(0) Obligation:

Runtime Complexity TRS:
The TRS R consists of the following rules:

active(sel(s(X), cons(Y, Z))) → mark(sel(X, Z))
active(sel(0, cons(X, Z))) → mark(X)
active(first(0, Z)) → mark(nil)
active(first(s(X), cons(Y, Z))) → mark(cons(Y, first(X, Z)))
active(from(X)) → mark(cons(X, from(s(X))))
active(sel1(s(X), cons(Y, Z))) → mark(sel1(X, Z))
active(sel1(0, cons(X, Z))) → mark(quote(X))
active(first1(0, Z)) → mark(nil1)
active(first1(s(X), cons(Y, Z))) → mark(cons1(quote(Y), first1(X, Z)))
active(quote(0)) → mark(01)
active(quote1(cons(X, Z))) → mark(cons1(quote(X), quote1(Z)))
active(quote1(nil)) → mark(nil1)
active(quote(s(X))) → mark(s1(quote(X)))
active(quote(sel(X, Z))) → mark(sel1(X, Z))
active(quote1(first(X, Z))) → mark(first1(X, Z))
active(unquote(01)) → mark(0)
active(unquote(s1(X))) → mark(s(unquote(X)))
active(unquote1(nil1)) → mark(nil)
active(unquote1(cons1(X, Z))) → mark(fcons(unquote(X), unquote1(Z)))
active(fcons(X, Z)) → mark(cons(X, Z))
active(sel(X1, X2)) → sel(active(X1), X2)
active(sel(X1, X2)) → sel(X1, active(X2))
active(s(X)) → s(active(X))
active(cons(X1, X2)) → cons(active(X1), X2)
active(first(X1, X2)) → first(active(X1), X2)
active(first(X1, X2)) → first(X1, active(X2))
active(from(X)) → from(active(X))
active(sel1(X1, X2)) → sel1(active(X1), X2)
active(sel1(X1, X2)) → sel1(X1, active(X2))
active(first1(X1, X2)) → first1(active(X1), X2)
active(first1(X1, X2)) → first1(X1, active(X2))
active(cons1(X1, X2)) → cons1(active(X1), X2)
active(cons1(X1, X2)) → cons1(X1, active(X2))
active(s1(X)) → s1(active(X))
active(unquote(X)) → unquote(active(X))
active(unquote1(X)) → unquote1(active(X))
active(fcons(X1, X2)) → fcons(active(X1), X2)
active(fcons(X1, X2)) → fcons(X1, active(X2))
sel(mark(X1), X2) → mark(sel(X1, X2))
sel(X1, mark(X2)) → mark(sel(X1, X2))
s(mark(X)) → mark(s(X))
cons(mark(X1), X2) → mark(cons(X1, X2))
first(mark(X1), X2) → mark(first(X1, X2))
first(X1, mark(X2)) → mark(first(X1, X2))
from(mark(X)) → mark(from(X))
sel1(mark(X1), X2) → mark(sel1(X1, X2))
sel1(X1, mark(X2)) → mark(sel1(X1, X2))
first1(mark(X1), X2) → mark(first1(X1, X2))
first1(X1, mark(X2)) → mark(first1(X1, X2))
cons1(mark(X1), X2) → mark(cons1(X1, X2))
cons1(X1, mark(X2)) → mark(cons1(X1, X2))
s1(mark(X)) → mark(s1(X))
unquote(mark(X)) → mark(unquote(X))
unquote1(mark(X)) → mark(unquote1(X))
fcons(mark(X1), X2) → mark(fcons(X1, X2))
fcons(X1, mark(X2)) → mark(fcons(X1, X2))
proper(sel(X1, X2)) → sel(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))
proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(0) → ok(0)
proper(first(X1, X2)) → first(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(from(X)) → from(proper(X))
proper(sel1(X1, X2)) → sel1(proper(X1), proper(X2))
proper(quote(X)) → quote(proper(X))
proper(first1(X1, X2)) → first1(proper(X1), proper(X2))
proper(nil1) → ok(nil1)
proper(cons1(X1, X2)) → cons1(proper(X1), proper(X2))
proper(01) → ok(01)
proper(quote1(X)) → quote1(proper(X))
proper(s1(X)) → s1(proper(X))
proper(unquote(X)) → unquote(proper(X))
proper(unquote1(X)) → unquote1(proper(X))
proper(fcons(X1, X2)) → fcons(proper(X1), proper(X2))
sel(ok(X1), ok(X2)) → ok(sel(X1, X2))
s(ok(X)) → ok(s(X))
cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
first(ok(X1), ok(X2)) → ok(first(X1, X2))
from(ok(X)) → ok(from(X))
sel1(ok(X1), ok(X2)) → ok(sel1(X1, X2))
quote(ok(X)) → ok(quote(X))
first1(ok(X1), ok(X2)) → ok(first1(X1, X2))
cons1(ok(X1), ok(X2)) → ok(cons1(X1, X2))
quote1(ok(X)) → ok(quote1(X))
s1(ok(X)) → ok(s1(X))
unquote(ok(X)) → ok(unquote(X))
unquote1(ok(X)) → ok(unquote1(X))
fcons(ok(X1), ok(X2)) → ok(fcons(X1, X2))
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(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
active(sel(0, cons(z0, z1))) → mark(z0)
active(first(0, z0)) → mark(nil)
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2)))
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(sel1(s(z0), cons(z1, z2))) → mark(sel1(z0, z2))
active(sel1(0, cons(z0, z1))) → mark(quote(z0))
active(first1(0, z0)) → mark(nil1)
active(first1(s(z0), cons(z1, z2))) → mark(cons1(quote(z1), first1(z0, z2)))
active(quote(0)) → mark(01)
active(quote1(cons(z0, z1))) → mark(cons1(quote(z0), quote1(z1)))
active(quote1(nil)) → mark(nil1)
active(quote(s(z0))) → mark(s1(quote(z0)))
active(quote(sel(z0, z1))) → mark(sel1(z0, z1))
active(quote1(first(z0, z1))) → mark(first1(z0, z1))
active(unquote(01)) → mark(0)
active(unquote(s1(z0))) → mark(s(unquote(z0)))
active(unquote1(nil1)) → mark(nil)
active(unquote1(cons1(z0, z1))) → mark(fcons(unquote(z0), unquote1(z1)))
active(fcons(z0, z1)) → mark(cons(z0, z1))
active(sel(z0, z1)) → sel(active(z0), z1)
active(sel(z0, z1)) → sel(z0, active(z1))
active(s(z0)) → s(active(z0))
active(cons(z0, z1)) → cons(active(z0), z1)
active(first(z0, z1)) → first(active(z0), z1)
active(first(z0, z1)) → first(z0, active(z1))
active(from(z0)) → from(active(z0))
active(sel1(z0, z1)) → sel1(active(z0), z1)
active(sel1(z0, z1)) → sel1(z0, active(z1))
active(first1(z0, z1)) → first1(active(z0), z1)
active(first1(z0, z1)) → first1(z0, active(z1))
active(cons1(z0, z1)) → cons1(active(z0), z1)
active(cons1(z0, z1)) → cons1(z0, active(z1))
active(s1(z0)) → s1(active(z0))
active(unquote(z0)) → unquote(active(z0))
active(unquote1(z0)) → unquote1(active(z0))
active(fcons(z0, z1)) → fcons(active(z0), z1)
active(fcons(z0, z1)) → fcons(z0, active(z1))
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))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
cons(mark(z0), z1) → mark(cons(z0, z1))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
first(mark(z0), z1) → mark(first(z0, z1))
first(z0, mark(z1)) → mark(first(z0, z1))
first(ok(z0), ok(z1)) → ok(first(z0, z1))
from(mark(z0)) → mark(from(z0))
from(ok(z0)) → ok(from(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))
first1(mark(z0), z1) → mark(first1(z0, z1))
first1(z0, mark(z1)) → mark(first1(z0, z1))
first1(ok(z0), ok(z1)) → ok(first1(z0, z1))
cons1(mark(z0), z1) → mark(cons1(z0, z1))
cons1(z0, mark(z1)) → mark(cons1(z0, z1))
cons1(ok(z0), ok(z1)) → ok(cons1(z0, z1))
s1(mark(z0)) → mark(s1(z0))
s1(ok(z0)) → ok(s1(z0))
unquote(mark(z0)) → mark(unquote(z0))
unquote(ok(z0)) → ok(unquote(z0))
unquote1(mark(z0)) → mark(unquote1(z0))
unquote1(ok(z0)) → ok(unquote1(z0))
fcons(mark(z0), z1) → mark(fcons(z0, z1))
fcons(z0, mark(z1)) → mark(fcons(z0, z1))
fcons(ok(z0), ok(z1)) → ok(fcons(z0, z1))
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
proper(s(z0)) → s(proper(z0))
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(0) → ok(0)
proper(first(z0, z1)) → first(proper(z0), proper(z1))
proper(nil) → ok(nil)
proper(from(z0)) → from(proper(z0))
proper(sel1(z0, z1)) → sel1(proper(z0), proper(z1))
proper(quote(z0)) → quote(proper(z0))
proper(first1(z0, z1)) → first1(proper(z0), proper(z1))
proper(nil1) → ok(nil1)
proper(cons1(z0, z1)) → cons1(proper(z0), proper(z1))
proper(01) → ok(01)
proper(quote1(z0)) → quote1(proper(z0))
proper(s1(z0)) → s1(proper(z0))
proper(unquote(z0)) → unquote(proper(z0))
proper(unquote1(z0)) → unquote1(proper(z0))
proper(fcons(z0, z1)) → fcons(proper(z0), proper(z1))
quote(ok(z0)) → ok(quote(z0))
quote1(ok(z0)) → ok(quote1(z0))
top(mark(z0)) → top(proper(z0))
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c(SEL(z0, z2))
ACTIVE(sel(0, cons(z0, z1))) → c1
ACTIVE(first(0, z0)) → c2
ACTIVE(first(s(z0), cons(z1, z2))) → c3(CONS(z1, first(z0, z2)), FIRST(z0, z2))
ACTIVE(from(z0)) → c4(CONS(z0, from(s(z0))), FROM(s(z0)), S(z0))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c5(SEL1(z0, z2))
ACTIVE(sel1(0, cons(z0, z1))) → c6(QUOTE(z0))
ACTIVE(first1(0, z0)) → c7
ACTIVE(first1(s(z0), cons(z1, z2))) → c8(CONS1(quote(z1), first1(z0, z2)), QUOTE(z1), FIRST1(z0, z2))
ACTIVE(quote(0)) → c9
ACTIVE(quote1(cons(z0, z1))) → c10(CONS1(quote(z0), quote1(z1)), QUOTE(z0), QUOTE1(z1))
ACTIVE(quote1(nil)) → c11
ACTIVE(quote(s(z0))) → c12(S1(quote(z0)), QUOTE(z0))
ACTIVE(quote(sel(z0, z1))) → c13(SEL1(z0, z1))
ACTIVE(quote1(first(z0, z1))) → c14(FIRST1(z0, z1))
ACTIVE(unquote(01)) → c15
ACTIVE(unquote(s1(z0))) → c16(S(unquote(z0)), UNQUOTE(z0))
ACTIVE(unquote1(nil1)) → c17
ACTIVE(unquote1(cons1(z0, z1))) → c18(FCONS(unquote(z0), unquote1(z1)), UNQUOTE(z0), UNQUOTE1(z1))
ACTIVE(fcons(z0, z1)) → c19(CONS(z0, z1))
ACTIVE(sel(z0, z1)) → c20(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c21(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(s(z0)) → c22(S(active(z0)), ACTIVE(z0))
ACTIVE(cons(z0, z1)) → c23(CONS(active(z0), z1), ACTIVE(z0))
ACTIVE(first(z0, z1)) → c24(FIRST(active(z0), z1), ACTIVE(z0))
ACTIVE(first(z0, z1)) → c25(FIRST(z0, active(z1)), ACTIVE(z1))
ACTIVE(from(z0)) → c26(FROM(active(z0)), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c27(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c28(SEL1(z0, active(z1)), ACTIVE(z1))
ACTIVE(first1(z0, z1)) → c29(FIRST1(active(z0), z1), ACTIVE(z0))
ACTIVE(first1(z0, z1)) → c30(FIRST1(z0, active(z1)), ACTIVE(z1))
ACTIVE(cons1(z0, z1)) → c31(CONS1(active(z0), z1), ACTIVE(z0))
ACTIVE(cons1(z0, z1)) → c32(CONS1(z0, active(z1)), ACTIVE(z1))
ACTIVE(s1(z0)) → c33(S1(active(z0)), ACTIVE(z0))
ACTIVE(unquote(z0)) → c34(UNQUOTE(active(z0)), ACTIVE(z0))
ACTIVE(unquote1(z0)) → c35(UNQUOTE1(active(z0)), ACTIVE(z0))
ACTIVE(fcons(z0, z1)) → c36(FCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(fcons(z0, z1)) → c37(FCONS(z0, active(z1)), ACTIVE(z1))
SEL(mark(z0), z1) → c38(SEL(z0, z1))
SEL(z0, mark(z1)) → c39(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c40(SEL(z0, z1))
S(mark(z0)) → c41(S(z0))
S(ok(z0)) → c42(S(z0))
CONS(mark(z0), z1) → c43(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c44(CONS(z0, z1))
FIRST(mark(z0), z1) → c45(FIRST(z0, z1))
FIRST(z0, mark(z1)) → c46(FIRST(z0, z1))
FIRST(ok(z0), ok(z1)) → c47(FIRST(z0, z1))
FROM(mark(z0)) → c48(FROM(z0))
FROM(ok(z0)) → c49(FROM(z0))
SEL1(mark(z0), z1) → c50(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c51(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c52(SEL1(z0, z1))
FIRST1(mark(z0), z1) → c53(FIRST1(z0, z1))
FIRST1(z0, mark(z1)) → c54(FIRST1(z0, z1))
FIRST1(ok(z0), ok(z1)) → c55(FIRST1(z0, z1))
CONS1(mark(z0), z1) → c56(CONS1(z0, z1))
CONS1(z0, mark(z1)) → c57(CONS1(z0, z1))
CONS1(ok(z0), ok(z1)) → c58(CONS1(z0, z1))
S1(mark(z0)) → c59(S1(z0))
S1(ok(z0)) → c60(S1(z0))
UNQUOTE(mark(z0)) → c61(UNQUOTE(z0))
UNQUOTE(ok(z0)) → c62(UNQUOTE(z0))
UNQUOTE1(mark(z0)) → c63(UNQUOTE1(z0))
UNQUOTE1(ok(z0)) → c64(UNQUOTE1(z0))
FCONS(mark(z0), z1) → c65(FCONS(z0, z1))
FCONS(z0, mark(z1)) → c66(FCONS(z0, z1))
FCONS(ok(z0), ok(z1)) → c67(FCONS(z0, z1))
PROPER(sel(z0, z1)) → c68(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(s(z0)) → c69(S(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c70(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(0) → c71
PROPER(first(z0, z1)) → c72(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(nil) → c73
PROPER(from(z0)) → c74(FROM(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c75(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c76(QUOTE(proper(z0)), PROPER(z0))
PROPER(first1(z0, z1)) → c77(FIRST1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(nil1) → c78
PROPER(cons1(z0, z1)) → c79(CONS1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(01) → c80
PROPER(quote1(z0)) → c81(QUOTE1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c82(S1(proper(z0)), PROPER(z0))
PROPER(unquote(z0)) → c83(UNQUOTE(proper(z0)), PROPER(z0))
PROPER(unquote1(z0)) → c84(UNQUOTE1(proper(z0)), PROPER(z0))
PROPER(fcons(z0, z1)) → c85(FCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
QUOTE(ok(z0)) → c86(QUOTE(z0))
QUOTE1(ok(z0)) → c87(QUOTE1(z0))
TOP(mark(z0)) → c88(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c89(TOP(active(z0)), ACTIVE(z0))
S tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c(SEL(z0, z2))
ACTIVE(sel(0, cons(z0, z1))) → c1
ACTIVE(first(0, z0)) → c2
ACTIVE(first(s(z0), cons(z1, z2))) → c3(CONS(z1, first(z0, z2)), FIRST(z0, z2))
ACTIVE(from(z0)) → c4(CONS(z0, from(s(z0))), FROM(s(z0)), S(z0))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c5(SEL1(z0, z2))
ACTIVE(sel1(0, cons(z0, z1))) → c6(QUOTE(z0))
ACTIVE(first1(0, z0)) → c7
ACTIVE(first1(s(z0), cons(z1, z2))) → c8(CONS1(quote(z1), first1(z0, z2)), QUOTE(z1), FIRST1(z0, z2))
ACTIVE(quote(0)) → c9
ACTIVE(quote1(cons(z0, z1))) → c10(CONS1(quote(z0), quote1(z1)), QUOTE(z0), QUOTE1(z1))
ACTIVE(quote1(nil)) → c11
ACTIVE(quote(s(z0))) → c12(S1(quote(z0)), QUOTE(z0))
ACTIVE(quote(sel(z0, z1))) → c13(SEL1(z0, z1))
ACTIVE(quote1(first(z0, z1))) → c14(FIRST1(z0, z1))
ACTIVE(unquote(01)) → c15
ACTIVE(unquote(s1(z0))) → c16(S(unquote(z0)), UNQUOTE(z0))
ACTIVE(unquote1(nil1)) → c17
ACTIVE(unquote1(cons1(z0, z1))) → c18(FCONS(unquote(z0), unquote1(z1)), UNQUOTE(z0), UNQUOTE1(z1))
ACTIVE(fcons(z0, z1)) → c19(CONS(z0, z1))
ACTIVE(sel(z0, z1)) → c20(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c21(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(s(z0)) → c22(S(active(z0)), ACTIVE(z0))
ACTIVE(cons(z0, z1)) → c23(CONS(active(z0), z1), ACTIVE(z0))
ACTIVE(first(z0, z1)) → c24(FIRST(active(z0), z1), ACTIVE(z0))
ACTIVE(first(z0, z1)) → c25(FIRST(z0, active(z1)), ACTIVE(z1))
ACTIVE(from(z0)) → c26(FROM(active(z0)), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c27(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c28(SEL1(z0, active(z1)), ACTIVE(z1))
ACTIVE(first1(z0, z1)) → c29(FIRST1(active(z0), z1), ACTIVE(z0))
ACTIVE(first1(z0, z1)) → c30(FIRST1(z0, active(z1)), ACTIVE(z1))
ACTIVE(cons1(z0, z1)) → c31(CONS1(active(z0), z1), ACTIVE(z0))
ACTIVE(cons1(z0, z1)) → c32(CONS1(z0, active(z1)), ACTIVE(z1))
ACTIVE(s1(z0)) → c33(S1(active(z0)), ACTIVE(z0))
ACTIVE(unquote(z0)) → c34(UNQUOTE(active(z0)), ACTIVE(z0))
ACTIVE(unquote1(z0)) → c35(UNQUOTE1(active(z0)), ACTIVE(z0))
ACTIVE(fcons(z0, z1)) → c36(FCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(fcons(z0, z1)) → c37(FCONS(z0, active(z1)), ACTIVE(z1))
SEL(mark(z0), z1) → c38(SEL(z0, z1))
SEL(z0, mark(z1)) → c39(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c40(SEL(z0, z1))
S(mark(z0)) → c41(S(z0))
S(ok(z0)) → c42(S(z0))
CONS(mark(z0), z1) → c43(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c44(CONS(z0, z1))
FIRST(mark(z0), z1) → c45(FIRST(z0, z1))
FIRST(z0, mark(z1)) → c46(FIRST(z0, z1))
FIRST(ok(z0), ok(z1)) → c47(FIRST(z0, z1))
FROM(mark(z0)) → c48(FROM(z0))
FROM(ok(z0)) → c49(FROM(z0))
SEL1(mark(z0), z1) → c50(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c51(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c52(SEL1(z0, z1))
FIRST1(mark(z0), z1) → c53(FIRST1(z0, z1))
FIRST1(z0, mark(z1)) → c54(FIRST1(z0, z1))
FIRST1(ok(z0), ok(z1)) → c55(FIRST1(z0, z1))
CONS1(mark(z0), z1) → c56(CONS1(z0, z1))
CONS1(z0, mark(z1)) → c57(CONS1(z0, z1))
CONS1(ok(z0), ok(z1)) → c58(CONS1(z0, z1))
S1(mark(z0)) → c59(S1(z0))
S1(ok(z0)) → c60(S1(z0))
UNQUOTE(mark(z0)) → c61(UNQUOTE(z0))
UNQUOTE(ok(z0)) → c62(UNQUOTE(z0))
UNQUOTE1(mark(z0)) → c63(UNQUOTE1(z0))
UNQUOTE1(ok(z0)) → c64(UNQUOTE1(z0))
FCONS(mark(z0), z1) → c65(FCONS(z0, z1))
FCONS(z0, mark(z1)) → c66(FCONS(z0, z1))
FCONS(ok(z0), ok(z1)) → c67(FCONS(z0, z1))
PROPER(sel(z0, z1)) → c68(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(s(z0)) → c69(S(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c70(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(0) → c71
PROPER(first(z0, z1)) → c72(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(nil) → c73
PROPER(from(z0)) → c74(FROM(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c75(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c76(QUOTE(proper(z0)), PROPER(z0))
PROPER(first1(z0, z1)) → c77(FIRST1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(nil1) → c78
PROPER(cons1(z0, z1)) → c79(CONS1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(01) → c80
PROPER(quote1(z0)) → c81(QUOTE1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c82(S1(proper(z0)), PROPER(z0))
PROPER(unquote(z0)) → c83(UNQUOTE(proper(z0)), PROPER(z0))
PROPER(unquote1(z0)) → c84(UNQUOTE1(proper(z0)), PROPER(z0))
PROPER(fcons(z0, z1)) → c85(FCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
QUOTE(ok(z0)) → c86(QUOTE(z0))
QUOTE1(ok(z0)) → c87(QUOTE1(z0))
TOP(mark(z0)) → c88(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c89(TOP(active(z0)), ACTIVE(z0))
K tuples:none
Defined Rule Symbols:

active, sel, s, cons, first, from, sel1, first1, cons1, s1, unquote, unquote1, fcons, proper, quote, quote1, top

Defined Pair Symbols:

ACTIVE, SEL, S, CONS, FIRST, FROM, SEL1, FIRST1, CONS1, S1, UNQUOTE, UNQUOTE1, FCONS, PROPER, QUOTE, QUOTE1, TOP

Compound Symbols:

c, c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c78, c79, c80, c81, c82, c83, c84, c85, c86, c87, c88, c89

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

Removed 11 trailing nodes:

ACTIVE(quote1(nil)) → c11
PROPER(01) → c80
ACTIVE(unquote1(nil1)) → c17
ACTIVE(unquote(01)) → c15
ACTIVE(sel(0, cons(z0, z1))) → c1
PROPER(nil) → c73
PROPER(0) → c71
ACTIVE(first(0, z0)) → c2
ACTIVE(quote(0)) → c9
PROPER(nil1) → c78
ACTIVE(first1(0, z0)) → c7

(4) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
active(sel(0, cons(z0, z1))) → mark(z0)
active(first(0, z0)) → mark(nil)
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2)))
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(sel1(s(z0), cons(z1, z2))) → mark(sel1(z0, z2))
active(sel1(0, cons(z0, z1))) → mark(quote(z0))
active(first1(0, z0)) → mark(nil1)
active(first1(s(z0), cons(z1, z2))) → mark(cons1(quote(z1), first1(z0, z2)))
active(quote(0)) → mark(01)
active(quote1(cons(z0, z1))) → mark(cons1(quote(z0), quote1(z1)))
active(quote1(nil)) → mark(nil1)
active(quote(s(z0))) → mark(s1(quote(z0)))
active(quote(sel(z0, z1))) → mark(sel1(z0, z1))
active(quote1(first(z0, z1))) → mark(first1(z0, z1))
active(unquote(01)) → mark(0)
active(unquote(s1(z0))) → mark(s(unquote(z0)))
active(unquote1(nil1)) → mark(nil)
active(unquote1(cons1(z0, z1))) → mark(fcons(unquote(z0), unquote1(z1)))
active(fcons(z0, z1)) → mark(cons(z0, z1))
active(sel(z0, z1)) → sel(active(z0), z1)
active(sel(z0, z1)) → sel(z0, active(z1))
active(s(z0)) → s(active(z0))
active(cons(z0, z1)) → cons(active(z0), z1)
active(first(z0, z1)) → first(active(z0), z1)
active(first(z0, z1)) → first(z0, active(z1))
active(from(z0)) → from(active(z0))
active(sel1(z0, z1)) → sel1(active(z0), z1)
active(sel1(z0, z1)) → sel1(z0, active(z1))
active(first1(z0, z1)) → first1(active(z0), z1)
active(first1(z0, z1)) → first1(z0, active(z1))
active(cons1(z0, z1)) → cons1(active(z0), z1)
active(cons1(z0, z1)) → cons1(z0, active(z1))
active(s1(z0)) → s1(active(z0))
active(unquote(z0)) → unquote(active(z0))
active(unquote1(z0)) → unquote1(active(z0))
active(fcons(z0, z1)) → fcons(active(z0), z1)
active(fcons(z0, z1)) → fcons(z0, active(z1))
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))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
cons(mark(z0), z1) → mark(cons(z0, z1))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
first(mark(z0), z1) → mark(first(z0, z1))
first(z0, mark(z1)) → mark(first(z0, z1))
first(ok(z0), ok(z1)) → ok(first(z0, z1))
from(mark(z0)) → mark(from(z0))
from(ok(z0)) → ok(from(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))
first1(mark(z0), z1) → mark(first1(z0, z1))
first1(z0, mark(z1)) → mark(first1(z0, z1))
first1(ok(z0), ok(z1)) → ok(first1(z0, z1))
cons1(mark(z0), z1) → mark(cons1(z0, z1))
cons1(z0, mark(z1)) → mark(cons1(z0, z1))
cons1(ok(z0), ok(z1)) → ok(cons1(z0, z1))
s1(mark(z0)) → mark(s1(z0))
s1(ok(z0)) → ok(s1(z0))
unquote(mark(z0)) → mark(unquote(z0))
unquote(ok(z0)) → ok(unquote(z0))
unquote1(mark(z0)) → mark(unquote1(z0))
unquote1(ok(z0)) → ok(unquote1(z0))
fcons(mark(z0), z1) → mark(fcons(z0, z1))
fcons(z0, mark(z1)) → mark(fcons(z0, z1))
fcons(ok(z0), ok(z1)) → ok(fcons(z0, z1))
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
proper(s(z0)) → s(proper(z0))
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(0) → ok(0)
proper(first(z0, z1)) → first(proper(z0), proper(z1))
proper(nil) → ok(nil)
proper(from(z0)) → from(proper(z0))
proper(sel1(z0, z1)) → sel1(proper(z0), proper(z1))
proper(quote(z0)) → quote(proper(z0))
proper(first1(z0, z1)) → first1(proper(z0), proper(z1))
proper(nil1) → ok(nil1)
proper(cons1(z0, z1)) → cons1(proper(z0), proper(z1))
proper(01) → ok(01)
proper(quote1(z0)) → quote1(proper(z0))
proper(s1(z0)) → s1(proper(z0))
proper(unquote(z0)) → unquote(proper(z0))
proper(unquote1(z0)) → unquote1(proper(z0))
proper(fcons(z0, z1)) → fcons(proper(z0), proper(z1))
quote(ok(z0)) → ok(quote(z0))
quote1(ok(z0)) → ok(quote1(z0))
top(mark(z0)) → top(proper(z0))
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c(SEL(z0, z2))
ACTIVE(first(s(z0), cons(z1, z2))) → c3(CONS(z1, first(z0, z2)), FIRST(z0, z2))
ACTIVE(from(z0)) → c4(CONS(z0, from(s(z0))), FROM(s(z0)), S(z0))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c5(SEL1(z0, z2))
ACTIVE(sel1(0, cons(z0, z1))) → c6(QUOTE(z0))
ACTIVE(first1(s(z0), cons(z1, z2))) → c8(CONS1(quote(z1), first1(z0, z2)), QUOTE(z1), FIRST1(z0, z2))
ACTIVE(quote1(cons(z0, z1))) → c10(CONS1(quote(z0), quote1(z1)), QUOTE(z0), QUOTE1(z1))
ACTIVE(quote(s(z0))) → c12(S1(quote(z0)), QUOTE(z0))
ACTIVE(quote(sel(z0, z1))) → c13(SEL1(z0, z1))
ACTIVE(quote1(first(z0, z1))) → c14(FIRST1(z0, z1))
ACTIVE(unquote(s1(z0))) → c16(S(unquote(z0)), UNQUOTE(z0))
ACTIVE(unquote1(cons1(z0, z1))) → c18(FCONS(unquote(z0), unquote1(z1)), UNQUOTE(z0), UNQUOTE1(z1))
ACTIVE(fcons(z0, z1)) → c19(CONS(z0, z1))
ACTIVE(sel(z0, z1)) → c20(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c21(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(s(z0)) → c22(S(active(z0)), ACTIVE(z0))
ACTIVE(cons(z0, z1)) → c23(CONS(active(z0), z1), ACTIVE(z0))
ACTIVE(first(z0, z1)) → c24(FIRST(active(z0), z1), ACTIVE(z0))
ACTIVE(first(z0, z1)) → c25(FIRST(z0, active(z1)), ACTIVE(z1))
ACTIVE(from(z0)) → c26(FROM(active(z0)), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c27(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c28(SEL1(z0, active(z1)), ACTIVE(z1))
ACTIVE(first1(z0, z1)) → c29(FIRST1(active(z0), z1), ACTIVE(z0))
ACTIVE(first1(z0, z1)) → c30(FIRST1(z0, active(z1)), ACTIVE(z1))
ACTIVE(cons1(z0, z1)) → c31(CONS1(active(z0), z1), ACTIVE(z0))
ACTIVE(cons1(z0, z1)) → c32(CONS1(z0, active(z1)), ACTIVE(z1))
ACTIVE(s1(z0)) → c33(S1(active(z0)), ACTIVE(z0))
ACTIVE(unquote(z0)) → c34(UNQUOTE(active(z0)), ACTIVE(z0))
ACTIVE(unquote1(z0)) → c35(UNQUOTE1(active(z0)), ACTIVE(z0))
ACTIVE(fcons(z0, z1)) → c36(FCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(fcons(z0, z1)) → c37(FCONS(z0, active(z1)), ACTIVE(z1))
SEL(mark(z0), z1) → c38(SEL(z0, z1))
SEL(z0, mark(z1)) → c39(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c40(SEL(z0, z1))
S(mark(z0)) → c41(S(z0))
S(ok(z0)) → c42(S(z0))
CONS(mark(z0), z1) → c43(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c44(CONS(z0, z1))
FIRST(mark(z0), z1) → c45(FIRST(z0, z1))
FIRST(z0, mark(z1)) → c46(FIRST(z0, z1))
FIRST(ok(z0), ok(z1)) → c47(FIRST(z0, z1))
FROM(mark(z0)) → c48(FROM(z0))
FROM(ok(z0)) → c49(FROM(z0))
SEL1(mark(z0), z1) → c50(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c51(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c52(SEL1(z0, z1))
FIRST1(mark(z0), z1) → c53(FIRST1(z0, z1))
FIRST1(z0, mark(z1)) → c54(FIRST1(z0, z1))
FIRST1(ok(z0), ok(z1)) → c55(FIRST1(z0, z1))
CONS1(mark(z0), z1) → c56(CONS1(z0, z1))
CONS1(z0, mark(z1)) → c57(CONS1(z0, z1))
CONS1(ok(z0), ok(z1)) → c58(CONS1(z0, z1))
S1(mark(z0)) → c59(S1(z0))
S1(ok(z0)) → c60(S1(z0))
UNQUOTE(mark(z0)) → c61(UNQUOTE(z0))
UNQUOTE(ok(z0)) → c62(UNQUOTE(z0))
UNQUOTE1(mark(z0)) → c63(UNQUOTE1(z0))
UNQUOTE1(ok(z0)) → c64(UNQUOTE1(z0))
FCONS(mark(z0), z1) → c65(FCONS(z0, z1))
FCONS(z0, mark(z1)) → c66(FCONS(z0, z1))
FCONS(ok(z0), ok(z1)) → c67(FCONS(z0, z1))
PROPER(sel(z0, z1)) → c68(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(s(z0)) → c69(S(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c70(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(first(z0, z1)) → c72(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c74(FROM(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c75(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c76(QUOTE(proper(z0)), PROPER(z0))
PROPER(first1(z0, z1)) → c77(FIRST1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(cons1(z0, z1)) → c79(CONS1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote1(z0)) → c81(QUOTE1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c82(S1(proper(z0)), PROPER(z0))
PROPER(unquote(z0)) → c83(UNQUOTE(proper(z0)), PROPER(z0))
PROPER(unquote1(z0)) → c84(UNQUOTE1(proper(z0)), PROPER(z0))
PROPER(fcons(z0, z1)) → c85(FCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
QUOTE(ok(z0)) → c86(QUOTE(z0))
QUOTE1(ok(z0)) → c87(QUOTE1(z0))
TOP(mark(z0)) → c88(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c89(TOP(active(z0)), ACTIVE(z0))
S tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c(SEL(z0, z2))
ACTIVE(first(s(z0), cons(z1, z2))) → c3(CONS(z1, first(z0, z2)), FIRST(z0, z2))
ACTIVE(from(z0)) → c4(CONS(z0, from(s(z0))), FROM(s(z0)), S(z0))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c5(SEL1(z0, z2))
ACTIVE(sel1(0, cons(z0, z1))) → c6(QUOTE(z0))
ACTIVE(first1(s(z0), cons(z1, z2))) → c8(CONS1(quote(z1), first1(z0, z2)), QUOTE(z1), FIRST1(z0, z2))
ACTIVE(quote1(cons(z0, z1))) → c10(CONS1(quote(z0), quote1(z1)), QUOTE(z0), QUOTE1(z1))
ACTIVE(quote(s(z0))) → c12(S1(quote(z0)), QUOTE(z0))
ACTIVE(quote(sel(z0, z1))) → c13(SEL1(z0, z1))
ACTIVE(quote1(first(z0, z1))) → c14(FIRST1(z0, z1))
ACTIVE(unquote(s1(z0))) → c16(S(unquote(z0)), UNQUOTE(z0))
ACTIVE(unquote1(cons1(z0, z1))) → c18(FCONS(unquote(z0), unquote1(z1)), UNQUOTE(z0), UNQUOTE1(z1))
ACTIVE(fcons(z0, z1)) → c19(CONS(z0, z1))
ACTIVE(sel(z0, z1)) → c20(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c21(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(s(z0)) → c22(S(active(z0)), ACTIVE(z0))
ACTIVE(cons(z0, z1)) → c23(CONS(active(z0), z1), ACTIVE(z0))
ACTIVE(first(z0, z1)) → c24(FIRST(active(z0), z1), ACTIVE(z0))
ACTIVE(first(z0, z1)) → c25(FIRST(z0, active(z1)), ACTIVE(z1))
ACTIVE(from(z0)) → c26(FROM(active(z0)), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c27(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c28(SEL1(z0, active(z1)), ACTIVE(z1))
ACTIVE(first1(z0, z1)) → c29(FIRST1(active(z0), z1), ACTIVE(z0))
ACTIVE(first1(z0, z1)) → c30(FIRST1(z0, active(z1)), ACTIVE(z1))
ACTIVE(cons1(z0, z1)) → c31(CONS1(active(z0), z1), ACTIVE(z0))
ACTIVE(cons1(z0, z1)) → c32(CONS1(z0, active(z1)), ACTIVE(z1))
ACTIVE(s1(z0)) → c33(S1(active(z0)), ACTIVE(z0))
ACTIVE(unquote(z0)) → c34(UNQUOTE(active(z0)), ACTIVE(z0))
ACTIVE(unquote1(z0)) → c35(UNQUOTE1(active(z0)), ACTIVE(z0))
ACTIVE(fcons(z0, z1)) → c36(FCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(fcons(z0, z1)) → c37(FCONS(z0, active(z1)), ACTIVE(z1))
SEL(mark(z0), z1) → c38(SEL(z0, z1))
SEL(z0, mark(z1)) → c39(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c40(SEL(z0, z1))
S(mark(z0)) → c41(S(z0))
S(ok(z0)) → c42(S(z0))
CONS(mark(z0), z1) → c43(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c44(CONS(z0, z1))
FIRST(mark(z0), z1) → c45(FIRST(z0, z1))
FIRST(z0, mark(z1)) → c46(FIRST(z0, z1))
FIRST(ok(z0), ok(z1)) → c47(FIRST(z0, z1))
FROM(mark(z0)) → c48(FROM(z0))
FROM(ok(z0)) → c49(FROM(z0))
SEL1(mark(z0), z1) → c50(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c51(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c52(SEL1(z0, z1))
FIRST1(mark(z0), z1) → c53(FIRST1(z0, z1))
FIRST1(z0, mark(z1)) → c54(FIRST1(z0, z1))
FIRST1(ok(z0), ok(z1)) → c55(FIRST1(z0, z1))
CONS1(mark(z0), z1) → c56(CONS1(z0, z1))
CONS1(z0, mark(z1)) → c57(CONS1(z0, z1))
CONS1(ok(z0), ok(z1)) → c58(CONS1(z0, z1))
S1(mark(z0)) → c59(S1(z0))
S1(ok(z0)) → c60(S1(z0))
UNQUOTE(mark(z0)) → c61(UNQUOTE(z0))
UNQUOTE(ok(z0)) → c62(UNQUOTE(z0))
UNQUOTE1(mark(z0)) → c63(UNQUOTE1(z0))
UNQUOTE1(ok(z0)) → c64(UNQUOTE1(z0))
FCONS(mark(z0), z1) → c65(FCONS(z0, z1))
FCONS(z0, mark(z1)) → c66(FCONS(z0, z1))
FCONS(ok(z0), ok(z1)) → c67(FCONS(z0, z1))
PROPER(sel(z0, z1)) → c68(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(s(z0)) → c69(S(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c70(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(first(z0, z1)) → c72(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c74(FROM(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c75(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c76(QUOTE(proper(z0)), PROPER(z0))
PROPER(first1(z0, z1)) → c77(FIRST1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(cons1(z0, z1)) → c79(CONS1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote1(z0)) → c81(QUOTE1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c82(S1(proper(z0)), PROPER(z0))
PROPER(unquote(z0)) → c83(UNQUOTE(proper(z0)), PROPER(z0))
PROPER(unquote1(z0)) → c84(UNQUOTE1(proper(z0)), PROPER(z0))
PROPER(fcons(z0, z1)) → c85(FCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
QUOTE(ok(z0)) → c86(QUOTE(z0))
QUOTE1(ok(z0)) → c87(QUOTE1(z0))
TOP(mark(z0)) → c88(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c89(TOP(active(z0)), ACTIVE(z0))
K tuples:none
Defined Rule Symbols:

active, sel, s, cons, first, from, sel1, first1, cons1, s1, unquote, unquote1, fcons, proper, quote, quote1, top

Defined Pair Symbols:

ACTIVE, SEL, S, CONS, FIRST, FROM, SEL1, FIRST1, CONS1, S1, UNQUOTE, UNQUOTE1, FCONS, PROPER, QUOTE, QUOTE1, TOP

Compound Symbols:

c, c3, c4, c5, c6, c8, c10, c12, c13, c14, c16, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c66, c67, c68, c69, c70, c72, c74, c75, c76, c77, c79, c81, c82, c83, c84, c85, c86, c87, c88, c89

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

Removed 4 trailing tuple parts

(6) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
active(sel(0, cons(z0, z1))) → mark(z0)
active(first(0, z0)) → mark(nil)
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2)))
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(sel1(s(z0), cons(z1, z2))) → mark(sel1(z0, z2))
active(sel1(0, cons(z0, z1))) → mark(quote(z0))
active(first1(0, z0)) → mark(nil1)
active(first1(s(z0), cons(z1, z2))) → mark(cons1(quote(z1), first1(z0, z2)))
active(quote(0)) → mark(01)
active(quote1(cons(z0, z1))) → mark(cons1(quote(z0), quote1(z1)))
active(quote1(nil)) → mark(nil1)
active(quote(s(z0))) → mark(s1(quote(z0)))
active(quote(sel(z0, z1))) → mark(sel1(z0, z1))
active(quote1(first(z0, z1))) → mark(first1(z0, z1))
active(unquote(01)) → mark(0)
active(unquote(s1(z0))) → mark(s(unquote(z0)))
active(unquote1(nil1)) → mark(nil)
active(unquote1(cons1(z0, z1))) → mark(fcons(unquote(z0), unquote1(z1)))
active(fcons(z0, z1)) → mark(cons(z0, z1))
active(sel(z0, z1)) → sel(active(z0), z1)
active(sel(z0, z1)) → sel(z0, active(z1))
active(s(z0)) → s(active(z0))
active(cons(z0, z1)) → cons(active(z0), z1)
active(first(z0, z1)) → first(active(z0), z1)
active(first(z0, z1)) → first(z0, active(z1))
active(from(z0)) → from(active(z0))
active(sel1(z0, z1)) → sel1(active(z0), z1)
active(sel1(z0, z1)) → sel1(z0, active(z1))
active(first1(z0, z1)) → first1(active(z0), z1)
active(first1(z0, z1)) → first1(z0, active(z1))
active(cons1(z0, z1)) → cons1(active(z0), z1)
active(cons1(z0, z1)) → cons1(z0, active(z1))
active(s1(z0)) → s1(active(z0))
active(unquote(z0)) → unquote(active(z0))
active(unquote1(z0)) → unquote1(active(z0))
active(fcons(z0, z1)) → fcons(active(z0), z1)
active(fcons(z0, z1)) → fcons(z0, active(z1))
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))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
cons(mark(z0), z1) → mark(cons(z0, z1))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
first(mark(z0), z1) → mark(first(z0, z1))
first(z0, mark(z1)) → mark(first(z0, z1))
first(ok(z0), ok(z1)) → ok(first(z0, z1))
from(mark(z0)) → mark(from(z0))
from(ok(z0)) → ok(from(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))
first1(mark(z0), z1) → mark(first1(z0, z1))
first1(z0, mark(z1)) → mark(first1(z0, z1))
first1(ok(z0), ok(z1)) → ok(first1(z0, z1))
cons1(mark(z0), z1) → mark(cons1(z0, z1))
cons1(z0, mark(z1)) → mark(cons1(z0, z1))
cons1(ok(z0), ok(z1)) → ok(cons1(z0, z1))
s1(mark(z0)) → mark(s1(z0))
s1(ok(z0)) → ok(s1(z0))
unquote(mark(z0)) → mark(unquote(z0))
unquote(ok(z0)) → ok(unquote(z0))
unquote1(mark(z0)) → mark(unquote1(z0))
unquote1(ok(z0)) → ok(unquote1(z0))
fcons(mark(z0), z1) → mark(fcons(z0, z1))
fcons(z0, mark(z1)) → mark(fcons(z0, z1))
fcons(ok(z0), ok(z1)) → ok(fcons(z0, z1))
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
proper(s(z0)) → s(proper(z0))
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(0) → ok(0)
proper(first(z0, z1)) → first(proper(z0), proper(z1))
proper(nil) → ok(nil)
proper(from(z0)) → from(proper(z0))
proper(sel1(z0, z1)) → sel1(proper(z0), proper(z1))
proper(quote(z0)) → quote(proper(z0))
proper(first1(z0, z1)) → first1(proper(z0), proper(z1))
proper(nil1) → ok(nil1)
proper(cons1(z0, z1)) → cons1(proper(z0), proper(z1))
proper(01) → ok(01)
proper(quote1(z0)) → quote1(proper(z0))
proper(s1(z0)) → s1(proper(z0))
proper(unquote(z0)) → unquote(proper(z0))
proper(unquote1(z0)) → unquote1(proper(z0))
proper(fcons(z0, z1)) → fcons(proper(z0), proper(z1))
quote(ok(z0)) → ok(quote(z0))
quote1(ok(z0)) → ok(quote1(z0))
top(mark(z0)) → top(proper(z0))
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c(SEL(z0, z2))
ACTIVE(first(s(z0), cons(z1, z2))) → c3(CONS(z1, first(z0, z2)), FIRST(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c5(SEL1(z0, z2))
ACTIVE(sel1(0, cons(z0, z1))) → c6(QUOTE(z0))
ACTIVE(first1(s(z0), cons(z1, z2))) → c8(CONS1(quote(z1), first1(z0, z2)), QUOTE(z1), FIRST1(z0, z2))
ACTIVE(quote1(cons(z0, z1))) → c10(CONS1(quote(z0), quote1(z1)), QUOTE(z0), QUOTE1(z1))
ACTIVE(quote(sel(z0, z1))) → c13(SEL1(z0, z1))
ACTIVE(quote1(first(z0, z1))) → c14(FIRST1(z0, z1))
ACTIVE(unquote1(cons1(z0, z1))) → c18(FCONS(unquote(z0), unquote1(z1)), UNQUOTE(z0), UNQUOTE1(z1))
ACTIVE(fcons(z0, z1)) → c19(CONS(z0, z1))
ACTIVE(sel(z0, z1)) → c20(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c21(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(s(z0)) → c22(S(active(z0)), ACTIVE(z0))
ACTIVE(cons(z0, z1)) → c23(CONS(active(z0), z1), ACTIVE(z0))
ACTIVE(first(z0, z1)) → c24(FIRST(active(z0), z1), ACTIVE(z0))
ACTIVE(first(z0, z1)) → c25(FIRST(z0, active(z1)), ACTIVE(z1))
ACTIVE(from(z0)) → c26(FROM(active(z0)), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c27(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c28(SEL1(z0, active(z1)), ACTIVE(z1))
ACTIVE(first1(z0, z1)) → c29(FIRST1(active(z0), z1), ACTIVE(z0))
ACTIVE(first1(z0, z1)) → c30(FIRST1(z0, active(z1)), ACTIVE(z1))
ACTIVE(cons1(z0, z1)) → c31(CONS1(active(z0), z1), ACTIVE(z0))
ACTIVE(cons1(z0, z1)) → c32(CONS1(z0, active(z1)), ACTIVE(z1))
ACTIVE(s1(z0)) → c33(S1(active(z0)), ACTIVE(z0))
ACTIVE(unquote(z0)) → c34(UNQUOTE(active(z0)), ACTIVE(z0))
ACTIVE(unquote1(z0)) → c35(UNQUOTE1(active(z0)), ACTIVE(z0))
ACTIVE(fcons(z0, z1)) → c36(FCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(fcons(z0, z1)) → c37(FCONS(z0, active(z1)), ACTIVE(z1))
SEL(mark(z0), z1) → c38(SEL(z0, z1))
SEL(z0, mark(z1)) → c39(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c40(SEL(z0, z1))
S(mark(z0)) → c41(S(z0))
S(ok(z0)) → c42(S(z0))
CONS(mark(z0), z1) → c43(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c44(CONS(z0, z1))
FIRST(mark(z0), z1) → c45(FIRST(z0, z1))
FIRST(z0, mark(z1)) → c46(FIRST(z0, z1))
FIRST(ok(z0), ok(z1)) → c47(FIRST(z0, z1))
FROM(mark(z0)) → c48(FROM(z0))
FROM(ok(z0)) → c49(FROM(z0))
SEL1(mark(z0), z1) → c50(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c51(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c52(SEL1(z0, z1))
FIRST1(mark(z0), z1) → c53(FIRST1(z0, z1))
FIRST1(z0, mark(z1)) → c54(FIRST1(z0, z1))
FIRST1(ok(z0), ok(z1)) → c55(FIRST1(z0, z1))
CONS1(mark(z0), z1) → c56(CONS1(z0, z1))
CONS1(z0, mark(z1)) → c57(CONS1(z0, z1))
CONS1(ok(z0), ok(z1)) → c58(CONS1(z0, z1))
S1(mark(z0)) → c59(S1(z0))
S1(ok(z0)) → c60(S1(z0))
UNQUOTE(mark(z0)) → c61(UNQUOTE(z0))
UNQUOTE(ok(z0)) → c62(UNQUOTE(z0))
UNQUOTE1(mark(z0)) → c63(UNQUOTE1(z0))
UNQUOTE1(ok(z0)) → c64(UNQUOTE1(z0))
FCONS(mark(z0), z1) → c65(FCONS(z0, z1))
FCONS(z0, mark(z1)) → c66(FCONS(z0, z1))
FCONS(ok(z0), ok(z1)) → c67(FCONS(z0, z1))
PROPER(sel(z0, z1)) → c68(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(s(z0)) → c69(S(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c70(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(first(z0, z1)) → c72(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c74(FROM(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c75(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c76(QUOTE(proper(z0)), PROPER(z0))
PROPER(first1(z0, z1)) → c77(FIRST1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(cons1(z0, z1)) → c79(CONS1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote1(z0)) → c81(QUOTE1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c82(S1(proper(z0)), PROPER(z0))
PROPER(unquote(z0)) → c83(UNQUOTE(proper(z0)), PROPER(z0))
PROPER(unquote1(z0)) → c84(UNQUOTE1(proper(z0)), PROPER(z0))
PROPER(fcons(z0, z1)) → c85(FCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
QUOTE(ok(z0)) → c86(QUOTE(z0))
QUOTE1(ok(z0)) → c87(QUOTE1(z0))
TOP(mark(z0)) → c88(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c89(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c4(S(z0))
ACTIVE(quote(s(z0))) → c12(QUOTE(z0))
ACTIVE(unquote(s1(z0))) → c16(UNQUOTE(z0))
S tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c(SEL(z0, z2))
ACTIVE(first(s(z0), cons(z1, z2))) → c3(CONS(z1, first(z0, z2)), FIRST(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c5(SEL1(z0, z2))
ACTIVE(sel1(0, cons(z0, z1))) → c6(QUOTE(z0))
ACTIVE(first1(s(z0), cons(z1, z2))) → c8(CONS1(quote(z1), first1(z0, z2)), QUOTE(z1), FIRST1(z0, z2))
ACTIVE(quote1(cons(z0, z1))) → c10(CONS1(quote(z0), quote1(z1)), QUOTE(z0), QUOTE1(z1))
ACTIVE(quote(sel(z0, z1))) → c13(SEL1(z0, z1))
ACTIVE(quote1(first(z0, z1))) → c14(FIRST1(z0, z1))
ACTIVE(unquote1(cons1(z0, z1))) → c18(FCONS(unquote(z0), unquote1(z1)), UNQUOTE(z0), UNQUOTE1(z1))
ACTIVE(fcons(z0, z1)) → c19(CONS(z0, z1))
ACTIVE(sel(z0, z1)) → c20(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c21(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(s(z0)) → c22(S(active(z0)), ACTIVE(z0))
ACTIVE(cons(z0, z1)) → c23(CONS(active(z0), z1), ACTIVE(z0))
ACTIVE(first(z0, z1)) → c24(FIRST(active(z0), z1), ACTIVE(z0))
ACTIVE(first(z0, z1)) → c25(FIRST(z0, active(z1)), ACTIVE(z1))
ACTIVE(from(z0)) → c26(FROM(active(z0)), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c27(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c28(SEL1(z0, active(z1)), ACTIVE(z1))
ACTIVE(first1(z0, z1)) → c29(FIRST1(active(z0), z1), ACTIVE(z0))
ACTIVE(first1(z0, z1)) → c30(FIRST1(z0, active(z1)), ACTIVE(z1))
ACTIVE(cons1(z0, z1)) → c31(CONS1(active(z0), z1), ACTIVE(z0))
ACTIVE(cons1(z0, z1)) → c32(CONS1(z0, active(z1)), ACTIVE(z1))
ACTIVE(s1(z0)) → c33(S1(active(z0)), ACTIVE(z0))
ACTIVE(unquote(z0)) → c34(UNQUOTE(active(z0)), ACTIVE(z0))
ACTIVE(unquote1(z0)) → c35(UNQUOTE1(active(z0)), ACTIVE(z0))
ACTIVE(fcons(z0, z1)) → c36(FCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(fcons(z0, z1)) → c37(FCONS(z0, active(z1)), ACTIVE(z1))
SEL(mark(z0), z1) → c38(SEL(z0, z1))
SEL(z0, mark(z1)) → c39(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c40(SEL(z0, z1))
S(mark(z0)) → c41(S(z0))
S(ok(z0)) → c42(S(z0))
CONS(mark(z0), z1) → c43(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c44(CONS(z0, z1))
FIRST(mark(z0), z1) → c45(FIRST(z0, z1))
FIRST(z0, mark(z1)) → c46(FIRST(z0, z1))
FIRST(ok(z0), ok(z1)) → c47(FIRST(z0, z1))
FROM(mark(z0)) → c48(FROM(z0))
FROM(ok(z0)) → c49(FROM(z0))
SEL1(mark(z0), z1) → c50(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c51(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c52(SEL1(z0, z1))
FIRST1(mark(z0), z1) → c53(FIRST1(z0, z1))
FIRST1(z0, mark(z1)) → c54(FIRST1(z0, z1))
FIRST1(ok(z0), ok(z1)) → c55(FIRST1(z0, z1))
CONS1(mark(z0), z1) → c56(CONS1(z0, z1))
CONS1(z0, mark(z1)) → c57(CONS1(z0, z1))
CONS1(ok(z0), ok(z1)) → c58(CONS1(z0, z1))
S1(mark(z0)) → c59(S1(z0))
S1(ok(z0)) → c60(S1(z0))
UNQUOTE(mark(z0)) → c61(UNQUOTE(z0))
UNQUOTE(ok(z0)) → c62(UNQUOTE(z0))
UNQUOTE1(mark(z0)) → c63(UNQUOTE1(z0))
UNQUOTE1(ok(z0)) → c64(UNQUOTE1(z0))
FCONS(mark(z0), z1) → c65(FCONS(z0, z1))
FCONS(z0, mark(z1)) → c66(FCONS(z0, z1))
FCONS(ok(z0), ok(z1)) → c67(FCONS(z0, z1))
PROPER(sel(z0, z1)) → c68(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(s(z0)) → c69(S(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c70(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(first(z0, z1)) → c72(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c74(FROM(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c75(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c76(QUOTE(proper(z0)), PROPER(z0))
PROPER(first1(z0, z1)) → c77(FIRST1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(cons1(z0, z1)) → c79(CONS1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote1(z0)) → c81(QUOTE1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c82(S1(proper(z0)), PROPER(z0))
PROPER(unquote(z0)) → c83(UNQUOTE(proper(z0)), PROPER(z0))
PROPER(unquote1(z0)) → c84(UNQUOTE1(proper(z0)), PROPER(z0))
PROPER(fcons(z0, z1)) → c85(FCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
QUOTE(ok(z0)) → c86(QUOTE(z0))
QUOTE1(ok(z0)) → c87(QUOTE1(z0))
TOP(mark(z0)) → c88(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c89(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c4(S(z0))
ACTIVE(quote(s(z0))) → c12(QUOTE(z0))
ACTIVE(unquote(s1(z0))) → c16(UNQUOTE(z0))
K tuples:none
Defined Rule Symbols:

active, sel, s, cons, first, from, sel1, first1, cons1, s1, unquote, unquote1, fcons, proper, quote, quote1, top

Defined Pair Symbols:

ACTIVE, SEL, S, CONS, FIRST, FROM, SEL1, FIRST1, CONS1, S1, UNQUOTE, UNQUOTE1, FCONS, PROPER, QUOTE, QUOTE1, TOP

Compound Symbols:

c, c3, c5, c6, c8, c10, c13, c14, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c66, c67, c68, c69, c70, c72, c74, c75, c76, c77, c79, c81, c82, c83, c84, c85, c86, c87, c88, c89, c4, c12, c16

(7) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID) transformation)

Split RHS of tuples not part of any SCC

(8) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
active(sel(0, cons(z0, z1))) → mark(z0)
active(first(0, z0)) → mark(nil)
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2)))
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(sel1(s(z0), cons(z1, z2))) → mark(sel1(z0, z2))
active(sel1(0, cons(z0, z1))) → mark(quote(z0))
active(first1(0, z0)) → mark(nil1)
active(first1(s(z0), cons(z1, z2))) → mark(cons1(quote(z1), first1(z0, z2)))
active(quote(0)) → mark(01)
active(quote1(cons(z0, z1))) → mark(cons1(quote(z0), quote1(z1)))
active(quote1(nil)) → mark(nil1)
active(quote(s(z0))) → mark(s1(quote(z0)))
active(quote(sel(z0, z1))) → mark(sel1(z0, z1))
active(quote1(first(z0, z1))) → mark(first1(z0, z1))
active(unquote(01)) → mark(0)
active(unquote(s1(z0))) → mark(s(unquote(z0)))
active(unquote1(nil1)) → mark(nil)
active(unquote1(cons1(z0, z1))) → mark(fcons(unquote(z0), unquote1(z1)))
active(fcons(z0, z1)) → mark(cons(z0, z1))
active(sel(z0, z1)) → sel(active(z0), z1)
active(sel(z0, z1)) → sel(z0, active(z1))
active(s(z0)) → s(active(z0))
active(cons(z0, z1)) → cons(active(z0), z1)
active(first(z0, z1)) → first(active(z0), z1)
active(first(z0, z1)) → first(z0, active(z1))
active(from(z0)) → from(active(z0))
active(sel1(z0, z1)) → sel1(active(z0), z1)
active(sel1(z0, z1)) → sel1(z0, active(z1))
active(first1(z0, z1)) → first1(active(z0), z1)
active(first1(z0, z1)) → first1(z0, active(z1))
active(cons1(z0, z1)) → cons1(active(z0), z1)
active(cons1(z0, z1)) → cons1(z0, active(z1))
active(s1(z0)) → s1(active(z0))
active(unquote(z0)) → unquote(active(z0))
active(unquote1(z0)) → unquote1(active(z0))
active(fcons(z0, z1)) → fcons(active(z0), z1)
active(fcons(z0, z1)) → fcons(z0, active(z1))
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))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
cons(mark(z0), z1) → mark(cons(z0, z1))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
first(mark(z0), z1) → mark(first(z0, z1))
first(z0, mark(z1)) → mark(first(z0, z1))
first(ok(z0), ok(z1)) → ok(first(z0, z1))
from(mark(z0)) → mark(from(z0))
from(ok(z0)) → ok(from(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))
first1(mark(z0), z1) → mark(first1(z0, z1))
first1(z0, mark(z1)) → mark(first1(z0, z1))
first1(ok(z0), ok(z1)) → ok(first1(z0, z1))
cons1(mark(z0), z1) → mark(cons1(z0, z1))
cons1(z0, mark(z1)) → mark(cons1(z0, z1))
cons1(ok(z0), ok(z1)) → ok(cons1(z0, z1))
s1(mark(z0)) → mark(s1(z0))
s1(ok(z0)) → ok(s1(z0))
unquote(mark(z0)) → mark(unquote(z0))
unquote(ok(z0)) → ok(unquote(z0))
unquote1(mark(z0)) → mark(unquote1(z0))
unquote1(ok(z0)) → ok(unquote1(z0))
fcons(mark(z0), z1) → mark(fcons(z0, z1))
fcons(z0, mark(z1)) → mark(fcons(z0, z1))
fcons(ok(z0), ok(z1)) → ok(fcons(z0, z1))
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
proper(s(z0)) → s(proper(z0))
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(0) → ok(0)
proper(first(z0, z1)) → first(proper(z0), proper(z1))
proper(nil) → ok(nil)
proper(from(z0)) → from(proper(z0))
proper(sel1(z0, z1)) → sel1(proper(z0), proper(z1))
proper(quote(z0)) → quote(proper(z0))
proper(first1(z0, z1)) → first1(proper(z0), proper(z1))
proper(nil1) → ok(nil1)
proper(cons1(z0, z1)) → cons1(proper(z0), proper(z1))
proper(01) → ok(01)
proper(quote1(z0)) → quote1(proper(z0))
proper(s1(z0)) → s1(proper(z0))
proper(unquote(z0)) → unquote(proper(z0))
proper(unquote1(z0)) → unquote1(proper(z0))
proper(fcons(z0, z1)) → fcons(proper(z0), proper(z1))
quote(ok(z0)) → ok(quote(z0))
quote1(ok(z0)) → ok(quote1(z0))
top(mark(z0)) → top(proper(z0))
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c5(SEL1(z0, z2))
ACTIVE(sel1(0, cons(z0, z1))) → c6(QUOTE(z0))
ACTIVE(quote(sel(z0, z1))) → c13(SEL1(z0, z1))
ACTIVE(quote1(first(z0, z1))) → c14(FIRST1(z0, z1))
ACTIVE(fcons(z0, z1)) → c19(CONS(z0, z1))
ACTIVE(sel(z0, z1)) → c20(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c21(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(s(z0)) → c22(S(active(z0)), ACTIVE(z0))
ACTIVE(cons(z0, z1)) → c23(CONS(active(z0), z1), ACTIVE(z0))
ACTIVE(first(z0, z1)) → c24(FIRST(active(z0), z1), ACTIVE(z0))
ACTIVE(first(z0, z1)) → c25(FIRST(z0, active(z1)), ACTIVE(z1))
ACTIVE(from(z0)) → c26(FROM(active(z0)), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c27(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c28(SEL1(z0, active(z1)), ACTIVE(z1))
ACTIVE(first1(z0, z1)) → c29(FIRST1(active(z0), z1), ACTIVE(z0))
ACTIVE(first1(z0, z1)) → c30(FIRST1(z0, active(z1)), ACTIVE(z1))
ACTIVE(cons1(z0, z1)) → c31(CONS1(active(z0), z1), ACTIVE(z0))
ACTIVE(cons1(z0, z1)) → c32(CONS1(z0, active(z1)), ACTIVE(z1))
ACTIVE(s1(z0)) → c33(S1(active(z0)), ACTIVE(z0))
ACTIVE(unquote(z0)) → c34(UNQUOTE(active(z0)), ACTIVE(z0))
ACTIVE(unquote1(z0)) → c35(UNQUOTE1(active(z0)), ACTIVE(z0))
ACTIVE(fcons(z0, z1)) → c36(FCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(fcons(z0, z1)) → c37(FCONS(z0, active(z1)), ACTIVE(z1))
SEL(mark(z0), z1) → c38(SEL(z0, z1))
SEL(z0, mark(z1)) → c39(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c40(SEL(z0, z1))
S(mark(z0)) → c41(S(z0))
S(ok(z0)) → c42(S(z0))
CONS(mark(z0), z1) → c43(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c44(CONS(z0, z1))
FIRST(mark(z0), z1) → c45(FIRST(z0, z1))
FIRST(z0, mark(z1)) → c46(FIRST(z0, z1))
FIRST(ok(z0), ok(z1)) → c47(FIRST(z0, z1))
FROM(mark(z0)) → c48(FROM(z0))
FROM(ok(z0)) → c49(FROM(z0))
SEL1(mark(z0), z1) → c50(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c51(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c52(SEL1(z0, z1))
FIRST1(mark(z0), z1) → c53(FIRST1(z0, z1))
FIRST1(z0, mark(z1)) → c54(FIRST1(z0, z1))
FIRST1(ok(z0), ok(z1)) → c55(FIRST1(z0, z1))
CONS1(mark(z0), z1) → c56(CONS1(z0, z1))
CONS1(z0, mark(z1)) → c57(CONS1(z0, z1))
CONS1(ok(z0), ok(z1)) → c58(CONS1(z0, z1))
S1(mark(z0)) → c59(S1(z0))
S1(ok(z0)) → c60(S1(z0))
UNQUOTE(mark(z0)) → c61(UNQUOTE(z0))
UNQUOTE(ok(z0)) → c62(UNQUOTE(z0))
UNQUOTE1(mark(z0)) → c63(UNQUOTE1(z0))
UNQUOTE1(ok(z0)) → c64(UNQUOTE1(z0))
FCONS(mark(z0), z1) → c65(FCONS(z0, z1))
FCONS(z0, mark(z1)) → c66(FCONS(z0, z1))
FCONS(ok(z0), ok(z1)) → c67(FCONS(z0, z1))
PROPER(sel(z0, z1)) → c68(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(s(z0)) → c69(S(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c70(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(first(z0, z1)) → c72(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c74(FROM(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c75(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c76(QUOTE(proper(z0)), PROPER(z0))
PROPER(first1(z0, z1)) → c77(FIRST1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(cons1(z0, z1)) → c79(CONS1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote1(z0)) → c81(QUOTE1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c82(S1(proper(z0)), PROPER(z0))
PROPER(unquote(z0)) → c83(UNQUOTE(proper(z0)), PROPER(z0))
PROPER(unquote1(z0)) → c84(UNQUOTE1(proper(z0)), PROPER(z0))
PROPER(fcons(z0, z1)) → c85(FCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
QUOTE(ok(z0)) → c86(QUOTE(z0))
QUOTE1(ok(z0)) → c87(QUOTE1(z0))
TOP(mark(z0)) → c88(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c89(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c4(S(z0))
ACTIVE(quote(s(z0))) → c12(QUOTE(z0))
ACTIVE(unquote(s1(z0))) → c16(UNQUOTE(z0))
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2)))
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2))
ACTIVE(first1(s(z0), cons(z1, z2))) → c1(CONS1(quote(z1), first1(z0, z2)))
ACTIVE(first1(s(z0), cons(z1, z2))) → c1(QUOTE(z1))
ACTIVE(first1(s(z0), cons(z1, z2))) → c1(FIRST1(z0, z2))
ACTIVE(quote1(cons(z0, z1))) → c1(CONS1(quote(z0), quote1(z1)))
ACTIVE(quote1(cons(z0, z1))) → c1(QUOTE(z0))
ACTIVE(quote1(cons(z0, z1))) → c1(QUOTE1(z1))
ACTIVE(unquote1(cons1(z0, z1))) → c1(FCONS(unquote(z0), unquote1(z1)))
ACTIVE(unquote1(cons1(z0, z1))) → c1(UNQUOTE(z0))
ACTIVE(unquote1(cons1(z0, z1))) → c1(UNQUOTE1(z1))
S tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c5(SEL1(z0, z2))
ACTIVE(sel1(0, cons(z0, z1))) → c6(QUOTE(z0))
ACTIVE(quote(sel(z0, z1))) → c13(SEL1(z0, z1))
ACTIVE(quote1(first(z0, z1))) → c14(FIRST1(z0, z1))
ACTIVE(fcons(z0, z1)) → c19(CONS(z0, z1))
ACTIVE(sel(z0, z1)) → c20(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c21(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(s(z0)) → c22(S(active(z0)), ACTIVE(z0))
ACTIVE(cons(z0, z1)) → c23(CONS(active(z0), z1), ACTIVE(z0))
ACTIVE(first(z0, z1)) → c24(FIRST(active(z0), z1), ACTIVE(z0))
ACTIVE(first(z0, z1)) → c25(FIRST(z0, active(z1)), ACTIVE(z1))
ACTIVE(from(z0)) → c26(FROM(active(z0)), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c27(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c28(SEL1(z0, active(z1)), ACTIVE(z1))
ACTIVE(first1(z0, z1)) → c29(FIRST1(active(z0), z1), ACTIVE(z0))
ACTIVE(first1(z0, z1)) → c30(FIRST1(z0, active(z1)), ACTIVE(z1))
ACTIVE(cons1(z0, z1)) → c31(CONS1(active(z0), z1), ACTIVE(z0))
ACTIVE(cons1(z0, z1)) → c32(CONS1(z0, active(z1)), ACTIVE(z1))
ACTIVE(s1(z0)) → c33(S1(active(z0)), ACTIVE(z0))
ACTIVE(unquote(z0)) → c34(UNQUOTE(active(z0)), ACTIVE(z0))
ACTIVE(unquote1(z0)) → c35(UNQUOTE1(active(z0)), ACTIVE(z0))
ACTIVE(fcons(z0, z1)) → c36(FCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(fcons(z0, z1)) → c37(FCONS(z0, active(z1)), ACTIVE(z1))
SEL(mark(z0), z1) → c38(SEL(z0, z1))
SEL(z0, mark(z1)) → c39(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c40(SEL(z0, z1))
S(mark(z0)) → c41(S(z0))
S(ok(z0)) → c42(S(z0))
CONS(mark(z0), z1) → c43(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c44(CONS(z0, z1))
FIRST(mark(z0), z1) → c45(FIRST(z0, z1))
FIRST(z0, mark(z1)) → c46(FIRST(z0, z1))
FIRST(ok(z0), ok(z1)) → c47(FIRST(z0, z1))
FROM(mark(z0)) → c48(FROM(z0))
FROM(ok(z0)) → c49(FROM(z0))
SEL1(mark(z0), z1) → c50(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c51(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c52(SEL1(z0, z1))
FIRST1(mark(z0), z1) → c53(FIRST1(z0, z1))
FIRST1(z0, mark(z1)) → c54(FIRST1(z0, z1))
FIRST1(ok(z0), ok(z1)) → c55(FIRST1(z0, z1))
CONS1(mark(z0), z1) → c56(CONS1(z0, z1))
CONS1(z0, mark(z1)) → c57(CONS1(z0, z1))
CONS1(ok(z0), ok(z1)) → c58(CONS1(z0, z1))
S1(mark(z0)) → c59(S1(z0))
S1(ok(z0)) → c60(S1(z0))
UNQUOTE(mark(z0)) → c61(UNQUOTE(z0))
UNQUOTE(ok(z0)) → c62(UNQUOTE(z0))
UNQUOTE1(mark(z0)) → c63(UNQUOTE1(z0))
UNQUOTE1(ok(z0)) → c64(UNQUOTE1(z0))
FCONS(mark(z0), z1) → c65(FCONS(z0, z1))
FCONS(z0, mark(z1)) → c66(FCONS(z0, z1))
FCONS(ok(z0), ok(z1)) → c67(FCONS(z0, z1))
PROPER(sel(z0, z1)) → c68(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(s(z0)) → c69(S(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c70(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(first(z0, z1)) → c72(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c74(FROM(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c75(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c76(QUOTE(proper(z0)), PROPER(z0))
PROPER(first1(z0, z1)) → c77(FIRST1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(cons1(z0, z1)) → c79(CONS1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote1(z0)) → c81(QUOTE1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c82(S1(proper(z0)), PROPER(z0))
PROPER(unquote(z0)) → c83(UNQUOTE(proper(z0)), PROPER(z0))
PROPER(unquote1(z0)) → c84(UNQUOTE1(proper(z0)), PROPER(z0))
PROPER(fcons(z0, z1)) → c85(FCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
QUOTE(ok(z0)) → c86(QUOTE(z0))
QUOTE1(ok(z0)) → c87(QUOTE1(z0))
TOP(mark(z0)) → c88(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c89(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c4(S(z0))
ACTIVE(quote(s(z0))) → c12(QUOTE(z0))
ACTIVE(unquote(s1(z0))) → c16(UNQUOTE(z0))
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2)))
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2))
ACTIVE(first1(s(z0), cons(z1, z2))) → c1(CONS1(quote(z1), first1(z0, z2)))
ACTIVE(first1(s(z0), cons(z1, z2))) → c1(QUOTE(z1))
ACTIVE(first1(s(z0), cons(z1, z2))) → c1(FIRST1(z0, z2))
ACTIVE(quote1(cons(z0, z1))) → c1(CONS1(quote(z0), quote1(z1)))
ACTIVE(quote1(cons(z0, z1))) → c1(QUOTE(z0))
ACTIVE(quote1(cons(z0, z1))) → c1(QUOTE1(z1))
ACTIVE(unquote1(cons1(z0, z1))) → c1(FCONS(unquote(z0), unquote1(z1)))
ACTIVE(unquote1(cons1(z0, z1))) → c1(UNQUOTE(z0))
ACTIVE(unquote1(cons1(z0, z1))) → c1(UNQUOTE1(z1))
K tuples:none
Defined Rule Symbols:

active, sel, s, cons, first, from, sel1, first1, cons1, s1, unquote, unquote1, fcons, proper, quote, quote1, top

Defined Pair Symbols:

ACTIVE, SEL, S, CONS, FIRST, FROM, SEL1, FIRST1, CONS1, S1, UNQUOTE, UNQUOTE1, FCONS, PROPER, QUOTE, QUOTE1, TOP

Compound Symbols:

c, c5, c6, c13, c14, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c66, c67, c68, c69, c70, c72, c74, c75, c76, c77, c79, c81, c82, c83, c84, c85, c86, c87, c88, c89, c4, c12, c16, c1

(9) CdtUsableRulesProof (EQUIVALENT transformation)

The following rules are not usable and were removed:

top(mark(z0)) → top(proper(z0))
top(ok(z0)) → top(active(z0))

(10) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
active(sel(0, cons(z0, z1))) → mark(z0)
active(first(0, z0)) → mark(nil)
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2)))
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(sel1(s(z0), cons(z1, z2))) → mark(sel1(z0, z2))
active(sel1(0, cons(z0, z1))) → mark(quote(z0))
active(first1(0, z0)) → mark(nil1)
active(first1(s(z0), cons(z1, z2))) → mark(cons1(quote(z1), first1(z0, z2)))
active(quote(0)) → mark(01)
active(quote1(cons(z0, z1))) → mark(cons1(quote(z0), quote1(z1)))
active(quote1(nil)) → mark(nil1)
active(quote(s(z0))) → mark(s1(quote(z0)))
active(quote(sel(z0, z1))) → mark(sel1(z0, z1))
active(quote1(first(z0, z1))) → mark(first1(z0, z1))
active(unquote(01)) → mark(0)
active(unquote(s1(z0))) → mark(s(unquote(z0)))
active(unquote1(nil1)) → mark(nil)
active(unquote1(cons1(z0, z1))) → mark(fcons(unquote(z0), unquote1(z1)))
active(fcons(z0, z1)) → mark(cons(z0, z1))
active(sel(z0, z1)) → sel(active(z0), z1)
active(sel(z0, z1)) → sel(z0, active(z1))
active(s(z0)) → s(active(z0))
active(cons(z0, z1)) → cons(active(z0), z1)
active(first(z0, z1)) → first(active(z0), z1)
active(first(z0, z1)) → first(z0, active(z1))
active(from(z0)) → from(active(z0))
active(sel1(z0, z1)) → sel1(active(z0), z1)
active(sel1(z0, z1)) → sel1(z0, active(z1))
active(first1(z0, z1)) → first1(active(z0), z1)
active(first1(z0, z1)) → first1(z0, active(z1))
active(cons1(z0, z1)) → cons1(active(z0), z1)
active(cons1(z0, z1)) → cons1(z0, active(z1))
active(s1(z0)) → s1(active(z0))
active(unquote(z0)) → unquote(active(z0))
active(unquote1(z0)) → unquote1(active(z0))
active(fcons(z0, z1)) → fcons(active(z0), z1)
active(fcons(z0, z1)) → fcons(z0, active(z1))
sel(z0, mark(z1)) → mark(sel(z0, z1))
sel(mark(z0), z1) → mark(sel(z0, z1))
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
cons(mark(z0), z1) → mark(cons(z0, z1))
first(z0, mark(z1)) → mark(first(z0, z1))
first(mark(z0), z1) → mark(first(z0, z1))
first(ok(z0), ok(z1)) → ok(first(z0, z1))
sel1(z0, mark(z1)) → mark(sel1(z0, z1))
sel1(mark(z0), z1) → mark(sel1(z0, z1))
sel1(ok(z0), ok(z1)) → ok(sel1(z0, z1))
quote(ok(z0)) → ok(quote(z0))
cons1(mark(z0), z1) → mark(cons1(z0, z1))
cons1(z0, mark(z1)) → mark(cons1(z0, z1))
cons1(ok(z0), ok(z1)) → ok(cons1(z0, z1))
first1(z0, mark(z1)) → mark(first1(z0, z1))
first1(mark(z0), z1) → mark(first1(z0, z1))
first1(ok(z0), ok(z1)) → ok(first1(z0, z1))
quote1(ok(z0)) → ok(quote1(z0))
fcons(mark(z0), z1) → mark(fcons(z0, z1))
fcons(z0, mark(z1)) → mark(fcons(z0, z1))
fcons(ok(z0), ok(z1)) → ok(fcons(z0, z1))
unquote(ok(z0)) → ok(unquote(z0))
unquote(mark(z0)) → mark(unquote(z0))
unquote1(ok(z0)) → ok(unquote1(z0))
unquote1(mark(z0)) → mark(unquote1(z0))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
from(mark(z0)) → mark(from(z0))
from(ok(z0)) → ok(from(z0))
s1(mark(z0)) → mark(s1(z0))
s1(ok(z0)) → ok(s1(z0))
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
proper(s(z0)) → s(proper(z0))
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(0) → ok(0)
proper(first(z0, z1)) → first(proper(z0), proper(z1))
proper(nil) → ok(nil)
proper(from(z0)) → from(proper(z0))
proper(sel1(z0, z1)) → sel1(proper(z0), proper(z1))
proper(quote(z0)) → quote(proper(z0))
proper(first1(z0, z1)) → first1(proper(z0), proper(z1))
proper(nil1) → ok(nil1)
proper(cons1(z0, z1)) → cons1(proper(z0), proper(z1))
proper(01) → ok(01)
proper(quote1(z0)) → quote1(proper(z0))
proper(s1(z0)) → s1(proper(z0))
proper(unquote(z0)) → unquote(proper(z0))
proper(unquote1(z0)) → unquote1(proper(z0))
proper(fcons(z0, z1)) → fcons(proper(z0), proper(z1))
Tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c5(SEL1(z0, z2))
ACTIVE(sel1(0, cons(z0, z1))) → c6(QUOTE(z0))
ACTIVE(quote(sel(z0, z1))) → c13(SEL1(z0, z1))
ACTIVE(quote1(first(z0, z1))) → c14(FIRST1(z0, z1))
ACTIVE(fcons(z0, z1)) → c19(CONS(z0, z1))
ACTIVE(sel(z0, z1)) → c20(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c21(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(s(z0)) → c22(S(active(z0)), ACTIVE(z0))
ACTIVE(cons(z0, z1)) → c23(CONS(active(z0), z1), ACTIVE(z0))
ACTIVE(first(z0, z1)) → c24(FIRST(active(z0), z1), ACTIVE(z0))
ACTIVE(first(z0, z1)) → c25(FIRST(z0, active(z1)), ACTIVE(z1))
ACTIVE(from(z0)) → c26(FROM(active(z0)), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c27(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c28(SEL1(z0, active(z1)), ACTIVE(z1))
ACTIVE(first1(z0, z1)) → c29(FIRST1(active(z0), z1), ACTIVE(z0))
ACTIVE(first1(z0, z1)) → c30(FIRST1(z0, active(z1)), ACTIVE(z1))
ACTIVE(cons1(z0, z1)) → c31(CONS1(active(z0), z1), ACTIVE(z0))
ACTIVE(cons1(z0, z1)) → c32(CONS1(z0, active(z1)), ACTIVE(z1))
ACTIVE(s1(z0)) → c33(S1(active(z0)), ACTIVE(z0))
ACTIVE(unquote(z0)) → c34(UNQUOTE(active(z0)), ACTIVE(z0))
ACTIVE(unquote1(z0)) → c35(UNQUOTE1(active(z0)), ACTIVE(z0))
ACTIVE(fcons(z0, z1)) → c36(FCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(fcons(z0, z1)) → c37(FCONS(z0, active(z1)), ACTIVE(z1))
SEL(mark(z0), z1) → c38(SEL(z0, z1))
SEL(z0, mark(z1)) → c39(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c40(SEL(z0, z1))
S(mark(z0)) → c41(S(z0))
S(ok(z0)) → c42(S(z0))
CONS(mark(z0), z1) → c43(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c44(CONS(z0, z1))
FIRST(mark(z0), z1) → c45(FIRST(z0, z1))
FIRST(z0, mark(z1)) → c46(FIRST(z0, z1))
FIRST(ok(z0), ok(z1)) → c47(FIRST(z0, z1))
FROM(mark(z0)) → c48(FROM(z0))
FROM(ok(z0)) → c49(FROM(z0))
SEL1(mark(z0), z1) → c50(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c51(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c52(SEL1(z0, z1))
FIRST1(mark(z0), z1) → c53(FIRST1(z0, z1))
FIRST1(z0, mark(z1)) → c54(FIRST1(z0, z1))
FIRST1(ok(z0), ok(z1)) → c55(FIRST1(z0, z1))
CONS1(mark(z0), z1) → c56(CONS1(z0, z1))
CONS1(z0, mark(z1)) → c57(CONS1(z0, z1))
CONS1(ok(z0), ok(z1)) → c58(CONS1(z0, z1))
S1(mark(z0)) → c59(S1(z0))
S1(ok(z0)) → c60(S1(z0))
UNQUOTE(mark(z0)) → c61(UNQUOTE(z0))
UNQUOTE(ok(z0)) → c62(UNQUOTE(z0))
UNQUOTE1(mark(z0)) → c63(UNQUOTE1(z0))
UNQUOTE1(ok(z0)) → c64(UNQUOTE1(z0))
FCONS(mark(z0), z1) → c65(FCONS(z0, z1))
FCONS(z0, mark(z1)) → c66(FCONS(z0, z1))
FCONS(ok(z0), ok(z1)) → c67(FCONS(z0, z1))
PROPER(sel(z0, z1)) → c68(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(s(z0)) → c69(S(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c70(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(first(z0, z1)) → c72(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c74(FROM(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c75(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c76(QUOTE(proper(z0)), PROPER(z0))
PROPER(first1(z0, z1)) → c77(FIRST1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(cons1(z0, z1)) → c79(CONS1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote1(z0)) → c81(QUOTE1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c82(S1(proper(z0)), PROPER(z0))
PROPER(unquote(z0)) → c83(UNQUOTE(proper(z0)), PROPER(z0))
PROPER(unquote1(z0)) → c84(UNQUOTE1(proper(z0)), PROPER(z0))
PROPER(fcons(z0, z1)) → c85(FCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
QUOTE(ok(z0)) → c86(QUOTE(z0))
QUOTE1(ok(z0)) → c87(QUOTE1(z0))
TOP(mark(z0)) → c88(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c89(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c4(S(z0))
ACTIVE(quote(s(z0))) → c12(QUOTE(z0))
ACTIVE(unquote(s1(z0))) → c16(UNQUOTE(z0))
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2)))
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2))
ACTIVE(first1(s(z0), cons(z1, z2))) → c1(CONS1(quote(z1), first1(z0, z2)))
ACTIVE(first1(s(z0), cons(z1, z2))) → c1(QUOTE(z1))
ACTIVE(first1(s(z0), cons(z1, z2))) → c1(FIRST1(z0, z2))
ACTIVE(quote1(cons(z0, z1))) → c1(CONS1(quote(z0), quote1(z1)))
ACTIVE(quote1(cons(z0, z1))) → c1(QUOTE(z0))
ACTIVE(quote1(cons(z0, z1))) → c1(QUOTE1(z1))
ACTIVE(unquote1(cons1(z0, z1))) → c1(FCONS(unquote(z0), unquote1(z1)))
ACTIVE(unquote1(cons1(z0, z1))) → c1(UNQUOTE(z0))
ACTIVE(unquote1(cons1(z0, z1))) → c1(UNQUOTE1(z1))
S tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c5(SEL1(z0, z2))
ACTIVE(sel1(0, cons(z0, z1))) → c6(QUOTE(z0))
ACTIVE(quote(sel(z0, z1))) → c13(SEL1(z0, z1))
ACTIVE(quote1(first(z0, z1))) → c14(FIRST1(z0, z1))
ACTIVE(fcons(z0, z1)) → c19(CONS(z0, z1))
ACTIVE(sel(z0, z1)) → c20(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c21(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(s(z0)) → c22(S(active(z0)), ACTIVE(z0))
ACTIVE(cons(z0, z1)) → c23(CONS(active(z0), z1), ACTIVE(z0))
ACTIVE(first(z0, z1)) → c24(FIRST(active(z0), z1), ACTIVE(z0))
ACTIVE(first(z0, z1)) → c25(FIRST(z0, active(z1)), ACTIVE(z1))
ACTIVE(from(z0)) → c26(FROM(active(z0)), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c27(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c28(SEL1(z0, active(z1)), ACTIVE(z1))
ACTIVE(first1(z0, z1)) → c29(FIRST1(active(z0), z1), ACTIVE(z0))
ACTIVE(first1(z0, z1)) → c30(FIRST1(z0, active(z1)), ACTIVE(z1))
ACTIVE(cons1(z0, z1)) → c31(CONS1(active(z0), z1), ACTIVE(z0))
ACTIVE(cons1(z0, z1)) → c32(CONS1(z0, active(z1)), ACTIVE(z1))
ACTIVE(s1(z0)) → c33(S1(active(z0)), ACTIVE(z0))
ACTIVE(unquote(z0)) → c34(UNQUOTE(active(z0)), ACTIVE(z0))
ACTIVE(unquote1(z0)) → c35(UNQUOTE1(active(z0)), ACTIVE(z0))
ACTIVE(fcons(z0, z1)) → c36(FCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(fcons(z0, z1)) → c37(FCONS(z0, active(z1)), ACTIVE(z1))
SEL(mark(z0), z1) → c38(SEL(z0, z1))
SEL(z0, mark(z1)) → c39(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c40(SEL(z0, z1))
S(mark(z0)) → c41(S(z0))
S(ok(z0)) → c42(S(z0))
CONS(mark(z0), z1) → c43(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c44(CONS(z0, z1))
FIRST(mark(z0), z1) → c45(FIRST(z0, z1))
FIRST(z0, mark(z1)) → c46(FIRST(z0, z1))
FIRST(ok(z0), ok(z1)) → c47(FIRST(z0, z1))
FROM(mark(z0)) → c48(FROM(z0))
FROM(ok(z0)) → c49(FROM(z0))
SEL1(mark(z0), z1) → c50(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c51(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c52(SEL1(z0, z1))
FIRST1(mark(z0), z1) → c53(FIRST1(z0, z1))
FIRST1(z0, mark(z1)) → c54(FIRST1(z0, z1))
FIRST1(ok(z0), ok(z1)) → c55(FIRST1(z0, z1))
CONS1(mark(z0), z1) → c56(CONS1(z0, z1))
CONS1(z0, mark(z1)) → c57(CONS1(z0, z1))
CONS1(ok(z0), ok(z1)) → c58(CONS1(z0, z1))
S1(mark(z0)) → c59(S1(z0))
S1(ok(z0)) → c60(S1(z0))
UNQUOTE(mark(z0)) → c61(UNQUOTE(z0))
UNQUOTE(ok(z0)) → c62(UNQUOTE(z0))
UNQUOTE1(mark(z0)) → c63(UNQUOTE1(z0))
UNQUOTE1(ok(z0)) → c64(UNQUOTE1(z0))
FCONS(mark(z0), z1) → c65(FCONS(z0, z1))
FCONS(z0, mark(z1)) → c66(FCONS(z0, z1))
FCONS(ok(z0), ok(z1)) → c67(FCONS(z0, z1))
PROPER(sel(z0, z1)) → c68(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(s(z0)) → c69(S(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c70(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(first(z0, z1)) → c72(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c74(FROM(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c75(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c76(QUOTE(proper(z0)), PROPER(z0))
PROPER(first1(z0, z1)) → c77(FIRST1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(cons1(z0, z1)) → c79(CONS1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote1(z0)) → c81(QUOTE1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c82(S1(proper(z0)), PROPER(z0))
PROPER(unquote(z0)) → c83(UNQUOTE(proper(z0)), PROPER(z0))
PROPER(unquote1(z0)) → c84(UNQUOTE1(proper(z0)), PROPER(z0))
PROPER(fcons(z0, z1)) → c85(FCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
QUOTE(ok(z0)) → c86(QUOTE(z0))
QUOTE1(ok(z0)) → c87(QUOTE1(z0))
TOP(mark(z0)) → c88(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c89(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c4(S(z0))
ACTIVE(quote(s(z0))) → c12(QUOTE(z0))
ACTIVE(unquote(s1(z0))) → c16(UNQUOTE(z0))
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2)))
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2))
ACTIVE(first1(s(z0), cons(z1, z2))) → c1(CONS1(quote(z1), first1(z0, z2)))
ACTIVE(first1(s(z0), cons(z1, z2))) → c1(QUOTE(z1))
ACTIVE(first1(s(z0), cons(z1, z2))) → c1(FIRST1(z0, z2))
ACTIVE(quote1(cons(z0, z1))) → c1(CONS1(quote(z0), quote1(z1)))
ACTIVE(quote1(cons(z0, z1))) → c1(QUOTE(z0))
ACTIVE(quote1(cons(z0, z1))) → c1(QUOTE1(z1))
ACTIVE(unquote1(cons1(z0, z1))) → c1(FCONS(unquote(z0), unquote1(z1)))
ACTIVE(unquote1(cons1(z0, z1))) → c1(UNQUOTE(z0))
ACTIVE(unquote1(cons1(z0, z1))) → c1(UNQUOTE1(z1))
K tuples:none
Defined Rule Symbols:

active, sel, cons, first, sel1, quote, cons1, first1, quote1, fcons, unquote, unquote1, s, from, s1, proper

Defined Pair Symbols:

ACTIVE, SEL, S, CONS, FIRST, FROM, SEL1, FIRST1, CONS1, S1, UNQUOTE, UNQUOTE1, FCONS, PROPER, QUOTE, QUOTE1, TOP

Compound Symbols:

c, c5, c6, c13, c14, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c66, c67, c68, c69, c70, c72, c74, c75, c76, c77, c79, c81, c82, c83, c84, c85, c86, c87, c88, c89, c4, c12, c16, c1

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

Use narrowing to replace ACTIVE(s(z0)) → c22(S(active(z0)), ACTIVE(z0)) by

ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c22(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(s(sel(0, cons(z0, z1)))) → c22(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(s(first(0, z0))) → c22(S(mark(nil)), ACTIVE(first(0, z0)))
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c22(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
ACTIVE(s(from(z0))) → c22(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(sel1(s(z0), cons(z1, z2)))) → c22(S(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(s(sel1(0, cons(z0, z1)))) → c22(S(mark(quote(z0))), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(s(first1(0, z0))) → c22(S(mark(nil1)), ACTIVE(first1(0, z0)))
ACTIVE(s(first1(s(z0), cons(z1, z2)))) → c22(S(mark(cons1(quote(z1), first1(z0, z2)))), ACTIVE(first1(s(z0), cons(z1, z2))))
ACTIVE(s(quote(0))) → c22(S(mark(01)), ACTIVE(quote(0)))
ACTIVE(s(quote1(cons(z0, z1)))) → c22(S(mark(cons1(quote(z0), quote1(z1)))), ACTIVE(quote1(cons(z0, z1))))
ACTIVE(s(quote1(nil))) → c22(S(mark(nil1)), ACTIVE(quote1(nil)))
ACTIVE(s(quote(s(z0)))) → c22(S(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(s(quote(sel(z0, z1)))) → c22(S(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(s(quote1(first(z0, z1)))) → c22(S(mark(first1(z0, z1))), ACTIVE(quote1(first(z0, z1))))
ACTIVE(s(unquote(01))) → c22(S(mark(0)), ACTIVE(unquote(01)))
ACTIVE(s(unquote(s1(z0)))) → c22(S(mark(s(unquote(z0)))), ACTIVE(unquote(s1(z0))))
ACTIVE(s(unquote1(nil1))) → c22(S(mark(nil)), ACTIVE(unquote1(nil1)))
ACTIVE(s(unquote1(cons1(z0, z1)))) → c22(S(mark(fcons(unquote(z0), unquote1(z1)))), ACTIVE(unquote1(cons1(z0, z1))))
ACTIVE(s(fcons(z0, z1))) → c22(S(mark(cons(z0, z1))), ACTIVE(fcons(z0, z1)))
ACTIVE(s(sel(z0, z1))) → c22(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(s(sel(z0, z1))) → c22(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(s(s(z0))) → c22(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(cons(z0, z1))) → c22(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(first(z0, z1))) → c22(S(first(active(z0), z1)), ACTIVE(first(z0, z1)))
ACTIVE(s(first(z0, z1))) → c22(S(first(z0, active(z1))), ACTIVE(first(z0, z1)))
ACTIVE(s(from(z0))) → c22(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(sel1(z0, z1))) → c22(S(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(s(sel1(z0, z1))) → c22(S(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(s(first1(z0, z1))) → c22(S(first1(active(z0), z1)), ACTIVE(first1(z0, z1)))
ACTIVE(s(first1(z0, z1))) → c22(S(first1(z0, active(z1))), ACTIVE(first1(z0, z1)))
ACTIVE(s(cons1(z0, z1))) → c22(S(cons1(active(z0), z1)), ACTIVE(cons1(z0, z1)))
ACTIVE(s(cons1(z0, z1))) → c22(S(cons1(z0, active(z1))), ACTIVE(cons1(z0, z1)))
ACTIVE(s(s1(z0))) → c22(S(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(s(unquote(z0))) → c22(S(unquote(active(z0))), ACTIVE(unquote(z0)))
ACTIVE(s(unquote1(z0))) → c22(S(unquote1(active(z0))), ACTIVE(unquote1(z0)))
ACTIVE(s(fcons(z0, z1))) → c22(S(fcons(active(z0), z1)), ACTIVE(fcons(z0, z1)))
ACTIVE(s(fcons(z0, z1))) → c22(S(fcons(z0, active(z1))), ACTIVE(fcons(z0, z1)))

(12) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
active(sel(0, cons(z0, z1))) → mark(z0)
active(first(0, z0)) → mark(nil)
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2)))
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(sel1(s(z0), cons(z1, z2))) → mark(sel1(z0, z2))
active(sel1(0, cons(z0, z1))) → mark(quote(z0))
active(first1(0, z0)) → mark(nil1)
active(first1(s(z0), cons(z1, z2))) → mark(cons1(quote(z1), first1(z0, z2)))
active(quote(0)) → mark(01)
active(quote1(cons(z0, z1))) → mark(cons1(quote(z0), quote1(z1)))
active(quote1(nil)) → mark(nil1)
active(quote(s(z0))) → mark(s1(quote(z0)))
active(quote(sel(z0, z1))) → mark(sel1(z0, z1))
active(quote1(first(z0, z1))) → mark(first1(z0, z1))
active(unquote(01)) → mark(0)
active(unquote(s1(z0))) → mark(s(unquote(z0)))
active(unquote1(nil1)) → mark(nil)
active(unquote1(cons1(z0, z1))) → mark(fcons(unquote(z0), unquote1(z1)))
active(fcons(z0, z1)) → mark(cons(z0, z1))
active(sel(z0, z1)) → sel(active(z0), z1)
active(sel(z0, z1)) → sel(z0, active(z1))
active(s(z0)) → s(active(z0))
active(cons(z0, z1)) → cons(active(z0), z1)
active(first(z0, z1)) → first(active(z0), z1)
active(first(z0, z1)) → first(z0, active(z1))
active(from(z0)) → from(active(z0))
active(sel1(z0, z1)) → sel1(active(z0), z1)
active(sel1(z0, z1)) → sel1(z0, active(z1))
active(first1(z0, z1)) → first1(active(z0), z1)
active(first1(z0, z1)) → first1(z0, active(z1))
active(cons1(z0, z1)) → cons1(active(z0), z1)
active(cons1(z0, z1)) → cons1(z0, active(z1))
active(s1(z0)) → s1(active(z0))
active(unquote(z0)) → unquote(active(z0))
active(unquote1(z0)) → unquote1(active(z0))
active(fcons(z0, z1)) → fcons(active(z0), z1)
active(fcons(z0, z1)) → fcons(z0, active(z1))
sel(z0, mark(z1)) → mark(sel(z0, z1))
sel(mark(z0), z1) → mark(sel(z0, z1))
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
cons(mark(z0), z1) → mark(cons(z0, z1))
first(z0, mark(z1)) → mark(first(z0, z1))
first(mark(z0), z1) → mark(first(z0, z1))
first(ok(z0), ok(z1)) → ok(first(z0, z1))
sel1(z0, mark(z1)) → mark(sel1(z0, z1))
sel1(mark(z0), z1) → mark(sel1(z0, z1))
sel1(ok(z0), ok(z1)) → ok(sel1(z0, z1))
quote(ok(z0)) → ok(quote(z0))
cons1(mark(z0), z1) → mark(cons1(z0, z1))
cons1(z0, mark(z1)) → mark(cons1(z0, z1))
cons1(ok(z0), ok(z1)) → ok(cons1(z0, z1))
first1(z0, mark(z1)) → mark(first1(z0, z1))
first1(mark(z0), z1) → mark(first1(z0, z1))
first1(ok(z0), ok(z1)) → ok(first1(z0, z1))
quote1(ok(z0)) → ok(quote1(z0))
fcons(mark(z0), z1) → mark(fcons(z0, z1))
fcons(z0, mark(z1)) → mark(fcons(z0, z1))
fcons(ok(z0), ok(z1)) → ok(fcons(z0, z1))
unquote(ok(z0)) → ok(unquote(z0))
unquote(mark(z0)) → mark(unquote(z0))
unquote1(ok(z0)) → ok(unquote1(z0))
unquote1(mark(z0)) → mark(unquote1(z0))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
from(mark(z0)) → mark(from(z0))
from(ok(z0)) → ok(from(z0))
s1(mark(z0)) → mark(s1(z0))
s1(ok(z0)) → ok(s1(z0))
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
proper(s(z0)) → s(proper(z0))
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(0) → ok(0)
proper(first(z0, z1)) → first(proper(z0), proper(z1))
proper(nil) → ok(nil)
proper(from(z0)) → from(proper(z0))
proper(sel1(z0, z1)) → sel1(proper(z0), proper(z1))
proper(quote(z0)) → quote(proper(z0))
proper(first1(z0, z1)) → first1(proper(z0), proper(z1))
proper(nil1) → ok(nil1)
proper(cons1(z0, z1)) → cons1(proper(z0), proper(z1))
proper(01) → ok(01)
proper(quote1(z0)) → quote1(proper(z0))
proper(s1(z0)) → s1(proper(z0))
proper(unquote(z0)) → unquote(proper(z0))
proper(unquote1(z0)) → unquote1(proper(z0))
proper(fcons(z0, z1)) → fcons(proper(z0), proper(z1))
Tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c5(SEL1(z0, z2))
ACTIVE(sel1(0, cons(z0, z1))) → c6(QUOTE(z0))
ACTIVE(quote(sel(z0, z1))) → c13(SEL1(z0, z1))
ACTIVE(quote1(first(z0, z1))) → c14(FIRST1(z0, z1))
ACTIVE(fcons(z0, z1)) → c19(CONS(z0, z1))
ACTIVE(sel(z0, z1)) → c20(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c21(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(cons(z0, z1)) → c23(CONS(active(z0), z1), ACTIVE(z0))
ACTIVE(first(z0, z1)) → c24(FIRST(active(z0), z1), ACTIVE(z0))
ACTIVE(first(z0, z1)) → c25(FIRST(z0, active(z1)), ACTIVE(z1))
ACTIVE(from(z0)) → c26(FROM(active(z0)), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c27(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c28(SEL1(z0, active(z1)), ACTIVE(z1))
ACTIVE(first1(z0, z1)) → c29(FIRST1(active(z0), z1), ACTIVE(z0))
ACTIVE(first1(z0, z1)) → c30(FIRST1(z0, active(z1)), ACTIVE(z1))
ACTIVE(cons1(z0, z1)) → c31(CONS1(active(z0), z1), ACTIVE(z0))
ACTIVE(cons1(z0, z1)) → c32(CONS1(z0, active(z1)), ACTIVE(z1))
ACTIVE(s1(z0)) → c33(S1(active(z0)), ACTIVE(z0))
ACTIVE(unquote(z0)) → c34(UNQUOTE(active(z0)), ACTIVE(z0))
ACTIVE(unquote1(z0)) → c35(UNQUOTE1(active(z0)), ACTIVE(z0))
ACTIVE(fcons(z0, z1)) → c36(FCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(fcons(z0, z1)) → c37(FCONS(z0, active(z1)), ACTIVE(z1))
SEL(mark(z0), z1) → c38(SEL(z0, z1))
SEL(z0, mark(z1)) → c39(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c40(SEL(z0, z1))
S(mark(z0)) → c41(S(z0))
S(ok(z0)) → c42(S(z0))
CONS(mark(z0), z1) → c43(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c44(CONS(z0, z1))
FIRST(mark(z0), z1) → c45(FIRST(z0, z1))
FIRST(z0, mark(z1)) → c46(FIRST(z0, z1))
FIRST(ok(z0), ok(z1)) → c47(FIRST(z0, z1))
FROM(mark(z0)) → c48(FROM(z0))
FROM(ok(z0)) → c49(FROM(z0))
SEL1(mark(z0), z1) → c50(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c51(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c52(SEL1(z0, z1))
FIRST1(mark(z0), z1) → c53(FIRST1(z0, z1))
FIRST1(z0, mark(z1)) → c54(FIRST1(z0, z1))
FIRST1(ok(z0), ok(z1)) → c55(FIRST1(z0, z1))
CONS1(mark(z0), z1) → c56(CONS1(z0, z1))
CONS1(z0, mark(z1)) → c57(CONS1(z0, z1))
CONS1(ok(z0), ok(z1)) → c58(CONS1(z0, z1))
S1(mark(z0)) → c59(S1(z0))
S1(ok(z0)) → c60(S1(z0))
UNQUOTE(mark(z0)) → c61(UNQUOTE(z0))
UNQUOTE(ok(z0)) → c62(UNQUOTE(z0))
UNQUOTE1(mark(z0)) → c63(UNQUOTE1(z0))
UNQUOTE1(ok(z0)) → c64(UNQUOTE1(z0))
FCONS(mark(z0), z1) → c65(FCONS(z0, z1))
FCONS(z0, mark(z1)) → c66(FCONS(z0, z1))
FCONS(ok(z0), ok(z1)) → c67(FCONS(z0, z1))
PROPER(sel(z0, z1)) → c68(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(s(z0)) → c69(S(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c70(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(first(z0, z1)) → c72(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c74(FROM(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c75(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c76(QUOTE(proper(z0)), PROPER(z0))
PROPER(first1(z0, z1)) → c77(FIRST1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(cons1(z0, z1)) → c79(CONS1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote1(z0)) → c81(QUOTE1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c82(S1(proper(z0)), PROPER(z0))
PROPER(unquote(z0)) → c83(UNQUOTE(proper(z0)), PROPER(z0))
PROPER(unquote1(z0)) → c84(UNQUOTE1(proper(z0)), PROPER(z0))
PROPER(fcons(z0, z1)) → c85(FCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
QUOTE(ok(z0)) → c86(QUOTE(z0))
QUOTE1(ok(z0)) → c87(QUOTE1(z0))
TOP(mark(z0)) → c88(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c89(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c4(S(z0))
ACTIVE(quote(s(z0))) → c12(QUOTE(z0))
ACTIVE(unquote(s1(z0))) → c16(UNQUOTE(z0))
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2)))
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2))
ACTIVE(first1(s(z0), cons(z1, z2))) → c1(CONS1(quote(z1), first1(z0, z2)))
ACTIVE(first1(s(z0), cons(z1, z2))) → c1(QUOTE(z1))
ACTIVE(first1(s(z0), cons(z1, z2))) → c1(FIRST1(z0, z2))
ACTIVE(quote1(cons(z0, z1))) → c1(CONS1(quote(z0), quote1(z1)))
ACTIVE(quote1(cons(z0, z1))) → c1(QUOTE(z0))
ACTIVE(quote1(cons(z0, z1))) → c1(QUOTE1(z1))
ACTIVE(unquote1(cons1(z0, z1))) → c1(FCONS(unquote(z0), unquote1(z1)))
ACTIVE(unquote1(cons1(z0, z1))) → c1(UNQUOTE(z0))
ACTIVE(unquote1(cons1(z0, z1))) → c1(UNQUOTE1(z1))
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c22(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(s(sel(0, cons(z0, z1)))) → c22(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(s(first(0, z0))) → c22(S(mark(nil)), ACTIVE(first(0, z0)))
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c22(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
ACTIVE(s(from(z0))) → c22(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(sel1(s(z0), cons(z1, z2)))) → c22(S(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(s(sel1(0, cons(z0, z1)))) → c22(S(mark(quote(z0))), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(s(first1(0, z0))) → c22(S(mark(nil1)), ACTIVE(first1(0, z0)))
ACTIVE(s(first1(s(z0), cons(z1, z2)))) → c22(S(mark(cons1(quote(z1), first1(z0, z2)))), ACTIVE(first1(s(z0), cons(z1, z2))))
ACTIVE(s(quote(0))) → c22(S(mark(01)), ACTIVE(quote(0)))
ACTIVE(s(quote1(cons(z0, z1)))) → c22(S(mark(cons1(quote(z0), quote1(z1)))), ACTIVE(quote1(cons(z0, z1))))
ACTIVE(s(quote1(nil))) → c22(S(mark(nil1)), ACTIVE(quote1(nil)))
ACTIVE(s(quote(s(z0)))) → c22(S(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(s(quote(sel(z0, z1)))) → c22(S(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(s(quote1(first(z0, z1)))) → c22(S(mark(first1(z0, z1))), ACTIVE(quote1(first(z0, z1))))
ACTIVE(s(unquote(01))) → c22(S(mark(0)), ACTIVE(unquote(01)))
ACTIVE(s(unquote(s1(z0)))) → c22(S(mark(s(unquote(z0)))), ACTIVE(unquote(s1(z0))))
ACTIVE(s(unquote1(nil1))) → c22(S(mark(nil)), ACTIVE(unquote1(nil1)))
ACTIVE(s(unquote1(cons1(z0, z1)))) → c22(S(mark(fcons(unquote(z0), unquote1(z1)))), ACTIVE(unquote1(cons1(z0, z1))))
ACTIVE(s(fcons(z0, z1))) → c22(S(mark(cons(z0, z1))), ACTIVE(fcons(z0, z1)))
ACTIVE(s(sel(z0, z1))) → c22(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(s(sel(z0, z1))) → c22(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(s(s(z0))) → c22(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(cons(z0, z1))) → c22(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(first(z0, z1))) → c22(S(first(active(z0), z1)), ACTIVE(first(z0, z1)))
ACTIVE(s(first(z0, z1))) → c22(S(first(z0, active(z1))), ACTIVE(first(z0, z1)))
ACTIVE(s(from(z0))) → c22(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(sel1(z0, z1))) → c22(S(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(s(sel1(z0, z1))) → c22(S(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(s(first1(z0, z1))) → c22(S(first1(active(z0), z1)), ACTIVE(first1(z0, z1)))
ACTIVE(s(first1(z0, z1))) → c22(S(first1(z0, active(z1))), ACTIVE(first1(z0, z1)))
ACTIVE(s(cons1(z0, z1))) → c22(S(cons1(active(z0), z1)), ACTIVE(cons1(z0, z1)))
ACTIVE(s(cons1(z0, z1))) → c22(S(cons1(z0, active(z1))), ACTIVE(cons1(z0, z1)))
ACTIVE(s(s1(z0))) → c22(S(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(s(unquote(z0))) → c22(S(unquote(active(z0))), ACTIVE(unquote(z0)))
ACTIVE(s(unquote1(z0))) → c22(S(unquote1(active(z0))), ACTIVE(unquote1(z0)))
ACTIVE(s(fcons(z0, z1))) → c22(S(fcons(active(z0), z1)), ACTIVE(fcons(z0, z1)))
ACTIVE(s(fcons(z0, z1))) → c22(S(fcons(z0, active(z1))), ACTIVE(fcons(z0, z1)))
S tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c5(SEL1(z0, z2))
ACTIVE(sel1(0, cons(z0, z1))) → c6(QUOTE(z0))
ACTIVE(quote(sel(z0, z1))) → c13(SEL1(z0, z1))
ACTIVE(quote1(first(z0, z1))) → c14(FIRST1(z0, z1))
ACTIVE(fcons(z0, z1)) → c19(CONS(z0, z1))
ACTIVE(sel(z0, z1)) → c20(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c21(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(cons(z0, z1)) → c23(CONS(active(z0), z1), ACTIVE(z0))
ACTIVE(first(z0, z1)) → c24(FIRST(active(z0), z1), ACTIVE(z0))
ACTIVE(first(z0, z1)) → c25(FIRST(z0, active(z1)), ACTIVE(z1))
ACTIVE(from(z0)) → c26(FROM(active(z0)), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c27(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c28(SEL1(z0, active(z1)), ACTIVE(z1))
ACTIVE(first1(z0, z1)) → c29(FIRST1(active(z0), z1), ACTIVE(z0))
ACTIVE(first1(z0, z1)) → c30(FIRST1(z0, active(z1)), ACTIVE(z1))
ACTIVE(cons1(z0, z1)) → c31(CONS1(active(z0), z1), ACTIVE(z0))
ACTIVE(cons1(z0, z1)) → c32(CONS1(z0, active(z1)), ACTIVE(z1))
ACTIVE(s1(z0)) → c33(S1(active(z0)), ACTIVE(z0))
ACTIVE(unquote(z0)) → c34(UNQUOTE(active(z0)), ACTIVE(z0))
ACTIVE(unquote1(z0)) → c35(UNQUOTE1(active(z0)), ACTIVE(z0))
ACTIVE(fcons(z0, z1)) → c36(FCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(fcons(z0, z1)) → c37(FCONS(z0, active(z1)), ACTIVE(z1))
SEL(mark(z0), z1) → c38(SEL(z0, z1))
SEL(z0, mark(z1)) → c39(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c40(SEL(z0, z1))
S(mark(z0)) → c41(S(z0))
S(ok(z0)) → c42(S(z0))
CONS(mark(z0), z1) → c43(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c44(CONS(z0, z1))
FIRST(mark(z0), z1) → c45(FIRST(z0, z1))
FIRST(z0, mark(z1)) → c46(FIRST(z0, z1))
FIRST(ok(z0), ok(z1)) → c47(FIRST(z0, z1))
FROM(mark(z0)) → c48(FROM(z0))
FROM(ok(z0)) → c49(FROM(z0))
SEL1(mark(z0), z1) → c50(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c51(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c52(SEL1(z0, z1))
FIRST1(mark(z0), z1) → c53(FIRST1(z0, z1))
FIRST1(z0, mark(z1)) → c54(FIRST1(z0, z1))
FIRST1(ok(z0), ok(z1)) → c55(FIRST1(z0, z1))
CONS1(mark(z0), z1) → c56(CONS1(z0, z1))
CONS1(z0, mark(z1)) → c57(CONS1(z0, z1))
CONS1(ok(z0), ok(z1)) → c58(CONS1(z0, z1))
S1(mark(z0)) → c59(S1(z0))
S1(ok(z0)) → c60(S1(z0))
UNQUOTE(mark(z0)) → c61(UNQUOTE(z0))
UNQUOTE(ok(z0)) → c62(UNQUOTE(z0))
UNQUOTE1(mark(z0)) → c63(UNQUOTE1(z0))
UNQUOTE1(ok(z0)) → c64(UNQUOTE1(z0))
FCONS(mark(z0), z1) → c65(FCONS(z0, z1))
FCONS(z0, mark(z1)) → c66(FCONS(z0, z1))
FCONS(ok(z0), ok(z1)) → c67(FCONS(z0, z1))
PROPER(sel(z0, z1)) → c68(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(s(z0)) → c69(S(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c70(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(first(z0, z1)) → c72(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c74(FROM(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c75(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c76(QUOTE(proper(z0)), PROPER(z0))
PROPER(first1(z0, z1)) → c77(FIRST1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(cons1(z0, z1)) → c79(CONS1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote1(z0)) → c81(QUOTE1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c82(S1(proper(z0)), PROPER(z0))
PROPER(unquote(z0)) → c83(UNQUOTE(proper(z0)), PROPER(z0))
PROPER(unquote1(z0)) → c84(UNQUOTE1(proper(z0)), PROPER(z0))
PROPER(fcons(z0, z1)) → c85(FCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
QUOTE(ok(z0)) → c86(QUOTE(z0))
QUOTE1(ok(z0)) → c87(QUOTE1(z0))
TOP(mark(z0)) → c88(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c89(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c4(S(z0))
ACTIVE(quote(s(z0))) → c12(QUOTE(z0))
ACTIVE(unquote(s1(z0))) → c16(UNQUOTE(z0))
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2)))
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2))
ACTIVE(first1(s(z0), cons(z1, z2))) → c1(CONS1(quote(z1), first1(z0, z2)))
ACTIVE(first1(s(z0), cons(z1, z2))) → c1(QUOTE(z1))
ACTIVE(first1(s(z0), cons(z1, z2))) → c1(FIRST1(z0, z2))
ACTIVE(quote1(cons(z0, z1))) → c1(CONS1(quote(z0), quote1(z1)))
ACTIVE(quote1(cons(z0, z1))) → c1(QUOTE(z0))
ACTIVE(quote1(cons(z0, z1))) → c1(QUOTE1(z1))
ACTIVE(unquote1(cons1(z0, z1))) → c1(FCONS(unquote(z0), unquote1(z1)))
ACTIVE(unquote1(cons1(z0, z1))) → c1(UNQUOTE(z0))
ACTIVE(unquote1(cons1(z0, z1))) → c1(UNQUOTE1(z1))
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c22(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(s(sel(0, cons(z0, z1)))) → c22(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(s(first(0, z0))) → c22(S(mark(nil)), ACTIVE(first(0, z0)))
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c22(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
ACTIVE(s(from(z0))) → c22(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(sel1(s(z0), cons(z1, z2)))) → c22(S(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(s(sel1(0, cons(z0, z1)))) → c22(S(mark(quote(z0))), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(s(first1(0, z0))) → c22(S(mark(nil1)), ACTIVE(first1(0, z0)))
ACTIVE(s(first1(s(z0), cons(z1, z2)))) → c22(S(mark(cons1(quote(z1), first1(z0, z2)))), ACTIVE(first1(s(z0), cons(z1, z2))))
ACTIVE(s(quote(0))) → c22(S(mark(01)), ACTIVE(quote(0)))
ACTIVE(s(quote1(cons(z0, z1)))) → c22(S(mark(cons1(quote(z0), quote1(z1)))), ACTIVE(quote1(cons(z0, z1))))
ACTIVE(s(quote1(nil))) → c22(S(mark(nil1)), ACTIVE(quote1(nil)))
ACTIVE(s(quote(s(z0)))) → c22(S(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(s(quote(sel(z0, z1)))) → c22(S(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(s(quote1(first(z0, z1)))) → c22(S(mark(first1(z0, z1))), ACTIVE(quote1(first(z0, z1))))
ACTIVE(s(unquote(01))) → c22(S(mark(0)), ACTIVE(unquote(01)))
ACTIVE(s(unquote(s1(z0)))) → c22(S(mark(s(unquote(z0)))), ACTIVE(unquote(s1(z0))))
ACTIVE(s(unquote1(nil1))) → c22(S(mark(nil)), ACTIVE(unquote1(nil1)))
ACTIVE(s(unquote1(cons1(z0, z1)))) → c22(S(mark(fcons(unquote(z0), unquote1(z1)))), ACTIVE(unquote1(cons1(z0, z1))))
ACTIVE(s(fcons(z0, z1))) → c22(S(mark(cons(z0, z1))), ACTIVE(fcons(z0, z1)))
ACTIVE(s(sel(z0, z1))) → c22(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(s(sel(z0, z1))) → c22(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(s(s(z0))) → c22(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(cons(z0, z1))) → c22(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(first(z0, z1))) → c22(S(first(active(z0), z1)), ACTIVE(first(z0, z1)))
ACTIVE(s(first(z0, z1))) → c22(S(first(z0, active(z1))), ACTIVE(first(z0, z1)))
ACTIVE(s(from(z0))) → c22(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(sel1(z0, z1))) → c22(S(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(s(sel1(z0, z1))) → c22(S(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(s(first1(z0, z1))) → c22(S(first1(active(z0), z1)), ACTIVE(first1(z0, z1)))
ACTIVE(s(first1(z0, z1))) → c22(S(first1(z0, active(z1))), ACTIVE(first1(z0, z1)))
ACTIVE(s(cons1(z0, z1))) → c22(S(cons1(active(z0), z1)), ACTIVE(cons1(z0, z1)))
ACTIVE(s(cons1(z0, z1))) → c22(S(cons1(z0, active(z1))), ACTIVE(cons1(z0, z1)))
ACTIVE(s(s1(z0))) → c22(S(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(s(unquote(z0))) → c22(S(unquote(active(z0))), ACTIVE(unquote(z0)))
ACTIVE(s(unquote1(z0))) → c22(S(unquote1(active(z0))), ACTIVE(unquote1(z0)))
ACTIVE(s(fcons(z0, z1))) → c22(S(fcons(active(z0), z1)), ACTIVE(fcons(z0, z1)))
ACTIVE(s(fcons(z0, z1))) → c22(S(fcons(z0, active(z1))), ACTIVE(fcons(z0, z1)))
K tuples:none
Defined Rule Symbols:

active, sel, cons, first, sel1, quote, cons1, first1, quote1, fcons, unquote, unquote1, s, from, s1, proper

Defined Pair Symbols:

ACTIVE, SEL, S, CONS, FIRST, FROM, SEL1, FIRST1, CONS1, S1, UNQUOTE, UNQUOTE1, FCONS, PROPER, QUOTE, QUOTE1, TOP

Compound Symbols:

c, c5, c6, c13, c14, c19, c20, c21, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c66, c67, c68, c69, c70, c72, c74, c75, c76, c77, c79, c81, c82, c83, c84, c85, c86, c87, c88, c89, c4, c12, c16, c1, c22

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

Removed 2 trailing tuple parts

(14) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
active(sel(0, cons(z0, z1))) → mark(z0)
active(first(0, z0)) → mark(nil)
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2)))
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(sel1(s(z0), cons(z1, z2))) → mark(sel1(z0, z2))
active(sel1(0, cons(z0, z1))) → mark(quote(z0))
active(first1(0, z0)) → mark(nil1)
active(first1(s(z0), cons(z1, z2))) → mark(cons1(quote(z1), first1(z0, z2)))
active(quote(0)) → mark(01)
active(quote1(cons(z0, z1))) → mark(cons1(quote(z0), quote1(z1)))
active(quote1(nil)) → mark(nil1)
active(quote(s(z0))) → mark(s1(quote(z0)))
active(quote(sel(z0, z1))) → mark(sel1(z0, z1))
active(quote1(first(z0, z1))) → mark(first1(z0, z1))
active(unquote(01)) → mark(0)
active(unquote(s1(z0))) → mark(s(unquote(z0)))
active(unquote1(nil1)) → mark(nil)
active(unquote1(cons1(z0, z1))) → mark(fcons(unquote(z0), unquote1(z1)))
active(fcons(z0, z1)) → mark(cons(z0, z1))
active(sel(z0, z1)) → sel(active(z0), z1)
active(sel(z0, z1)) → sel(z0, active(z1))
active(s(z0)) → s(active(z0))
active(cons(z0, z1)) → cons(active(z0), z1)
active(first(z0, z1)) → first(active(z0), z1)
active(first(z0, z1)) → first(z0, active(z1))
active(from(z0)) → from(active(z0))
active(sel1(z0, z1)) → sel1(active(z0), z1)
active(sel1(z0, z1)) → sel1(z0, active(z1))
active(first1(z0, z1)) → first1(active(z0), z1)
active(first1(z0, z1)) → first1(z0, active(z1))
active(cons1(z0, z1)) → cons1(active(z0), z1)
active(cons1(z0, z1)) → cons1(z0, active(z1))
active(s1(z0)) → s1(active(z0))
active(unquote(z0)) → unquote(active(z0))
active(unquote1(z0)) → unquote1(active(z0))
active(fcons(z0, z1)) → fcons(active(z0), z1)
active(fcons(z0, z1)) → fcons(z0, active(z1))
sel(z0, mark(z1)) → mark(sel(z0, z1))
sel(mark(z0), z1) → mark(sel(z0, z1))
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
cons(mark(z0), z1) → mark(cons(z0, z1))
first(z0, mark(z1)) → mark(first(z0, z1))
first(mark(z0), z1) → mark(first(z0, z1))
first(ok(z0), ok(z1)) → ok(first(z0, z1))
sel1(z0, mark(z1)) → mark(sel1(z0, z1))
sel1(mark(z0), z1) → mark(sel1(z0, z1))
sel1(ok(z0), ok(z1)) → ok(sel1(z0, z1))
quote(ok(z0)) → ok(quote(z0))
cons1(mark(z0), z1) → mark(cons1(z0, z1))
cons1(z0, mark(z1)) → mark(cons1(z0, z1))
cons1(ok(z0), ok(z1)) → ok(cons1(z0, z1))
first1(z0, mark(z1)) → mark(first1(z0, z1))
first1(mark(z0), z1) → mark(first1(z0, z1))
first1(ok(z0), ok(z1)) → ok(first1(z0, z1))
quote1(ok(z0)) → ok(quote1(z0))
fcons(mark(z0), z1) → mark(fcons(z0, z1))
fcons(z0, mark(z1)) → mark(fcons(z0, z1))
fcons(ok(z0), ok(z1)) → ok(fcons(z0, z1))
unquote(ok(z0)) → ok(unquote(z0))
unquote(mark(z0)) → mark(unquote(z0))
unquote1(ok(z0)) → ok(unquote1(z0))
unquote1(mark(z0)) → mark(unquote1(z0))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
from(mark(z0)) → mark(from(z0))
from(ok(z0)) → ok(from(z0))
s1(mark(z0)) → mark(s1(z0))
s1(ok(z0)) → ok(s1(z0))
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
proper(s(z0)) → s(proper(z0))
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(0) → ok(0)
proper(first(z0, z1)) → first(proper(z0), proper(z1))
proper(nil) → ok(nil)
proper(from(z0)) → from(proper(z0))
proper(sel1(z0, z1)) → sel1(proper(z0), proper(z1))
proper(quote(z0)) → quote(proper(z0))
proper(first1(z0, z1)) → first1(proper(z0), proper(z1))
proper(nil1) → ok(nil1)
proper(cons1(z0, z1)) → cons1(proper(z0), proper(z1))
proper(01) → ok(01)
proper(quote1(z0)) → quote1(proper(z0))
proper(s1(z0)) → s1(proper(z0))
proper(unquote(z0)) → unquote(proper(z0))
proper(unquote1(z0)) → unquote1(proper(z0))
proper(fcons(z0, z1)) → fcons(proper(z0), proper(z1))
Tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c5(SEL1(z0, z2))
ACTIVE(sel1(0, cons(z0, z1))) → c6(QUOTE(z0))
ACTIVE(quote(sel(z0, z1))) → c13(SEL1(z0, z1))
ACTIVE(quote1(first(z0, z1))) → c14(FIRST1(z0, z1))
ACTIVE(fcons(z0, z1)) → c19(CONS(z0, z1))
ACTIVE(sel(z0, z1)) → c20(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c21(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(cons(z0, z1)) → c23(CONS(active(z0), z1), ACTIVE(z0))
ACTIVE(first(z0, z1)) → c24(FIRST(active(z0), z1), ACTIVE(z0))
ACTIVE(first(z0, z1)) → c25(FIRST(z0, active(z1)), ACTIVE(z1))
ACTIVE(from(z0)) → c26(FROM(active(z0)), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c27(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c28(SEL1(z0, active(z1)), ACTIVE(z1))
ACTIVE(first1(z0, z1)) → c29(FIRST1(active(z0), z1), ACTIVE(z0))
ACTIVE(first1(z0, z1)) → c30(FIRST1(z0, active(z1)), ACTIVE(z1))
ACTIVE(cons1(z0, z1)) → c31(CONS1(active(z0), z1), ACTIVE(z0))
ACTIVE(cons1(z0, z1)) → c32(CONS1(z0, active(z1)), ACTIVE(z1))
ACTIVE(s1(z0)) → c33(S1(active(z0)), ACTIVE(z0))
ACTIVE(unquote(z0)) → c34(UNQUOTE(active(z0)), ACTIVE(z0))
ACTIVE(unquote1(z0)) → c35(UNQUOTE1(active(z0)), ACTIVE(z0))
ACTIVE(fcons(z0, z1)) → c36(FCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(fcons(z0, z1)) → c37(FCONS(z0, active(z1)), ACTIVE(z1))
SEL(mark(z0), z1) → c38(SEL(z0, z1))
SEL(z0, mark(z1)) → c39(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c40(SEL(z0, z1))
S(mark(z0)) → c41(S(z0))
S(ok(z0)) → c42(S(z0))
CONS(mark(z0), z1) → c43(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c44(CONS(z0, z1))
FIRST(mark(z0), z1) → c45(FIRST(z0, z1))
FIRST(z0, mark(z1)) → c46(FIRST(z0, z1))
FIRST(ok(z0), ok(z1)) → c47(FIRST(z0, z1))
FROM(mark(z0)) → c48(FROM(z0))
FROM(ok(z0)) → c49(FROM(z0))
SEL1(mark(z0), z1) → c50(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c51(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c52(SEL1(z0, z1))
FIRST1(mark(z0), z1) → c53(FIRST1(z0, z1))
FIRST1(z0, mark(z1)) → c54(FIRST1(z0, z1))
FIRST1(ok(z0), ok(z1)) → c55(FIRST1(z0, z1))
CONS1(mark(z0), z1) → c56(CONS1(z0, z1))
CONS1(z0, mark(z1)) → c57(CONS1(z0, z1))
CONS1(ok(z0), ok(z1)) → c58(CONS1(z0, z1))
S1(mark(z0)) → c59(S1(z0))
S1(ok(z0)) → c60(S1(z0))
UNQUOTE(mark(z0)) → c61(UNQUOTE(z0))
UNQUOTE(ok(z0)) → c62(UNQUOTE(z0))
UNQUOTE1(mark(z0)) → c63(UNQUOTE1(z0))
UNQUOTE1(ok(z0)) → c64(UNQUOTE1(z0))
FCONS(mark(z0), z1) → c65(FCONS(z0, z1))
FCONS(z0, mark(z1)) → c66(FCONS(z0, z1))
FCONS(ok(z0), ok(z1)) → c67(FCONS(z0, z1))
PROPER(sel(z0, z1)) → c68(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(s(z0)) → c69(S(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c70(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(first(z0, z1)) → c72(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c74(FROM(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c75(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c76(QUOTE(proper(z0)), PROPER(z0))
PROPER(first1(z0, z1)) → c77(FIRST1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(cons1(z0, z1)) → c79(CONS1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote1(z0)) → c81(QUOTE1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c82(S1(proper(z0)), PROPER(z0))
PROPER(unquote(z0)) → c83(UNQUOTE(proper(z0)), PROPER(z0))
PROPER(unquote1(z0)) → c84(UNQUOTE1(proper(z0)), PROPER(z0))
PROPER(fcons(z0, z1)) → c85(FCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
QUOTE(ok(z0)) → c86(QUOTE(z0))
QUOTE1(ok(z0)) → c87(QUOTE1(z0))
TOP(mark(z0)) → c88(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c89(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c4(S(z0))
ACTIVE(quote(s(z0))) → c12(QUOTE(z0))
ACTIVE(unquote(s1(z0))) → c16(UNQUOTE(z0))
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2)))
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2))
ACTIVE(first1(s(z0), cons(z1, z2))) → c1(CONS1(quote(z1), first1(z0, z2)))
ACTIVE(first1(s(z0), cons(z1, z2))) → c1(QUOTE(z1))
ACTIVE(first1(s(z0), cons(z1, z2))) → c1(FIRST1(z0, z2))
ACTIVE(quote1(cons(z0, z1))) → c1(CONS1(quote(z0), quote1(z1)))
ACTIVE(quote1(cons(z0, z1))) → c1(QUOTE(z0))
ACTIVE(quote1(cons(z0, z1))) → c1(QUOTE1(z1))
ACTIVE(unquote1(cons1(z0, z1))) → c1(FCONS(unquote(z0), unquote1(z1)))
ACTIVE(unquote1(cons1(z0, z1))) → c1(UNQUOTE(z0))
ACTIVE(unquote1(cons1(z0, z1))) → c1(UNQUOTE1(z1))
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c22(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(s(sel(0, cons(z0, z1)))) → c22(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(s(first(0, z0))) → c22(S(mark(nil)), ACTIVE(first(0, z0)))
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c22(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
ACTIVE(s(from(z0))) → c22(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(sel1(s(z0), cons(z1, z2)))) → c22(S(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(s(sel1(0, cons(z0, z1)))) → c22(S(mark(quote(z0))), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(s(first1(0, z0))) → c22(S(mark(nil1)), ACTIVE(first1(0, z0)))
ACTIVE(s(first1(s(z0), cons(z1, z2)))) → c22(S(mark(cons1(quote(z1), first1(z0, z2)))), ACTIVE(first1(s(z0), cons(z1, z2))))
ACTIVE(s(quote1(cons(z0, z1)))) → c22(S(mark(cons1(quote(z0), quote1(z1)))), ACTIVE(quote1(cons(z0, z1))))
ACTIVE(s(quote(s(z0)))) → c22(S(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(s(quote(sel(z0, z1)))) → c22(S(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(s(quote1(first(z0, z1)))) → c22(S(mark(first1(z0, z1))), ACTIVE(quote1(first(z0, z1))))
ACTIVE(s(unquote(01))) → c22(S(mark(0)), ACTIVE(unquote(01)))
ACTIVE(s(unquote(s1(z0)))) → c22(S(mark(s(unquote(z0)))), ACTIVE(unquote(s1(z0))))
ACTIVE(s(unquote1(nil1))) → c22(S(mark(nil)), ACTIVE(unquote1(nil1)))
ACTIVE(s(unquote1(cons1(z0, z1)))) → c22(S(mark(fcons(unquote(z0), unquote1(z1)))), ACTIVE(unquote1(cons1(z0, z1))))
ACTIVE(s(fcons(z0, z1))) → c22(S(mark(cons(z0, z1))), ACTIVE(fcons(z0, z1)))
ACTIVE(s(sel(z0, z1))) → c22(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(s(sel(z0, z1))) → c22(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(s(s(z0))) → c22(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(cons(z0, z1))) → c22(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(first(z0, z1))) → c22(S(first(active(z0), z1)), ACTIVE(first(z0, z1)))
ACTIVE(s(first(z0, z1))) → c22(S(first(z0, active(z1))), ACTIVE(first(z0, z1)))
ACTIVE(s(from(z0))) → c22(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(sel1(z0, z1))) → c22(S(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(s(sel1(z0, z1))) → c22(S(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(s(first1(z0, z1))) → c22(S(first1(active(z0), z1)), ACTIVE(first1(z0, z1)))
ACTIVE(s(first1(z0, z1))) → c22(S(first1(z0, active(z1))), ACTIVE(first1(z0, z1)))
ACTIVE(s(cons1(z0, z1))) → c22(S(cons1(active(z0), z1)), ACTIVE(cons1(z0, z1)))
ACTIVE(s(cons1(z0, z1))) → c22(S(cons1(z0, active(z1))), ACTIVE(cons1(z0, z1)))
ACTIVE(s(s1(z0))) → c22(S(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(s(unquote(z0))) → c22(S(unquote(active(z0))), ACTIVE(unquote(z0)))
ACTIVE(s(unquote1(z0))) → c22(S(unquote1(active(z0))), ACTIVE(unquote1(z0)))
ACTIVE(s(fcons(z0, z1))) → c22(S(fcons(active(z0), z1)), ACTIVE(fcons(z0, z1)))
ACTIVE(s(fcons(z0, z1))) → c22(S(fcons(z0, active(z1))), ACTIVE(fcons(z0, z1)))
ACTIVE(s(quote(0))) → c22(S(mark(01)))
ACTIVE(s(quote1(nil))) → c22(S(mark(nil1)))
S tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c5(SEL1(z0, z2))
ACTIVE(sel1(0, cons(z0, z1))) → c6(QUOTE(z0))
ACTIVE(quote(sel(z0, z1))) → c13(SEL1(z0, z1))
ACTIVE(quote1(first(z0, z1))) → c14(FIRST1(z0, z1))
ACTIVE(fcons(z0, z1)) → c19(CONS(z0, z1))
ACTIVE(sel(z0, z1)) → c20(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c21(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(cons(z0, z1)) → c23(CONS(active(z0), z1), ACTIVE(z0))
ACTIVE(first(z0, z1)) → c24(FIRST(active(z0), z1), ACTIVE(z0))
ACTIVE(first(z0, z1)) → c25(FIRST(z0, active(z1)), ACTIVE(z1))
ACTIVE(from(z0)) → c26(FROM(active(z0)), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c27(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c28(SEL1(z0, active(z1)), ACTIVE(z1))
ACTIVE(first1(z0, z1)) → c29(FIRST1(active(z0), z1), ACTIVE(z0))
ACTIVE(first1(z0, z1)) → c30(FIRST1(z0, active(z1)), ACTIVE(z1))
ACTIVE(cons1(z0, z1)) → c31(CONS1(active(z0), z1), ACTIVE(z0))
ACTIVE(cons1(z0, z1)) → c32(CONS1(z0, active(z1)), ACTIVE(z1))
ACTIVE(s1(z0)) → c33(S1(active(z0)), ACTIVE(z0))
ACTIVE(unquote(z0)) → c34(UNQUOTE(active(z0)), ACTIVE(z0))
ACTIVE(unquote1(z0)) → c35(UNQUOTE1(active(z0)), ACTIVE(z0))
ACTIVE(fcons(z0, z1)) → c36(FCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(fcons(z0, z1)) → c37(FCONS(z0, active(z1)), ACTIVE(z1))
SEL(mark(z0), z1) → c38(SEL(z0, z1))
SEL(z0, mark(z1)) → c39(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c40(SEL(z0, z1))
S(mark(z0)) → c41(S(z0))
S(ok(z0)) → c42(S(z0))
CONS(mark(z0), z1) → c43(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c44(CONS(z0, z1))
FIRST(mark(z0), z1) → c45(FIRST(z0, z1))
FIRST(z0, mark(z1)) → c46(FIRST(z0, z1))
FIRST(ok(z0), ok(z1)) → c47(FIRST(z0, z1))
FROM(mark(z0)) → c48(FROM(z0))
FROM(ok(z0)) → c49(FROM(z0))
SEL1(mark(z0), z1) → c50(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c51(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c52(SEL1(z0, z1))
FIRST1(mark(z0), z1) → c53(FIRST1(z0, z1))
FIRST1(z0, mark(z1)) → c54(FIRST1(z0, z1))
FIRST1(ok(z0), ok(z1)) → c55(FIRST1(z0, z1))
CONS1(mark(z0), z1) → c56(CONS1(z0, z1))
CONS1(z0, mark(z1)) → c57(CONS1(z0, z1))
CONS1(ok(z0), ok(z1)) → c58(CONS1(z0, z1))
S1(mark(z0)) → c59(S1(z0))
S1(ok(z0)) → c60(S1(z0))
UNQUOTE(mark(z0)) → c61(UNQUOTE(z0))
UNQUOTE(ok(z0)) → c62(UNQUOTE(z0))
UNQUOTE1(mark(z0)) → c63(UNQUOTE1(z0))
UNQUOTE1(ok(z0)) → c64(UNQUOTE1(z0))
FCONS(mark(z0), z1) → c65(FCONS(z0, z1))
FCONS(z0, mark(z1)) → c66(FCONS(z0, z1))
FCONS(ok(z0), ok(z1)) → c67(FCONS(z0, z1))
PROPER(sel(z0, z1)) → c68(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(s(z0)) → c69(S(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c70(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(first(z0, z1)) → c72(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c74(FROM(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c75(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c76(QUOTE(proper(z0)), PROPER(z0))
PROPER(first1(z0, z1)) → c77(FIRST1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(cons1(z0, z1)) → c79(CONS1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote1(z0)) → c81(QUOTE1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c82(S1(proper(z0)), PROPER(z0))
PROPER(unquote(z0)) → c83(UNQUOTE(proper(z0)), PROPER(z0))
PROPER(unquote1(z0)) → c84(UNQUOTE1(proper(z0)), PROPER(z0))
PROPER(fcons(z0, z1)) → c85(FCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
QUOTE(ok(z0)) → c86(QUOTE(z0))
QUOTE1(ok(z0)) → c87(QUOTE1(z0))
TOP(mark(z0)) → c88(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c89(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c4(S(z0))
ACTIVE(quote(s(z0))) → c12(QUOTE(z0))
ACTIVE(unquote(s1(z0))) → c16(UNQUOTE(z0))
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2)))
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2))
ACTIVE(first1(s(z0), cons(z1, z2))) → c1(CONS1(quote(z1), first1(z0, z2)))
ACTIVE(first1(s(z0), cons(z1, z2))) → c1(QUOTE(z1))
ACTIVE(first1(s(z0), cons(z1, z2))) → c1(FIRST1(z0, z2))
ACTIVE(quote1(cons(z0, z1))) → c1(CONS1(quote(z0), quote1(z1)))
ACTIVE(quote1(cons(z0, z1))) → c1(QUOTE(z0))
ACTIVE(quote1(cons(z0, z1))) → c1(QUOTE1(z1))
ACTIVE(unquote1(cons1(z0, z1))) → c1(FCONS(unquote(z0), unquote1(z1)))
ACTIVE(unquote1(cons1(z0, z1))) → c1(UNQUOTE(z0))
ACTIVE(unquote1(cons1(z0, z1))) → c1(UNQUOTE1(z1))
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c22(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(s(sel(0, cons(z0, z1)))) → c22(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(s(first(0, z0))) → c22(S(mark(nil)), ACTIVE(first(0, z0)))
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c22(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
ACTIVE(s(from(z0))) → c22(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(sel1(s(z0), cons(z1, z2)))) → c22(S(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(s(sel1(0, cons(z0, z1)))) → c22(S(mark(quote(z0))), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(s(first1(0, z0))) → c22(S(mark(nil1)), ACTIVE(first1(0, z0)))
ACTIVE(s(first1(s(z0), cons(z1, z2)))) → c22(S(mark(cons1(quote(z1), first1(z0, z2)))), ACTIVE(first1(s(z0), cons(z1, z2))))
ACTIVE(s(quote1(cons(z0, z1)))) → c22(S(mark(cons1(quote(z0), quote1(z1)))), ACTIVE(quote1(cons(z0, z1))))
ACTIVE(s(quote(s(z0)))) → c22(S(mark(s1(quote(z0)))), ACTIVE(quote(s(z0))))
ACTIVE(s(quote(sel(z0, z1)))) → c22(S(mark(sel1(z0, z1))), ACTIVE(quote(sel(z0, z1))))
ACTIVE(s(quote1(first(z0, z1)))) → c22(S(mark(first1(z0, z1))), ACTIVE(quote1(first(z0, z1))))
ACTIVE(s(unquote(01))) → c22(S(mark(0)), ACTIVE(unquote(01)))
ACTIVE(s(unquote(s1(z0)))) → c22(S(mark(s(unquote(z0)))), ACTIVE(unquote(s1(z0))))
ACTIVE(s(unquote1(nil1))) → c22(S(mark(nil)), ACTIVE(unquote1(nil1)))
ACTIVE(s(unquote1(cons1(z0, z1)))) → c22(S(mark(fcons(unquote(z0), unquote1(z1)))), ACTIVE(unquote1(cons1(z0, z1))))
ACTIVE(s(fcons(z0, z1))) → c22(S(mark(cons(z0, z1))), ACTIVE(fcons(z0, z1)))
ACTIVE(s(sel(z0, z1))) → c22(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(s(sel(z0, z1))) → c22(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(s(s(z0))) → c22(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(cons(z0, z1))) → c22(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(first(z0, z1))) → c22(S(first(active(z0), z1)), ACTIVE(first(z0, z1)))
ACTIVE(s(first(z0, z1))) → c22(S(first(z0, active(z1))), ACTIVE(first(z0, z1)))
ACTIVE(s(from(z0))) → c22(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(sel1(z0, z1))) → c22(S(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(s(sel1(z0, z1))) → c22(S(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(s(first1(z0, z1))) → c22(S(first1(active(z0), z1)), ACTIVE(first1(z0, z1)))
ACTIVE(s(first1(z0, z1))) → c22(S(first1(z0, active(z1))), ACTIVE(first1(z0, z1)))
ACTIVE(s(cons1(z0, z1))) → c22(S(cons1(active(z0), z1)), ACTIVE(cons1(z0, z1)))
ACTIVE(s(cons1(z0, z1))) → c22(S(cons1(z0, active(z1))), ACTIVE(cons1(z0, z1)))
ACTIVE(s(s1(z0))) → c22(S(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(s(unquote(z0))) → c22(S(unquote(active(z0))), ACTIVE(unquote(z0)))
ACTIVE(s(unquote1(z0))) → c22(S(unquote1(active(z0))), ACTIVE(unquote1(z0)))
ACTIVE(s(fcons(z0, z1))) → c22(S(fcons(active(z0), z1)), ACTIVE(fcons(z0, z1)))
ACTIVE(s(fcons(z0, z1))) → c22(S(fcons(z0, active(z1))), ACTIVE(fcons(z0, z1)))
ACTIVE(s(quote(0))) → c22(S(mark(01)))
ACTIVE(s(quote1(nil))) → c22(S(mark(nil1)))
K tuples:none
Defined Rule Symbols:

active, sel, cons, first, sel1, quote, cons1, first1, quote1, fcons, unquote, unquote1, s, from, s1, proper

Defined Pair Symbols:

ACTIVE, SEL, S, CONS, FIRST, FROM, SEL1, FIRST1, CONS1, S1, UNQUOTE, UNQUOTE1, FCONS, PROPER, QUOTE, QUOTE1, TOP

Compound Symbols:

c, c5, c6, c13, c14, c19, c20, c21, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c66, c67, c68, c69, c70, c72, c74, c75, c76, c77, c79, c81, c82, c83, c84, c85, c86, c87, c88, c89, c4, c12, c16, c1, c22, c22

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

Split RHS of tuples not part of any SCC

(16) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
active(sel(0, cons(z0, z1))) → mark(z0)
active(first(0, z0)) → mark(nil)
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2)))
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(sel1(s(z0), cons(z1, z2))) → mark(sel1(z0, z2))
active(sel1(0, cons(z0, z1))) → mark(quote(z0))
active(first1(0, z0)) → mark(nil1)
active(first1(s(z0), cons(z1, z2))) → mark(cons1(quote(z1), first1(z0, z2)))
active(quote(0)) → mark(01)
active(quote1(cons(z0, z1))) → mark(cons1(quote(z0), quote1(z1)))
active(quote1(nil)) → mark(nil1)
active(quote(s(z0))) → mark(s1(quote(z0)))
active(quote(sel(z0, z1))) → mark(sel1(z0, z1))
active(quote1(first(z0, z1))) → mark(first1(z0, z1))
active(unquote(01)) → mark(0)
active(unquote(s1(z0))) → mark(s(unquote(z0)))
active(unquote1(nil1)) → mark(nil)
active(unquote1(cons1(z0, z1))) → mark(fcons(unquote(z0), unquote1(z1)))
active(fcons(z0, z1)) → mark(cons(z0, z1))
active(sel(z0, z1)) → sel(active(z0), z1)
active(sel(z0, z1)) → sel(z0, active(z1))
active(s(z0)) → s(active(z0))
active(cons(z0, z1)) → cons(active(z0), z1)
active(first(z0, z1)) → first(active(z0), z1)
active(first(z0, z1)) → first(z0, active(z1))
active(from(z0)) → from(active(z0))
active(sel1(z0, z1)) → sel1(active(z0), z1)
active(sel1(z0, z1)) → sel1(z0, active(z1))
active(first1(z0, z1)) → first1(active(z0), z1)
active(first1(z0, z1)) → first1(z0, active(z1))
active(cons1(z0, z1)) → cons1(active(z0), z1)
active(cons1(z0, z1)) → cons1(z0, active(z1))
active(s1(z0)) → s1(active(z0))
active(unquote(z0)) → unquote(active(z0))
active(unquote1(z0)) → unquote1(active(z0))
active(fcons(z0, z1)) → fcons(active(z0), z1)
active(fcons(z0, z1)) → fcons(z0, active(z1))
sel(z0, mark(z1)) → mark(sel(z0, z1))
sel(mark(z0), z1) → mark(sel(z0, z1))
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
cons(mark(z0), z1) → mark(cons(z0, z1))
first(z0, mark(z1)) → mark(first(z0, z1))
first(mark(z0), z1) → mark(first(z0, z1))
first(ok(z0), ok(z1)) → ok(first(z0, z1))
sel1(z0, mark(z1)) → mark(sel1(z0, z1))
sel1(mark(z0), z1) → mark(sel1(z0, z1))
sel1(ok(z0), ok(z1)) → ok(sel1(z0, z1))
quote(ok(z0)) → ok(quote(z0))
cons1(mark(z0), z1) → mark(cons1(z0, z1))
cons1(z0, mark(z1)) → mark(cons1(z0, z1))
cons1(ok(z0), ok(z1)) → ok(cons1(z0, z1))
first1(z0, mark(z1)) → mark(first1(z0, z1))
first1(mark(z0), z1) → mark(first1(z0, z1))
first1(ok(z0), ok(z1)) → ok(first1(z0, z1))
quote1(ok(z0)) → ok(quote1(z0))
fcons(mark(z0), z1) → mark(fcons(z0, z1))
fcons(z0, mark(z1)) → mark(fcons(z0, z1))
fcons(ok(z0), ok(z1)) → ok(fcons(z0, z1))
unquote(ok(z0)) → ok(unquote(z0))
unquote(mark(z0)) → mark(unquote(z0))
unquote1(ok(z0)) → ok(unquote1(z0))
unquote1(mark(z0)) → mark(unquote1(z0))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
from(mark(z0)) → mark(from(z0))
from(ok(z0)) → ok(from(z0))
s1(mark(z0)) → mark(s1(z0))
s1(ok(z0)) → ok(s1(z0))
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
proper(s(z0)) → s(proper(z0))
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(0) → ok(0)
proper(first(z0, z1)) → first(proper(z0), proper(z1))
proper(nil) → ok(nil)
proper(from(z0)) → from(proper(z0))
proper(sel1(z0, z1)) → sel1(proper(z0), proper(z1))
proper(quote(z0)) → quote(proper(z0))
proper(first1(z0, z1)) → first1(proper(z0), proper(z1))
proper(nil1) → ok(nil1)
proper(cons1(z0, z1)) → cons1(proper(z0), proper(z1))
proper(01) → ok(01)
proper(quote1(z0)) → quote1(proper(z0))
proper(s1(z0)) → s1(proper(z0))
proper(unquote(z0)) → unquote(proper(z0))
proper(unquote1(z0)) → unquote1(proper(z0))
proper(fcons(z0, z1)) → fcons(proper(z0), proper(z1))
Tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c5(SEL1(z0, z2))
ACTIVE(sel1(0, cons(z0, z1))) → c6(QUOTE(z0))
ACTIVE(quote(sel(z0, z1))) → c13(SEL1(z0, z1))
ACTIVE(quote1(first(z0, z1))) → c14(FIRST1(z0, z1))
ACTIVE(fcons(z0, z1)) → c19(CONS(z0, z1))
ACTIVE(sel(z0, z1)) → c20(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c21(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(cons(z0, z1)) → c23(CONS(active(z0), z1), ACTIVE(z0))
ACTIVE(first(z0, z1)) → c24(FIRST(active(z0), z1), ACTIVE(z0))
ACTIVE(first(z0, z1)) → c25(FIRST(z0, active(z1)), ACTIVE(z1))
ACTIVE(from(z0)) → c26(FROM(active(z0)), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c27(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c28(SEL1(z0, active(z1)), ACTIVE(z1))
ACTIVE(first1(z0, z1)) → c29(FIRST1(active(z0), z1), ACTIVE(z0))
ACTIVE(first1(z0, z1)) → c30(FIRST1(z0, active(z1)), ACTIVE(z1))
ACTIVE(cons1(z0, z1)) → c31(CONS1(active(z0), z1), ACTIVE(z0))
ACTIVE(cons1(z0, z1)) → c32(CONS1(z0, active(z1)), ACTIVE(z1))
ACTIVE(s1(z0)) → c33(S1(active(z0)), ACTIVE(z0))
ACTIVE(unquote(z0)) → c34(UNQUOTE(active(z0)), ACTIVE(z0))
ACTIVE(unquote1(z0)) → c35(UNQUOTE1(active(z0)), ACTIVE(z0))
ACTIVE(fcons(z0, z1)) → c36(FCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(fcons(z0, z1)) → c37(FCONS(z0, active(z1)), ACTIVE(z1))
SEL(mark(z0), z1) → c38(SEL(z0, z1))
SEL(z0, mark(z1)) → c39(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c40(SEL(z0, z1))
S(mark(z0)) → c41(S(z0))
S(ok(z0)) → c42(S(z0))
CONS(mark(z0), z1) → c43(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c44(CONS(z0, z1))
FIRST(mark(z0), z1) → c45(FIRST(z0, z1))
FIRST(z0, mark(z1)) → c46(FIRST(z0, z1))
FIRST(ok(z0), ok(z1)) → c47(FIRST(z0, z1))
FROM(mark(z0)) → c48(FROM(z0))
FROM(ok(z0)) → c49(FROM(z0))
SEL1(mark(z0), z1) → c50(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c51(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c52(SEL1(z0, z1))
FIRST1(mark(z0), z1) → c53(FIRST1(z0, z1))
FIRST1(z0, mark(z1)) → c54(FIRST1(z0, z1))
FIRST1(ok(z0), ok(z1)) → c55(FIRST1(z0, z1))
CONS1(mark(z0), z1) → c56(CONS1(z0, z1))
CONS1(z0, mark(z1)) → c57(CONS1(z0, z1))
CONS1(ok(z0), ok(z1)) → c58(CONS1(z0, z1))
S1(mark(z0)) → c59(S1(z0))
S1(ok(z0)) → c60(S1(z0))
UNQUOTE(mark(z0)) → c61(UNQUOTE(z0))
UNQUOTE(ok(z0)) → c62(UNQUOTE(z0))
UNQUOTE1(mark(z0)) → c63(UNQUOTE1(z0))
UNQUOTE1(ok(z0)) → c64(UNQUOTE1(z0))
FCONS(mark(z0), z1) → c65(FCONS(z0, z1))
FCONS(z0, mark(z1)) → c66(FCONS(z0, z1))
FCONS(ok(z0), ok(z1)) → c67(FCONS(z0, z1))
PROPER(sel(z0, z1)) → c68(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(s(z0)) → c69(S(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c70(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(first(z0, z1)) → c72(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c74(FROM(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c75(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c76(QUOTE(proper(z0)), PROPER(z0))
PROPER(first1(z0, z1)) → c77(FIRST1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(cons1(z0, z1)) → c79(CONS1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote1(z0)) → c81(QUOTE1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c82(S1(proper(z0)), PROPER(z0))
PROPER(unquote(z0)) → c83(UNQUOTE(proper(z0)), PROPER(z0))
PROPER(unquote1(z0)) → c84(UNQUOTE1(proper(z0)), PROPER(z0))
PROPER(fcons(z0, z1)) → c85(FCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
QUOTE(ok(z0)) → c86(QUOTE(z0))
QUOTE1(ok(z0)) → c87(QUOTE1(z0))
TOP(mark(z0)) → c88(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c89(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c4(S(z0))
ACTIVE(quote(s(z0))) → c12(QUOTE(z0))
ACTIVE(unquote(s1(z0))) → c16(UNQUOTE(z0))
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2)))
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2))
ACTIVE(first1(s(z0), cons(z1, z2))) → c1(CONS1(quote(z1), first1(z0, z2)))
ACTIVE(first1(s(z0), cons(z1, z2))) → c1(QUOTE(z1))
ACTIVE(first1(s(z0), cons(z1, z2))) → c1(FIRST1(z0, z2))
ACTIVE(quote1(cons(z0, z1))) → c1(CONS1(quote(z0), quote1(z1)))
ACTIVE(quote1(cons(z0, z1))) → c1(QUOTE(z0))
ACTIVE(quote1(cons(z0, z1))) → c1(QUOTE1(z1))
ACTIVE(unquote1(cons1(z0, z1))) → c1(FCONS(unquote(z0), unquote1(z1)))
ACTIVE(unquote1(cons1(z0, z1))) → c1(UNQUOTE(z0))
ACTIVE(unquote1(cons1(z0, z1))) → c1(UNQUOTE1(z1))
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c22(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(s(sel(0, cons(z0, z1)))) → c22(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(s(first(0, z0))) → c22(S(mark(nil)), ACTIVE(first(0, z0)))
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c22(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
ACTIVE(s(from(z0))) → c22(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(sel1(s(z0), cons(z1, z2)))) → c22(S(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(s(sel1(0, cons(z0, z1)))) → c22(S(mark(quote(z0))), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(s(first1(0, z0))) → c22(S(mark(nil1)), ACTIVE(first1(0, z0)))
ACTIVE(s(first1(s(z0), cons(z1, z2)))) → c22(S(mark(cons1(quote(z1), first1(z0, z2)))), ACTIVE(first1(s(z0), cons(z1, z2))))
ACTIVE(s(unquote(01))) → c22(S(mark(0)), ACTIVE(unquote(01)))
ACTIVE(s(unquote(s1(z0)))) → c22(S(mark(s(unquote(z0)))), ACTIVE(unquote(s1(z0))))
ACTIVE(s(unquote1(nil1))) → c22(S(mark(nil)), ACTIVE(unquote1(nil1)))
ACTIVE(s(unquote1(cons1(z0, z1)))) → c22(S(mark(fcons(unquote(z0), unquote1(z1)))), ACTIVE(unquote1(cons1(z0, z1))))
ACTIVE(s(fcons(z0, z1))) → c22(S(mark(cons(z0, z1))), ACTIVE(fcons(z0, z1)))
ACTIVE(s(sel(z0, z1))) → c22(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(s(sel(z0, z1))) → c22(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(s(s(z0))) → c22(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(cons(z0, z1))) → c22(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(first(z0, z1))) → c22(S(first(active(z0), z1)), ACTIVE(first(z0, z1)))
ACTIVE(s(first(z0, z1))) → c22(S(first(z0, active(z1))), ACTIVE(first(z0, z1)))
ACTIVE(s(from(z0))) → c22(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(sel1(z0, z1))) → c22(S(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(s(sel1(z0, z1))) → c22(S(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(s(first1(z0, z1))) → c22(S(first1(active(z0), z1)), ACTIVE(first1(z0, z1)))
ACTIVE(s(first1(z0, z1))) → c22(S(first1(z0, active(z1))), ACTIVE(first1(z0, z1)))
ACTIVE(s(cons1(z0, z1))) → c22(S(cons1(active(z0), z1)), ACTIVE(cons1(z0, z1)))
ACTIVE(s(cons1(z0, z1))) → c22(S(cons1(z0, active(z1))), ACTIVE(cons1(z0, z1)))
ACTIVE(s(s1(z0))) → c22(S(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(s(unquote(z0))) → c22(S(unquote(active(z0))), ACTIVE(unquote(z0)))
ACTIVE(s(unquote1(z0))) → c22(S(unquote1(active(z0))), ACTIVE(unquote1(z0)))
ACTIVE(s(fcons(z0, z1))) → c22(S(fcons(active(z0), z1)), ACTIVE(fcons(z0, z1)))
ACTIVE(s(fcons(z0, z1))) → c22(S(fcons(z0, active(z1))), ACTIVE(fcons(z0, z1)))
ACTIVE(s(quote(0))) → c22(S(mark(01)))
ACTIVE(s(quote1(nil))) → c22(S(mark(nil1)))
ACTIVE(s(quote1(cons(z0, z1)))) → c2(S(mark(cons1(quote(z0), quote1(z1)))))
ACTIVE(s(quote1(cons(z0, z1)))) → c2(ACTIVE(quote1(cons(z0, z1))))
ACTIVE(s(quote(s(z0)))) → c2(S(mark(s1(quote(z0)))))
ACTIVE(s(quote(s(z0)))) → c2(ACTIVE(quote(s(z0))))
ACTIVE(s(quote(sel(z0, z1)))) → c2(S(mark(sel1(z0, z1))))
ACTIVE(s(quote(sel(z0, z1)))) → c2(ACTIVE(quote(sel(z0, z1))))
ACTIVE(s(quote1(first(z0, z1)))) → c2(S(mark(first1(z0, z1))))
ACTIVE(s(quote1(first(z0, z1)))) → c2(ACTIVE(quote1(first(z0, z1))))
S tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c5(SEL1(z0, z2))
ACTIVE(sel1(0, cons(z0, z1))) → c6(QUOTE(z0))
ACTIVE(quote(sel(z0, z1))) → c13(SEL1(z0, z1))
ACTIVE(quote1(first(z0, z1))) → c14(FIRST1(z0, z1))
ACTIVE(fcons(z0, z1)) → c19(CONS(z0, z1))
ACTIVE(sel(z0, z1)) → c20(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c21(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(cons(z0, z1)) → c23(CONS(active(z0), z1), ACTIVE(z0))
ACTIVE(first(z0, z1)) → c24(FIRST(active(z0), z1), ACTIVE(z0))
ACTIVE(first(z0, z1)) → c25(FIRST(z0, active(z1)), ACTIVE(z1))
ACTIVE(from(z0)) → c26(FROM(active(z0)), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c27(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c28(SEL1(z0, active(z1)), ACTIVE(z1))
ACTIVE(first1(z0, z1)) → c29(FIRST1(active(z0), z1), ACTIVE(z0))
ACTIVE(first1(z0, z1)) → c30(FIRST1(z0, active(z1)), ACTIVE(z1))
ACTIVE(cons1(z0, z1)) → c31(CONS1(active(z0), z1), ACTIVE(z0))
ACTIVE(cons1(z0, z1)) → c32(CONS1(z0, active(z1)), ACTIVE(z1))
ACTIVE(s1(z0)) → c33(S1(active(z0)), ACTIVE(z0))
ACTIVE(unquote(z0)) → c34(UNQUOTE(active(z0)), ACTIVE(z0))
ACTIVE(unquote1(z0)) → c35(UNQUOTE1(active(z0)), ACTIVE(z0))
ACTIVE(fcons(z0, z1)) → c36(FCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(fcons(z0, z1)) → c37(FCONS(z0, active(z1)), ACTIVE(z1))
SEL(mark(z0), z1) → c38(SEL(z0, z1))
SEL(z0, mark(z1)) → c39(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c40(SEL(z0, z1))
S(mark(z0)) → c41(S(z0))
S(ok(z0)) → c42(S(z0))
CONS(mark(z0), z1) → c43(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c44(CONS(z0, z1))
FIRST(mark(z0), z1) → c45(FIRST(z0, z1))
FIRST(z0, mark(z1)) → c46(FIRST(z0, z1))
FIRST(ok(z0), ok(z1)) → c47(FIRST(z0, z1))
FROM(mark(z0)) → c48(FROM(z0))
FROM(ok(z0)) → c49(FROM(z0))
SEL1(mark(z0), z1) → c50(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c51(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c52(SEL1(z0, z1))
FIRST1(mark(z0), z1) → c53(FIRST1(z0, z1))
FIRST1(z0, mark(z1)) → c54(FIRST1(z0, z1))
FIRST1(ok(z0), ok(z1)) → c55(FIRST1(z0, z1))
CONS1(mark(z0), z1) → c56(CONS1(z0, z1))
CONS1(z0, mark(z1)) → c57(CONS1(z0, z1))
CONS1(ok(z0), ok(z1)) → c58(CONS1(z0, z1))
S1(mark(z0)) → c59(S1(z0))
S1(ok(z0)) → c60(S1(z0))
UNQUOTE(mark(z0)) → c61(UNQUOTE(z0))
UNQUOTE(ok(z0)) → c62(UNQUOTE(z0))
UNQUOTE1(mark(z0)) → c63(UNQUOTE1(z0))
UNQUOTE1(ok(z0)) → c64(UNQUOTE1(z0))
FCONS(mark(z0), z1) → c65(FCONS(z0, z1))
FCONS(z0, mark(z1)) → c66(FCONS(z0, z1))
FCONS(ok(z0), ok(z1)) → c67(FCONS(z0, z1))
PROPER(sel(z0, z1)) → c68(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(s(z0)) → c69(S(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c70(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(first(z0, z1)) → c72(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c74(FROM(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c75(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c76(QUOTE(proper(z0)), PROPER(z0))
PROPER(first1(z0, z1)) → c77(FIRST1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(cons1(z0, z1)) → c79(CONS1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote1(z0)) → c81(QUOTE1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c82(S1(proper(z0)), PROPER(z0))
PROPER(unquote(z0)) → c83(UNQUOTE(proper(z0)), PROPER(z0))
PROPER(unquote1(z0)) → c84(UNQUOTE1(proper(z0)), PROPER(z0))
PROPER(fcons(z0, z1)) → c85(FCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
QUOTE(ok(z0)) → c86(QUOTE(z0))
QUOTE1(ok(z0)) → c87(QUOTE1(z0))
TOP(mark(z0)) → c88(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c89(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c4(S(z0))
ACTIVE(quote(s(z0))) → c12(QUOTE(z0))
ACTIVE(unquote(s1(z0))) → c16(UNQUOTE(z0))
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2)))
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2))
ACTIVE(first1(s(z0), cons(z1, z2))) → c1(CONS1(quote(z1), first1(z0, z2)))
ACTIVE(first1(s(z0), cons(z1, z2))) → c1(QUOTE(z1))
ACTIVE(first1(s(z0), cons(z1, z2))) → c1(FIRST1(z0, z2))
ACTIVE(quote1(cons(z0, z1))) → c1(CONS1(quote(z0), quote1(z1)))
ACTIVE(quote1(cons(z0, z1))) → c1(QUOTE(z0))
ACTIVE(quote1(cons(z0, z1))) → c1(QUOTE1(z1))
ACTIVE(unquote1(cons1(z0, z1))) → c1(FCONS(unquote(z0), unquote1(z1)))
ACTIVE(unquote1(cons1(z0, z1))) → c1(UNQUOTE(z0))
ACTIVE(unquote1(cons1(z0, z1))) → c1(UNQUOTE1(z1))
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c22(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(s(sel(0, cons(z0, z1)))) → c22(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(s(first(0, z0))) → c22(S(mark(nil)), ACTIVE(first(0, z0)))
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c22(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
ACTIVE(s(from(z0))) → c22(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(sel1(s(z0), cons(z1, z2)))) → c22(S(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(s(sel1(0, cons(z0, z1)))) → c22(S(mark(quote(z0))), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(s(first1(0, z0))) → c22(S(mark(nil1)), ACTIVE(first1(0, z0)))
ACTIVE(s(first1(s(z0), cons(z1, z2)))) → c22(S(mark(cons1(quote(z1), first1(z0, z2)))), ACTIVE(first1(s(z0), cons(z1, z2))))
ACTIVE(s(unquote(01))) → c22(S(mark(0)), ACTIVE(unquote(01)))
ACTIVE(s(unquote(s1(z0)))) → c22(S(mark(s(unquote(z0)))), ACTIVE(unquote(s1(z0))))
ACTIVE(s(unquote1(nil1))) → c22(S(mark(nil)), ACTIVE(unquote1(nil1)))
ACTIVE(s(unquote1(cons1(z0, z1)))) → c22(S(mark(fcons(unquote(z0), unquote1(z1)))), ACTIVE(unquote1(cons1(z0, z1))))
ACTIVE(s(fcons(z0, z1))) → c22(S(mark(cons(z0, z1))), ACTIVE(fcons(z0, z1)))
ACTIVE(s(sel(z0, z1))) → c22(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(s(sel(z0, z1))) → c22(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(s(s(z0))) → c22(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(cons(z0, z1))) → c22(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(first(z0, z1))) → c22(S(first(active(z0), z1)), ACTIVE(first(z0, z1)))
ACTIVE(s(first(z0, z1))) → c22(S(first(z0, active(z1))), ACTIVE(first(z0, z1)))
ACTIVE(s(from(z0))) → c22(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(sel1(z0, z1))) → c22(S(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(s(sel1(z0, z1))) → c22(S(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(s(first1(z0, z1))) → c22(S(first1(active(z0), z1)), ACTIVE(first1(z0, z1)))
ACTIVE(s(first1(z0, z1))) → c22(S(first1(z0, active(z1))), ACTIVE(first1(z0, z1)))
ACTIVE(s(cons1(z0, z1))) → c22(S(cons1(active(z0), z1)), ACTIVE(cons1(z0, z1)))
ACTIVE(s(cons1(z0, z1))) → c22(S(cons1(z0, active(z1))), ACTIVE(cons1(z0, z1)))
ACTIVE(s(s1(z0))) → c22(S(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(s(unquote(z0))) → c22(S(unquote(active(z0))), ACTIVE(unquote(z0)))
ACTIVE(s(unquote1(z0))) → c22(S(unquote1(active(z0))), ACTIVE(unquote1(z0)))
ACTIVE(s(fcons(z0, z1))) → c22(S(fcons(active(z0), z1)), ACTIVE(fcons(z0, z1)))
ACTIVE(s(fcons(z0, z1))) → c22(S(fcons(z0, active(z1))), ACTIVE(fcons(z0, z1)))
ACTIVE(s(quote(0))) → c22(S(mark(01)))
ACTIVE(s(quote1(nil))) → c22(S(mark(nil1)))
ACTIVE(s(quote1(cons(z0, z1)))) → c2(S(mark(cons1(quote(z0), quote1(z1)))))
ACTIVE(s(quote1(cons(z0, z1)))) → c2(ACTIVE(quote1(cons(z0, z1))))
ACTIVE(s(quote(s(z0)))) → c2(S(mark(s1(quote(z0)))))
ACTIVE(s(quote(s(z0)))) → c2(ACTIVE(quote(s(z0))))
ACTIVE(s(quote(sel(z0, z1)))) → c2(S(mark(sel1(z0, z1))))
ACTIVE(s(quote(sel(z0, z1)))) → c2(ACTIVE(quote(sel(z0, z1))))
ACTIVE(s(quote1(first(z0, z1)))) → c2(S(mark(first1(z0, z1))))
ACTIVE(s(quote1(first(z0, z1)))) → c2(ACTIVE(quote1(first(z0, z1))))
K tuples:none
Defined Rule Symbols:

active, sel, cons, first, sel1, quote, cons1, first1, quote1, fcons, unquote, unquote1, s, from, s1, proper

Defined Pair Symbols:

ACTIVE, SEL, S, CONS, FIRST, FROM, SEL1, FIRST1, CONS1, S1, UNQUOTE, UNQUOTE1, FCONS, PROPER, QUOTE, QUOTE1, TOP

Compound Symbols:

c, c5, c6, c13, c14, c19, c20, c21, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c66, c67, c68, c69, c70, c72, c74, c75, c76, c77, c79, c81, c82, c83, c84, c85, c86, c87, c88, c89, c4, c12, c16, c1, c22, c22, c2

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

Use narrowing to replace ACTIVE(cons(z0, z1)) → c23(CONS(active(z0), z1), ACTIVE(z0)) by

ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c23(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c23(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(cons(first(0, z0), x1)) → c23(CONS(mark(nil), x1), ACTIVE(first(0, z0)))
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c23(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2))))
ACTIVE(cons(from(z0), x1)) → c23(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(sel1(s(z0), cons(z1, z2)), x1)) → c23(CONS(mark(sel1(z0, z2)), x1), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(cons(sel1(0, cons(z0, z1)), x1)) → c23(CONS(mark(quote(z0)), x1), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(cons(first1(0, z0), x1)) → c23(CONS(mark(nil1), x1), ACTIVE(first1(0, z0)))
ACTIVE(cons(first1(s(z0), cons(z1, z2)), x1)) → c23(CONS(mark(cons1(quote(z1), first1(z0, z2))), x1), ACTIVE(first1(s(z0), cons(z1, z2))))
ACTIVE(cons(quote(0), x1)) → c23(CONS(mark(01), x1), ACTIVE(quote(0)))
ACTIVE(cons(quote1(cons(z0, z1)), x1)) → c23(CONS(mark(cons1(quote(z0), quote1(z1))), x1), ACTIVE(quote1(cons(z0, z1))))
ACTIVE(cons(quote1(nil), x1)) → c23(CONS(mark(nil1), x1), ACTIVE(quote1(nil)))
ACTIVE(cons(quote(s(z0)), x1)) → c23(CONS(mark(s1(quote(z0))), x1), ACTIVE(quote(s(z0))))
ACTIVE(cons(quote(sel(z0, z1)), x1)) → c23(CONS(mark(sel1(z0, z1)), x1), ACTIVE(quote(sel(z0, z1))))
ACTIVE(cons(quote1(first(z0, z1)), x1)) → c23(CONS(mark(first1(z0, z1)), x1), ACTIVE(quote1(first(z0, z1))))
ACTIVE(cons(unquote(01), x1)) → c23(CONS(mark(0), x1), ACTIVE(unquote(01)))
ACTIVE(cons(unquote(s1(z0)), x1)) → c23(CONS(mark(s(unquote(z0))), x1), ACTIVE(unquote(s1(z0))))
ACTIVE(cons(unquote1(nil1), x1)) → c23(CONS(mark(nil), x1), ACTIVE(unquote1(nil1)))
ACTIVE(cons(unquote1(cons1(z0, z1)), x1)) → c23(CONS(mark(fcons(unquote(z0), unquote1(z1))), x1), ACTIVE(unquote1(cons1(z0, z1))))
ACTIVE(cons(fcons(z0, z1), x1)) → c23(CONS(mark(cons(z0, z1)), x1), ACTIVE(fcons(z0, z1)))
ACTIVE(cons(sel(z0, z1), x1)) → c23(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
ACTIVE(cons(sel(z0, z1), x1)) → c23(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
ACTIVE(cons(s(z0), x1)) → c23(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c23(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(first(z0, z1), x1)) → c23(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1)))
ACTIVE(cons(first(z0, z1), x1)) → c23(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c23(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(sel1(z0, z1), x1)) → c23(CONS(sel1(active(z0), z1), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(cons(sel1(z0, z1), x1)) → c23(CONS(sel1(z0, active(z1)), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(cons(first1(z0, z1), x1)) → c23(CONS(first1(active(z0), z1), x1), ACTIVE(first1(z0, z1)))
ACTIVE(cons(first1(z0, z1), x1)) → c23(CONS(first1(z0, active(z1)), x1), ACTIVE(first1(z0, z1)))
ACTIVE(cons(cons1(z0, z1), x1)) → c23(CONS(cons1(active(z0), z1), x1), ACTIVE(cons1(z0, z1)))
ACTIVE(cons(cons1(z0, z1), x1)) → c23(CONS(cons1(z0, active(z1)), x1), ACTIVE(cons1(z0, z1)))
ACTIVE(cons(s1(z0), x1)) → c23(CONS(s1(active(z0)), x1), ACTIVE(s1(z0)))
ACTIVE(cons(unquote(z0), x1)) → c23(CONS(unquote(active(z0)), x1), ACTIVE(unquote(z0)))
ACTIVE(cons(unquote1(z0), x1)) → c23(CONS(unquote1(active(z0)), x1), ACTIVE(unquote1(z0)))
ACTIVE(cons(fcons(z0, z1), x1)) → c23(CONS(fcons(active(z0), z1), x1), ACTIVE(fcons(z0, z1)))
ACTIVE(cons(fcons(z0, z1), x1)) → c23(CONS(fcons(z0, active(z1)), x1), ACTIVE(fcons(z0, z1)))

(18) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2))
active(sel(0, cons(z0, z1))) → mark(z0)
active(first(0, z0)) → mark(nil)
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2)))
active(from(z0)) → mark(cons(z0, from(s(z0))))
active(sel1(s(z0), cons(z1, z2))) → mark(sel1(z0, z2))
active(sel1(0, cons(z0, z1))) → mark(quote(z0))
active(first1(0, z0)) → mark(nil1)
active(first1(s(z0), cons(z1, z2))) → mark(cons1(quote(z1), first1(z0, z2)))
active(quote(0)) → mark(01)
active(quote1(cons(z0, z1))) → mark(cons1(quote(z0), quote1(z1)))
active(quote1(nil)) → mark(nil1)
active(quote(s(z0))) → mark(s1(quote(z0)))
active(quote(sel(z0, z1))) → mark(sel1(z0, z1))
active(quote1(first(z0, z1))) → mark(first1(z0, z1))
active(unquote(01)) → mark(0)
active(unquote(s1(z0))) → mark(s(unquote(z0)))
active(unquote1(nil1)) → mark(nil)
active(unquote1(cons1(z0, z1))) → mark(fcons(unquote(z0), unquote1(z1)))
active(fcons(z0, z1)) → mark(cons(z0, z1))
active(sel(z0, z1)) → sel(active(z0), z1)
active(sel(z0, z1)) → sel(z0, active(z1))
active(s(z0)) → s(active(z0))
active(cons(z0, z1)) → cons(active(z0), z1)
active(first(z0, z1)) → first(active(z0), z1)
active(first(z0, z1)) → first(z0, active(z1))
active(from(z0)) → from(active(z0))
active(sel1(z0, z1)) → sel1(active(z0), z1)
active(sel1(z0, z1)) → sel1(z0, active(z1))
active(first1(z0, z1)) → first1(active(z0), z1)
active(first1(z0, z1)) → first1(z0, active(z1))
active(cons1(z0, z1)) → cons1(active(z0), z1)
active(cons1(z0, z1)) → cons1(z0, active(z1))
active(s1(z0)) → s1(active(z0))
active(unquote(z0)) → unquote(active(z0))
active(unquote1(z0)) → unquote1(active(z0))
active(fcons(z0, z1)) → fcons(active(z0), z1)
active(fcons(z0, z1)) → fcons(z0, active(z1))
sel(z0, mark(z1)) → mark(sel(z0, z1))
sel(mark(z0), z1) → mark(sel(z0, z1))
sel(ok(z0), ok(z1)) → ok(sel(z0, z1))
cons(ok(z0), ok(z1)) → ok(cons(z0, z1))
cons(mark(z0), z1) → mark(cons(z0, z1))
first(z0, mark(z1)) → mark(first(z0, z1))
first(mark(z0), z1) → mark(first(z0, z1))
first(ok(z0), ok(z1)) → ok(first(z0, z1))
sel1(z0, mark(z1)) → mark(sel1(z0, z1))
sel1(mark(z0), z1) → mark(sel1(z0, z1))
sel1(ok(z0), ok(z1)) → ok(sel1(z0, z1))
quote(ok(z0)) → ok(quote(z0))
cons1(mark(z0), z1) → mark(cons1(z0, z1))
cons1(z0, mark(z1)) → mark(cons1(z0, z1))
cons1(ok(z0), ok(z1)) → ok(cons1(z0, z1))
first1(z0, mark(z1)) → mark(first1(z0, z1))
first1(mark(z0), z1) → mark(first1(z0, z1))
first1(ok(z0), ok(z1)) → ok(first1(z0, z1))
quote1(ok(z0)) → ok(quote1(z0))
fcons(mark(z0), z1) → mark(fcons(z0, z1))
fcons(z0, mark(z1)) → mark(fcons(z0, z1))
fcons(ok(z0), ok(z1)) → ok(fcons(z0, z1))
unquote(ok(z0)) → ok(unquote(z0))
unquote(mark(z0)) → mark(unquote(z0))
unquote1(ok(z0)) → ok(unquote1(z0))
unquote1(mark(z0)) → mark(unquote1(z0))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
from(mark(z0)) → mark(from(z0))
from(ok(z0)) → ok(from(z0))
s1(mark(z0)) → mark(s1(z0))
s1(ok(z0)) → ok(s1(z0))
proper(sel(z0, z1)) → sel(proper(z0), proper(z1))
proper(s(z0)) → s(proper(z0))
proper(cons(z0, z1)) → cons(proper(z0), proper(z1))
proper(0) → ok(0)
proper(first(z0, z1)) → first(proper(z0), proper(z1))
proper(nil) → ok(nil)
proper(from(z0)) → from(proper(z0))
proper(sel1(z0, z1)) → sel1(proper(z0), proper(z1))
proper(quote(z0)) → quote(proper(z0))
proper(first1(z0, z1)) → first1(proper(z0), proper(z1))
proper(nil1) → ok(nil1)
proper(cons1(z0, z1)) → cons1(proper(z0), proper(z1))
proper(01) → ok(01)
proper(quote1(z0)) → quote1(proper(z0))
proper(s1(z0)) → s1(proper(z0))
proper(unquote(z0)) → unquote(proper(z0))
proper(unquote1(z0)) → unquote1(proper(z0))
proper(fcons(z0, z1)) → fcons(proper(z0), proper(z1))
Tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c5(SEL1(z0, z2))
ACTIVE(sel1(0, cons(z0, z1))) → c6(QUOTE(z0))
ACTIVE(quote(sel(z0, z1))) → c13(SEL1(z0, z1))
ACTIVE(quote1(first(z0, z1))) → c14(FIRST1(z0, z1))
ACTIVE(fcons(z0, z1)) → c19(CONS(z0, z1))
ACTIVE(sel(z0, z1)) → c20(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c21(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(first(z0, z1)) → c24(FIRST(active(z0), z1), ACTIVE(z0))
ACTIVE(first(z0, z1)) → c25(FIRST(z0, active(z1)), ACTIVE(z1))
ACTIVE(from(z0)) → c26(FROM(active(z0)), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c27(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c28(SEL1(z0, active(z1)), ACTIVE(z1))
ACTIVE(first1(z0, z1)) → c29(FIRST1(active(z0), z1), ACTIVE(z0))
ACTIVE(first1(z0, z1)) → c30(FIRST1(z0, active(z1)), ACTIVE(z1))
ACTIVE(cons1(z0, z1)) → c31(CONS1(active(z0), z1), ACTIVE(z0))
ACTIVE(cons1(z0, z1)) → c32(CONS1(z0, active(z1)), ACTIVE(z1))
ACTIVE(s1(z0)) → c33(S1(active(z0)), ACTIVE(z0))
ACTIVE(unquote(z0)) → c34(UNQUOTE(active(z0)), ACTIVE(z0))
ACTIVE(unquote1(z0)) → c35(UNQUOTE1(active(z0)), ACTIVE(z0))
ACTIVE(fcons(z0, z1)) → c36(FCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(fcons(z0, z1)) → c37(FCONS(z0, active(z1)), ACTIVE(z1))
SEL(mark(z0), z1) → c38(SEL(z0, z1))
SEL(z0, mark(z1)) → c39(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c40(SEL(z0, z1))
S(mark(z0)) → c41(S(z0))
S(ok(z0)) → c42(S(z0))
CONS(mark(z0), z1) → c43(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c44(CONS(z0, z1))
FIRST(mark(z0), z1) → c45(FIRST(z0, z1))
FIRST(z0, mark(z1)) → c46(FIRST(z0, z1))
FIRST(ok(z0), ok(z1)) → c47(FIRST(z0, z1))
FROM(mark(z0)) → c48(FROM(z0))
FROM(ok(z0)) → c49(FROM(z0))
SEL1(mark(z0), z1) → c50(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c51(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c52(SEL1(z0, z1))
FIRST1(mark(z0), z1) → c53(FIRST1(z0, z1))
FIRST1(z0, mark(z1)) → c54(FIRST1(z0, z1))
FIRST1(ok(z0), ok(z1)) → c55(FIRST1(z0, z1))
CONS1(mark(z0), z1) → c56(CONS1(z0, z1))
CONS1(z0, mark(z1)) → c57(CONS1(z0, z1))
CONS1(ok(z0), ok(z1)) → c58(CONS1(z0, z1))
S1(mark(z0)) → c59(S1(z0))
S1(ok(z0)) → c60(S1(z0))
UNQUOTE(mark(z0)) → c61(UNQUOTE(z0))
UNQUOTE(ok(z0)) → c62(UNQUOTE(z0))
UNQUOTE1(mark(z0)) → c63(UNQUOTE1(z0))
UNQUOTE1(ok(z0)) → c64(UNQUOTE1(z0))
FCONS(mark(z0), z1) → c65(FCONS(z0, z1))
FCONS(z0, mark(z1)) → c66(FCONS(z0, z1))
FCONS(ok(z0), ok(z1)) → c67(FCONS(z0, z1))
PROPER(sel(z0, z1)) → c68(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(s(z0)) → c69(S(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c70(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(first(z0, z1)) → c72(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c74(FROM(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c75(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c76(QUOTE(proper(z0)), PROPER(z0))
PROPER(first1(z0, z1)) → c77(FIRST1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(cons1(z0, z1)) → c79(CONS1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote1(z0)) → c81(QUOTE1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c82(S1(proper(z0)), PROPER(z0))
PROPER(unquote(z0)) → c83(UNQUOTE(proper(z0)), PROPER(z0))
PROPER(unquote1(z0)) → c84(UNQUOTE1(proper(z0)), PROPER(z0))
PROPER(fcons(z0, z1)) → c85(FCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
QUOTE(ok(z0)) → c86(QUOTE(z0))
QUOTE1(ok(z0)) → c87(QUOTE1(z0))
TOP(mark(z0)) → c88(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c89(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c4(S(z0))
ACTIVE(quote(s(z0))) → c12(QUOTE(z0))
ACTIVE(unquote(s1(z0))) → c16(UNQUOTE(z0))
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2)))
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2))
ACTIVE(first1(s(z0), cons(z1, z2))) → c1(CONS1(quote(z1), first1(z0, z2)))
ACTIVE(first1(s(z0), cons(z1, z2))) → c1(QUOTE(z1))
ACTIVE(first1(s(z0), cons(z1, z2))) → c1(FIRST1(z0, z2))
ACTIVE(quote1(cons(z0, z1))) → c1(CONS1(quote(z0), quote1(z1)))
ACTIVE(quote1(cons(z0, z1))) → c1(QUOTE(z0))
ACTIVE(quote1(cons(z0, z1))) → c1(QUOTE1(z1))
ACTIVE(unquote1(cons1(z0, z1))) → c1(FCONS(unquote(z0), unquote1(z1)))
ACTIVE(unquote1(cons1(z0, z1))) → c1(UNQUOTE(z0))
ACTIVE(unquote1(cons1(z0, z1))) → c1(UNQUOTE1(z1))
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c22(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(s(sel(0, cons(z0, z1)))) → c22(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(s(first(0, z0))) → c22(S(mark(nil)), ACTIVE(first(0, z0)))
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c22(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
ACTIVE(s(from(z0))) → c22(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(sel1(s(z0), cons(z1, z2)))) → c22(S(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(s(sel1(0, cons(z0, z1)))) → c22(S(mark(quote(z0))), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(s(first1(0, z0))) → c22(S(mark(nil1)), ACTIVE(first1(0, z0)))
ACTIVE(s(first1(s(z0), cons(z1, z2)))) → c22(S(mark(cons1(quote(z1), first1(z0, z2)))), ACTIVE(first1(s(z0), cons(z1, z2))))
ACTIVE(s(unquote(01))) → c22(S(mark(0)), ACTIVE(unquote(01)))
ACTIVE(s(unquote(s1(z0)))) → c22(S(mark(s(unquote(z0)))), ACTIVE(unquote(s1(z0))))
ACTIVE(s(unquote1(nil1))) → c22(S(mark(nil)), ACTIVE(unquote1(nil1)))
ACTIVE(s(unquote1(cons1(z0, z1)))) → c22(S(mark(fcons(unquote(z0), unquote1(z1)))), ACTIVE(unquote1(cons1(z0, z1))))
ACTIVE(s(fcons(z0, z1))) → c22(S(mark(cons(z0, z1))), ACTIVE(fcons(z0, z1)))
ACTIVE(s(sel(z0, z1))) → c22(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(s(sel(z0, z1))) → c22(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(s(s(z0))) → c22(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(cons(z0, z1))) → c22(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(first(z0, z1))) → c22(S(first(active(z0), z1)), ACTIVE(first(z0, z1)))
ACTIVE(s(first(z0, z1))) → c22(S(first(z0, active(z1))), ACTIVE(first(z0, z1)))
ACTIVE(s(from(z0))) → c22(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(sel1(z0, z1))) → c22(S(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(s(sel1(z0, z1))) → c22(S(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(s(first1(z0, z1))) → c22(S(first1(active(z0), z1)), ACTIVE(first1(z0, z1)))
ACTIVE(s(first1(z0, z1))) → c22(S(first1(z0, active(z1))), ACTIVE(first1(z0, z1)))
ACTIVE(s(cons1(z0, z1))) → c22(S(cons1(active(z0), z1)), ACTIVE(cons1(z0, z1)))
ACTIVE(s(cons1(z0, z1))) → c22(S(cons1(z0, active(z1))), ACTIVE(cons1(z0, z1)))
ACTIVE(s(s1(z0))) → c22(S(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(s(unquote(z0))) → c22(S(unquote(active(z0))), ACTIVE(unquote(z0)))
ACTIVE(s(unquote1(z0))) → c22(S(unquote1(active(z0))), ACTIVE(unquote1(z0)))
ACTIVE(s(fcons(z0, z1))) → c22(S(fcons(active(z0), z1)), ACTIVE(fcons(z0, z1)))
ACTIVE(s(fcons(z0, z1))) → c22(S(fcons(z0, active(z1))), ACTIVE(fcons(z0, z1)))
ACTIVE(s(quote(0))) → c22(S(mark(01)))
ACTIVE(s(quote1(nil))) → c22(S(mark(nil1)))
ACTIVE(s(quote1(cons(z0, z1)))) → c2(S(mark(cons1(quote(z0), quote1(z1)))))
ACTIVE(s(quote1(cons(z0, z1)))) → c2(ACTIVE(quote1(cons(z0, z1))))
ACTIVE(s(quote(s(z0)))) → c2(S(mark(s1(quote(z0)))))
ACTIVE(s(quote(s(z0)))) → c2(ACTIVE(quote(s(z0))))
ACTIVE(s(quote(sel(z0, z1)))) → c2(S(mark(sel1(z0, z1))))
ACTIVE(s(quote(sel(z0, z1)))) → c2(ACTIVE(quote(sel(z0, z1))))
ACTIVE(s(quote1(first(z0, z1)))) → c2(S(mark(first1(z0, z1))))
ACTIVE(s(quote1(first(z0, z1)))) → c2(ACTIVE(quote1(first(z0, z1))))
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c23(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c23(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(cons(first(0, z0), x1)) → c23(CONS(mark(nil), x1), ACTIVE(first(0, z0)))
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c23(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2))))
ACTIVE(cons(from(z0), x1)) → c23(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(sel1(s(z0), cons(z1, z2)), x1)) → c23(CONS(mark(sel1(z0, z2)), x1), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(cons(sel1(0, cons(z0, z1)), x1)) → c23(CONS(mark(quote(z0)), x1), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(cons(first1(0, z0), x1)) → c23(CONS(mark(nil1), x1), ACTIVE(first1(0, z0)))
ACTIVE(cons(first1(s(z0), cons(z1, z2)), x1)) → c23(CONS(mark(cons1(quote(z1), first1(z0, z2))), x1), ACTIVE(first1(s(z0), cons(z1, z2))))
ACTIVE(cons(quote(0), x1)) → c23(CONS(mark(01), x1), ACTIVE(quote(0)))
ACTIVE(cons(quote1(cons(z0, z1)), x1)) → c23(CONS(mark(cons1(quote(z0), quote1(z1))), x1), ACTIVE(quote1(cons(z0, z1))))
ACTIVE(cons(quote1(nil), x1)) → c23(CONS(mark(nil1), x1), ACTIVE(quote1(nil)))
ACTIVE(cons(quote(s(z0)), x1)) → c23(CONS(mark(s1(quote(z0))), x1), ACTIVE(quote(s(z0))))
ACTIVE(cons(quote(sel(z0, z1)), x1)) → c23(CONS(mark(sel1(z0, z1)), x1), ACTIVE(quote(sel(z0, z1))))
ACTIVE(cons(quote1(first(z0, z1)), x1)) → c23(CONS(mark(first1(z0, z1)), x1), ACTIVE(quote1(first(z0, z1))))
ACTIVE(cons(unquote(01), x1)) → c23(CONS(mark(0), x1), ACTIVE(unquote(01)))
ACTIVE(cons(unquote(s1(z0)), x1)) → c23(CONS(mark(s(unquote(z0))), x1), ACTIVE(unquote(s1(z0))))
ACTIVE(cons(unquote1(nil1), x1)) → c23(CONS(mark(nil), x1), ACTIVE(unquote1(nil1)))
ACTIVE(cons(unquote1(cons1(z0, z1)), x1)) → c23(CONS(mark(fcons(unquote(z0), unquote1(z1))), x1), ACTIVE(unquote1(cons1(z0, z1))))
ACTIVE(cons(fcons(z0, z1), x1)) → c23(CONS(mark(cons(z0, z1)), x1), ACTIVE(fcons(z0, z1)))
ACTIVE(cons(sel(z0, z1), x1)) → c23(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
ACTIVE(cons(sel(z0, z1), x1)) → c23(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
ACTIVE(cons(s(z0), x1)) → c23(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c23(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(first(z0, z1), x1)) → c23(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1)))
ACTIVE(cons(first(z0, z1), x1)) → c23(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c23(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(sel1(z0, z1), x1)) → c23(CONS(sel1(active(z0), z1), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(cons(sel1(z0, z1), x1)) → c23(CONS(sel1(z0, active(z1)), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(cons(first1(z0, z1), x1)) → c23(CONS(first1(active(z0), z1), x1), ACTIVE(first1(z0, z1)))
ACTIVE(cons(first1(z0, z1), x1)) → c23(CONS(first1(z0, active(z1)), x1), ACTIVE(first1(z0, z1)))
ACTIVE(cons(cons1(z0, z1), x1)) → c23(CONS(cons1(active(z0), z1), x1), ACTIVE(cons1(z0, z1)))
ACTIVE(cons(cons1(z0, z1), x1)) → c23(CONS(cons1(z0, active(z1)), x1), ACTIVE(cons1(z0, z1)))
ACTIVE(cons(s1(z0), x1)) → c23(CONS(s1(active(z0)), x1), ACTIVE(s1(z0)))
ACTIVE(cons(unquote(z0), x1)) → c23(CONS(unquote(active(z0)), x1), ACTIVE(unquote(z0)))
ACTIVE(cons(unquote1(z0), x1)) → c23(CONS(unquote1(active(z0)), x1), ACTIVE(unquote1(z0)))
ACTIVE(cons(fcons(z0, z1), x1)) → c23(CONS(fcons(active(z0), z1), x1), ACTIVE(fcons(z0, z1)))
ACTIVE(cons(fcons(z0, z1), x1)) → c23(CONS(fcons(z0, active(z1)), x1), ACTIVE(fcons(z0, z1)))
S tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c(SEL(z0, z2))
ACTIVE(sel1(s(z0), cons(z1, z2))) → c5(SEL1(z0, z2))
ACTIVE(sel1(0, cons(z0, z1))) → c6(QUOTE(z0))
ACTIVE(quote(sel(z0, z1))) → c13(SEL1(z0, z1))
ACTIVE(quote1(first(z0, z1))) → c14(FIRST1(z0, z1))
ACTIVE(fcons(z0, z1)) → c19(CONS(z0, z1))
ACTIVE(sel(z0, z1)) → c20(SEL(active(z0), z1), ACTIVE(z0))
ACTIVE(sel(z0, z1)) → c21(SEL(z0, active(z1)), ACTIVE(z1))
ACTIVE(first(z0, z1)) → c24(FIRST(active(z0), z1), ACTIVE(z0))
ACTIVE(first(z0, z1)) → c25(FIRST(z0, active(z1)), ACTIVE(z1))
ACTIVE(from(z0)) → c26(FROM(active(z0)), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c27(SEL1(active(z0), z1), ACTIVE(z0))
ACTIVE(sel1(z0, z1)) → c28(SEL1(z0, active(z1)), ACTIVE(z1))
ACTIVE(first1(z0, z1)) → c29(FIRST1(active(z0), z1), ACTIVE(z0))
ACTIVE(first1(z0, z1)) → c30(FIRST1(z0, active(z1)), ACTIVE(z1))
ACTIVE(cons1(z0, z1)) → c31(CONS1(active(z0), z1), ACTIVE(z0))
ACTIVE(cons1(z0, z1)) → c32(CONS1(z0, active(z1)), ACTIVE(z1))
ACTIVE(s1(z0)) → c33(S1(active(z0)), ACTIVE(z0))
ACTIVE(unquote(z0)) → c34(UNQUOTE(active(z0)), ACTIVE(z0))
ACTIVE(unquote1(z0)) → c35(UNQUOTE1(active(z0)), ACTIVE(z0))
ACTIVE(fcons(z0, z1)) → c36(FCONS(active(z0), z1), ACTIVE(z0))
ACTIVE(fcons(z0, z1)) → c37(FCONS(z0, active(z1)), ACTIVE(z1))
SEL(mark(z0), z1) → c38(SEL(z0, z1))
SEL(z0, mark(z1)) → c39(SEL(z0, z1))
SEL(ok(z0), ok(z1)) → c40(SEL(z0, z1))
S(mark(z0)) → c41(S(z0))
S(ok(z0)) → c42(S(z0))
CONS(mark(z0), z1) → c43(CONS(z0, z1))
CONS(ok(z0), ok(z1)) → c44(CONS(z0, z1))
FIRST(mark(z0), z1) → c45(FIRST(z0, z1))
FIRST(z0, mark(z1)) → c46(FIRST(z0, z1))
FIRST(ok(z0), ok(z1)) → c47(FIRST(z0, z1))
FROM(mark(z0)) → c48(FROM(z0))
FROM(ok(z0)) → c49(FROM(z0))
SEL1(mark(z0), z1) → c50(SEL1(z0, z1))
SEL1(z0, mark(z1)) → c51(SEL1(z0, z1))
SEL1(ok(z0), ok(z1)) → c52(SEL1(z0, z1))
FIRST1(mark(z0), z1) → c53(FIRST1(z0, z1))
FIRST1(z0, mark(z1)) → c54(FIRST1(z0, z1))
FIRST1(ok(z0), ok(z1)) → c55(FIRST1(z0, z1))
CONS1(mark(z0), z1) → c56(CONS1(z0, z1))
CONS1(z0, mark(z1)) → c57(CONS1(z0, z1))
CONS1(ok(z0), ok(z1)) → c58(CONS1(z0, z1))
S1(mark(z0)) → c59(S1(z0))
S1(ok(z0)) → c60(S1(z0))
UNQUOTE(mark(z0)) → c61(UNQUOTE(z0))
UNQUOTE(ok(z0)) → c62(UNQUOTE(z0))
UNQUOTE1(mark(z0)) → c63(UNQUOTE1(z0))
UNQUOTE1(ok(z0)) → c64(UNQUOTE1(z0))
FCONS(mark(z0), z1) → c65(FCONS(z0, z1))
FCONS(z0, mark(z1)) → c66(FCONS(z0, z1))
FCONS(ok(z0), ok(z1)) → c67(FCONS(z0, z1))
PROPER(sel(z0, z1)) → c68(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(s(z0)) → c69(S(proper(z0)), PROPER(z0))
PROPER(cons(z0, z1)) → c70(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(first(z0, z1)) → c72(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(from(z0)) → c74(FROM(proper(z0)), PROPER(z0))
PROPER(sel1(z0, z1)) → c75(SEL1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote(z0)) → c76(QUOTE(proper(z0)), PROPER(z0))
PROPER(first1(z0, z1)) → c77(FIRST1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(cons1(z0, z1)) → c79(CONS1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(quote1(z0)) → c81(QUOTE1(proper(z0)), PROPER(z0))
PROPER(s1(z0)) → c82(S1(proper(z0)), PROPER(z0))
PROPER(unquote(z0)) → c83(UNQUOTE(proper(z0)), PROPER(z0))
PROPER(unquote1(z0)) → c84(UNQUOTE1(proper(z0)), PROPER(z0))
PROPER(fcons(z0, z1)) → c85(FCONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
QUOTE(ok(z0)) → c86(QUOTE(z0))
QUOTE1(ok(z0)) → c87(QUOTE1(z0))
TOP(mark(z0)) → c88(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c89(TOP(active(z0)), ACTIVE(z0))
ACTIVE(from(z0)) → c4(S(z0))
ACTIVE(quote(s(z0))) → c12(QUOTE(z0))
ACTIVE(unquote(s1(z0))) → c16(UNQUOTE(z0))
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2)))
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2))
ACTIVE(first1(s(z0), cons(z1, z2))) → c1(CONS1(quote(z1), first1(z0, z2)))
ACTIVE(first1(s(z0), cons(z1, z2))) → c1(QUOTE(z1))
ACTIVE(first1(s(z0), cons(z1, z2))) → c1(FIRST1(z0, z2))
ACTIVE(quote1(cons(z0, z1))) → c1(CONS1(quote(z0), quote1(z1)))
ACTIVE(quote1(cons(z0, z1))) → c1(QUOTE(z0))
ACTIVE(quote1(cons(z0, z1))) → c1(QUOTE1(z1))
ACTIVE(unquote1(cons1(z0, z1))) → c1(FCONS(unquote(z0), unquote1(z1)))
ACTIVE(unquote1(cons1(z0, z1))) → c1(UNQUOTE(z0))
ACTIVE(unquote1(cons1(z0, z1))) → c1(UNQUOTE1(z1))
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c22(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(s(sel(0, cons(z0, z1)))) → c22(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(s(first(0, z0))) → c22(S(mark(nil)), ACTIVE(first(0, z0)))
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c22(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2))))
ACTIVE(s(from(z0))) → c22(S(mark(cons(z0, from(s(z0))))), ACTIVE(from(z0)))
ACTIVE(s(sel1(s(z0), cons(z1, z2)))) → c22(S(mark(sel1(z0, z2))), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(s(sel1(0, cons(z0, z1)))) → c22(S(mark(quote(z0))), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(s(first1(0, z0))) → c22(S(mark(nil1)), ACTIVE(first1(0, z0)))
ACTIVE(s(first1(s(z0), cons(z1, z2)))) → c22(S(mark(cons1(quote(z1), first1(z0, z2)))), ACTIVE(first1(s(z0), cons(z1, z2))))
ACTIVE(s(unquote(01))) → c22(S(mark(0)), ACTIVE(unquote(01)))
ACTIVE(s(unquote(s1(z0)))) → c22(S(mark(s(unquote(z0)))), ACTIVE(unquote(s1(z0))))
ACTIVE(s(unquote1(nil1))) → c22(S(mark(nil)), ACTIVE(unquote1(nil1)))
ACTIVE(s(unquote1(cons1(z0, z1)))) → c22(S(mark(fcons(unquote(z0), unquote1(z1)))), ACTIVE(unquote1(cons1(z0, z1))))
ACTIVE(s(fcons(z0, z1))) → c22(S(mark(cons(z0, z1))), ACTIVE(fcons(z0, z1)))
ACTIVE(s(sel(z0, z1))) → c22(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1)))
ACTIVE(s(sel(z0, z1))) → c22(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1)))
ACTIVE(s(s(z0))) → c22(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(cons(z0, z1))) → c22(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1)))
ACTIVE(s(first(z0, z1))) → c22(S(first(active(z0), z1)), ACTIVE(first(z0, z1)))
ACTIVE(s(first(z0, z1))) → c22(S(first(z0, active(z1))), ACTIVE(first(z0, z1)))
ACTIVE(s(from(z0))) → c22(S(from(active(z0))), ACTIVE(from(z0)))
ACTIVE(s(sel1(z0, z1))) → c22(S(sel1(active(z0), z1)), ACTIVE(sel1(z0, z1)))
ACTIVE(s(sel1(z0, z1))) → c22(S(sel1(z0, active(z1))), ACTIVE(sel1(z0, z1)))
ACTIVE(s(first1(z0, z1))) → c22(S(first1(active(z0), z1)), ACTIVE(first1(z0, z1)))
ACTIVE(s(first1(z0, z1))) → c22(S(first1(z0, active(z1))), ACTIVE(first1(z0, z1)))
ACTIVE(s(cons1(z0, z1))) → c22(S(cons1(active(z0), z1)), ACTIVE(cons1(z0, z1)))
ACTIVE(s(cons1(z0, z1))) → c22(S(cons1(z0, active(z1))), ACTIVE(cons1(z0, z1)))
ACTIVE(s(s1(z0))) → c22(S(s1(active(z0))), ACTIVE(s1(z0)))
ACTIVE(s(unquote(z0))) → c22(S(unquote(active(z0))), ACTIVE(unquote(z0)))
ACTIVE(s(unquote1(z0))) → c22(S(unquote1(active(z0))), ACTIVE(unquote1(z0)))
ACTIVE(s(fcons(z0, z1))) → c22(S(fcons(active(z0), z1)), ACTIVE(fcons(z0, z1)))
ACTIVE(s(fcons(z0, z1))) → c22(S(fcons(z0, active(z1))), ACTIVE(fcons(z0, z1)))
ACTIVE(s(quote(0))) → c22(S(mark(01)))
ACTIVE(s(quote1(nil))) → c22(S(mark(nil1)))
ACTIVE(s(quote1(cons(z0, z1)))) → c2(S(mark(cons1(quote(z0), quote1(z1)))))
ACTIVE(s(quote1(cons(z0, z1)))) → c2(ACTIVE(quote1(cons(z0, z1))))
ACTIVE(s(quote(s(z0)))) → c2(S(mark(s1(quote(z0)))))
ACTIVE(s(quote(s(z0)))) → c2(ACTIVE(quote(s(z0))))
ACTIVE(s(quote(sel(z0, z1)))) → c2(S(mark(sel1(z0, z1))))
ACTIVE(s(quote(sel(z0, z1)))) → c2(ACTIVE(quote(sel(z0, z1))))
ACTIVE(s(quote1(first(z0, z1)))) → c2(S(mark(first1(z0, z1))))
ACTIVE(s(quote1(first(z0, z1)))) → c2(ACTIVE(quote1(first(z0, z1))))
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c23(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2))))
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c23(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1))))
ACTIVE(cons(first(0, z0), x1)) → c23(CONS(mark(nil), x1), ACTIVE(first(0, z0)))
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c23(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2))))
ACTIVE(cons(from(z0), x1)) → c23(CONS(mark(cons(z0, from(s(z0)))), x1), ACTIVE(from(z0)))
ACTIVE(cons(sel1(s(z0), cons(z1, z2)), x1)) → c23(CONS(mark(sel1(z0, z2)), x1), ACTIVE(sel1(s(z0), cons(z1, z2))))
ACTIVE(cons(sel1(0, cons(z0, z1)), x1)) → c23(CONS(mark(quote(z0)), x1), ACTIVE(sel1(0, cons(z0, z1))))
ACTIVE(cons(first1(0, z0), x1)) → c23(CONS(mark(nil1), x1), ACTIVE(first1(0, z0)))
ACTIVE(cons(first1(s(z0), cons(z1, z2)), x1)) → c23(CONS(mark(cons1(quote(z1), first1(z0, z2))), x1), ACTIVE(first1(s(z0), cons(z1, z2))))
ACTIVE(cons(quote(0), x1)) → c23(CONS(mark(01), x1), ACTIVE(quote(0)))
ACTIVE(cons(quote1(cons(z0, z1)), x1)) → c23(CONS(mark(cons1(quote(z0), quote1(z1))), x1), ACTIVE(quote1(cons(z0, z1))))
ACTIVE(cons(quote1(nil), x1)) → c23(CONS(mark(nil1), x1), ACTIVE(quote1(nil)))
ACTIVE(cons(quote(s(z0)), x1)) → c23(CONS(mark(s1(quote(z0))), x1), ACTIVE(quote(s(z0))))
ACTIVE(cons(quote(sel(z0, z1)), x1)) → c23(CONS(mark(sel1(z0, z1)), x1), ACTIVE(quote(sel(z0, z1))))
ACTIVE(cons(quote1(first(z0, z1)), x1)) → c23(CONS(mark(first1(z0, z1)), x1), ACTIVE(quote1(first(z0, z1))))
ACTIVE(cons(unquote(01), x1)) → c23(CONS(mark(0), x1), ACTIVE(unquote(01)))
ACTIVE(cons(unquote(s1(z0)), x1)) → c23(CONS(mark(s(unquote(z0))), x1), ACTIVE(unquote(s1(z0))))
ACTIVE(cons(unquote1(nil1), x1)) → c23(CONS(mark(nil), x1), ACTIVE(unquote1(nil1)))
ACTIVE(cons(unquote1(cons1(z0, z1)), x1)) → c23(CONS(mark(fcons(unquote(z0), unquote1(z1))), x1), ACTIVE(unquote1(cons1(z0, z1))))
ACTIVE(cons(fcons(z0, z1), x1)) → c23(CONS(mark(cons(z0, z1)), x1), ACTIVE(fcons(z0, z1)))
ACTIVE(cons(sel(z0, z1), x1)) → c23(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1)))
ACTIVE(cons(sel(z0, z1), x1)) → c23(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1)))
ACTIVE(cons(s(z0), x1)) → c23(CONS(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(cons(cons(z0, z1), x1)) → c23(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1)))
ACTIVE(cons(first(z0, z1), x1)) → c23(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1)))
ACTIVE(cons(first(z0, z1), x1)) → c23(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1)))
ACTIVE(cons(from(z0), x1)) → c23(CONS(from(active(z0)), x1), ACTIVE(from(z0)))
ACTIVE(cons(sel1(z0, z1), x1)) → c23(CONS(sel1(active(z0), z1), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(cons(sel1(z0, z1), x1)) → c23(CONS(sel1(z0, active(z1)), x1), ACTIVE(sel1(z0, z1)))
ACTIVE(cons(first1(z0, z1), x1)) → c23(CONS(first1(active(z0), z1), x1), ACTIVE(first1(z0, z1)))
ACTIVE(cons(first1(z0, z1), x1)) → c23(CONS(first1(z0, active(z1)), x1), ACTIVE(first1(z0, z1)))
ACTIVE(cons(cons1(z0, z1), x1)) → c23(CONS(cons1(active(z0), z1), x1), ACTIVE(cons1(z0, z1)))
ACTIVE(cons(cons1(z0, z1), x1)) → c23(CONS(cons1(z0, active(z1)), x1), ACTIVE(cons1(z0, z1)))
ACTIVE(cons(s1(z0), x1)) → c23(CONS(s1(active(z0)), x1), ACTIVE(s1(z0)))
ACTIVE(cons(unquote(z0), x1)) → c23(CONS(unquote(active(z0)), x1), ACTIVE(unquote(z0)))
ACTIVE(cons(unquote1(z0), x1)) → c23(CONS(unquote1(active(z0)), x1), ACTIVE(unquote1(z0)))
ACTIVE(cons(fcons(z0, z1), x1)) → c23(CONS(fcons(active(