rules:none
Tuples:
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
S tuples:
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
K tuples:
DBLS(mark(z0)) → c29(DBLS(z0))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
Defined Rule Symbols:none
Defined Pair Symbols:
DBL, DBLS, SEL, INDX, DBL1, S1, SEL1, QUOTE, S, CONS, FROM
Compound Symbols:
c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c59, c60, c61
(105) CdtRuleRemovalProof (UPPER BOUND (ADD(O(n^1))) transformation)
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
We considered the (Usable) Rules:none
And the Tuples:
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
The order we found is given by the following interpretation:
Polynomial interpretation :
POL(CONS(x1, x2)) = 0
POL(DBL(x1)) = [2]x1
POL(DBL1(x1)) = [2]x1
POL(DBLS(x1)) = [3]x1
POL(FROM(x1)) = 0
POL(INDX(x1, x2)) = x1
POL(QUOTE(x1)) = [2]x1
POL(S(x1)) = 0
POL(S1(x1)) = [2]x1
POL(SEL(x1, x2)) = [4]x1 + [2]x2
POL(SEL1(x1, x2)) = [3]x1 + [5]x2
POL(c27(x1)) = 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(c59(x1)) = x1
POL(c60(x1)) = x1
POL(c61(x1)) = x1
POL(mark(x1)) = [4] + x1
POL(ok(x1)) = [2] + x1
(106) Obligation:
Complexity Dependency Tuples Problem
Rules:none
Tuples:
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
S tuples:
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
K tuples:
DBLS(mark(z0)) → c29(DBLS(z0))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
Defined Rule Symbols:none
Defined Pair Symbols:
DBL, DBLS, SEL, INDX, DBL1, S1, SEL1, QUOTE, S, CONS, FROM
Compound Symbols:
c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c59, c60, c61
(107) CdtRuleRemovalProof (UPPER BOUND (ADD(O(n^1))) transformation)
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
S(ok(z0)) → c59(S(z0))
We considered the (Usable) Rules:none
And the Tuples:
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
The order we found is given by the following interpretation:
Polynomial interpretation :
POL(CONS(x1, x2)) = 0
POL(DBL(x1)) = 0
POL(DBL1(x1)) = 0
POL(DBLS(x1)) = [4]x1
POL(FROM(x1)) = 0
POL(INDX(x1, x2)) = 0
POL(QUOTE(x1)) = 0
POL(S(x1)) = [4]x1
POL(S1(x1)) = 0
POL(SEL(x1, x2)) = [4]x1
POL(SEL1(x1, x2)) = [2]x1 + [2]x2
POL(c27(x1)) = 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(c59(x1)) = x1
POL(c60(x1)) = x1
POL(c61(x1)) = x1
POL(mark(x1)) = x1
POL(ok(x1)) = [2] + x1
(108) Obligation:
Complexity Dependency Tuples Problem
Rules:none
Tuples:
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
S tuples:
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
K tuples:
DBLS(mark(z0)) → c29(DBLS(z0))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
S(ok(z0)) → c59(S(z0))
Defined Rule Symbols:none
Defined Pair Symbols:
DBL, DBLS, SEL, INDX, DBL1, S1, SEL1, QUOTE, S, CONS, FROM
Compound Symbols:
c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c59, c60, c61
(109) CdtRuleRemovalProof (UPPER BOUND (ADD(O(n^1))) transformation)
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
We considered the (Usable) Rules:none
And the Tuples:
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
The order we found is given by the following interpretation:
Polynomial interpretation :
POL(CONS(x1, x2)) = [2]x2
POL(DBL(x1)) = 0
POL(DBL1(x1)) = 0
POL(DBLS(x1)) = 0
POL(FROM(x1)) = 0
POL(INDX(x1, x2)) = 0
POL(QUOTE(x1)) = 0
POL(S(x1)) = [3]x1
POL(S1(x1)) = 0
POL(SEL(x1, x2)) = 0
POL(SEL1(x1, x2)) = 0
POL(c27(x1)) = 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(c59(x1)) = x1
POL(c60(x1)) = x1
POL(c61(x1)) = x1
POL(mark(x1)) = 0
POL(ok(x1)) = [4] + x1
(110) Obligation:
Complexity Dependency Tuples Problem
Rules:none
Tuples:
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
S tuples:
FROM(ok(z0)) → c61(FROM(z0))
K tuples:
DBLS(mark(z0)) → c29(DBLS(z0))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
Defined Rule Symbols:none
Defined Pair Symbols:
DBL, DBLS, SEL, INDX, DBL1, S1, SEL1, QUOTE, S, CONS, FROM
Compound Symbols:
c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c59, c60, c61
(111) CdtRuleRemovalProof (UPPER BOUND (ADD(O(n^1))) transformation)
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
FROM(ok(z0)) → c61(FROM(z0))
We considered the (Usable) Rules:none
And the Tuples:
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
The order we found is given by the following interpretation:
Polynomial interpretation :
POL(CONS(x1, x2)) = [3]x1 + [2]x2
POL(DBL(x1)) = 0
POL(DBL1(x1)) = 0
POL(DBLS(x1)) = 0
POL(FROM(x1)) = [2]x1
POL(INDX(x1, x2)) = 0
POL(QUOTE(x1)) = 0
POL(S(x1)) = [4]x1
POL(S1(x1)) = 0
POL(SEL(x1, x2)) = 0
POL(SEL1(x1, x2)) = 0
POL(c27(x1)) = 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(c59(x1)) = x1
POL(c60(x1)) = x1
POL(c61(x1)) = x1
POL(mark(x1)) = 0
POL(ok(x1)) = [1] + x1
(112) Obligation:
Complexity Dependency Tuples Problem
Rules:none
Tuples:
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(mark(z0)) → c29(DBLS(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
S tuples:none
K tuples:
DBLS(mark(z0)) → c29(DBLS(z0))
SEL(z0, mark(z1)) → c32(SEL(z0, z1))
DBL1(mark(z0)) → c36(DBL1(z0))
S1(mark(z0)) → c38(S1(z0))
DBL(mark(z0)) → c27(DBL(z0))
DBL(ok(z0)) → c28(DBL(z0))
DBLS(ok(z0)) → c30(DBLS(z0))
SEL(mark(z0), z1) → c31(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c33(SEL(z0, z1))
INDX(mark(z0), z1) → c34(INDX(z0, z1))
INDX(ok(z0), ok(z1)) → c35(INDX(z0, z1))
DBL1(ok(z0)) → c37(DBL1(z0))
S1(ok(z0)) → c39(S1(z0))
SEL1(mark(z0), z1) → c40(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c41(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c42(SEL1(z0, z1))
QUOTE(mark(z0)) → c43(QUOTE(z0))
QUOTE(ok(z0)) → c44(QUOTE(z0))
S(ok(z0)) → c59(S(z0))
CONS(ok(z0), ok(z1)) → c60(CONS(z0, z1))
FROM(ok(z0)) → c61(FROM(z0))
Defined Rule Symbols:none
Defined Pair Symbols:
DBL, DBLS, SEL, INDX, DBL1, S1, SEL1, QUOTE, S, CONS, FROM
Compound Symbols:
c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c59, c60, c61
(113) SIsEmptyProof (BOTH BOUNDS(ID, ID) transformation)
The set S is empty
(114) BOUNDS(O(1), O(1))